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a guide to treasury in banking
Lex van der Wielen
Guide to Treasury
in Banking
Responsibilities, Products and Risks
the financial markets academy
Financial Markets Books
Geelvinckstraat 56, 1901 AJ Castricum
www.tfma.nl
Book design www.magentaxtra.nl
Photo front cover ING Amsterdam dealing room. Courtesy of ING Bank
ISBN 978-90-816351-0-3
NUR 793
© 2016 Lex van der Wielen
Copyright reserved. Subject to the exceptions provided for by law, no part of this publication may be
reproduced and/or published in print, by photocopying, on microfilm or in any other way without the
written consent of the publisher.
Contents
Chapter 1 The Responsibilities of Banks and of Their Financial Markets Division 13
1.1
1.2
1.3 1.4
Banking activities and the bank’s balance sheet 13
1.1.1
The process of money creation 14
1.1.2 Commercial banking, investment banking and the treasury
function 17
1.1.3 The items on a bank’s balance sheet 18
The responsibilities of a bank’s financial markets division 21
1.2.1 Cash management 22
1.2.2 Attracting funding 23
1.2.3 Execution of foreign exchange risk management 23
1.2.4 Execution of interest rate risk management 24
1.2.5 Proprietary trading 24
1.2.6 Sales 25
1.2.7 Arranging securities issues 26
Concluding and processing transactions in financial instruments 27
1.3.1 Exchange and MTF 27
1.3.2 The OTC market 28
1.3.3 Systematic internalization 30
Settling transactions 31
1.4.1 Money accounts and securities accounts 31
1.4.2 Sending settlement instructions 32
Chapter 2
Interest Calculations and Yield Curves 33
2.1
2.2
2.3
2.4
Calculation of interest amounts 33
2.1.1 The duration of the coupon period 34
2.1.2 Daycount conventions 36
Interest rates for broken periods 39
Converting interest rates for different daycount conventions 40
Converting interest rates for different coupon frequencies 41
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guide to treasury in banking
2.5
2.6
2.7 2.8 Present value and future value 42
2.5.1 Future value with single interest 42
2.5.2 Present value with single interest 43
2.5.3 Present value and future value with interim coupon payments and
annual coupon 44
2.5.4 Present value and future value with interim coupon payments and
n coupons per year 45
Yield and pure discount rate 46
2.6.1 Yield 46
2.6.2 Pure discount rate 47
2.6.3 Equations for converting the yield to pure discount rate and vice
versa 48
Yield curves 49
Forward rates 50
2.8.1 Calculation of forward rates 51
2.8.2 Strip forwards 53
Chapter 3
The Money Market 57
3.1 3.2 3.3 3.4 3.5 3.6 6
Domestic and Euro money markets 57
Deposit 58
Money market paper 59
3.3.1 Commercial paper 60
3.3.2 Treasury Bills and bank bills 61
3.3.3 Certificate of deposit 62
Repurchase agreements 64
3.4.1 Initial and maturity consideration 65
3.4.2 General and special collateral 66
3.4.3 Transfer of collateral 67
3.4.4 Sell/buy back 67
Trading on the money market 68
Money market benchmarks 71
contents
Chapter 4
Foreign Exchange 73
4.1
4.2 4.3 4.4 4.5 FX spot rates 73
4.1.1 Exchange rates 73
4.1.2 Bid rate, ask rate and two way prices 75
4.1.3 Big figure and points/pips 76
4.1.4 Cross rates 77
4.1.5 Spot trading positions 79
FX forward 80
4.2.1 Theoretical calculation of an FX forward rate 81
4.2.2 Swap points, premium and discount 82
4.2.3 Forward value dates and corresponding FX forward rates 85
4.2.4 FX forward cross rates 88
4.2.5 Value tomorrow and value today FX rates 90
4.2.6 Time option forward contracts 93
4.2.7 Offsetting FX forwards 94
4.2.8 Valuation of an FX forward contract 95
4.2.9 Theoretical hedge of an FX forward via FX spot and deposits 96
FX swaps 96
4.3.1 Unmatched principal swaps and matched principal swaps 99
4.3.2 FX swaps out of today / out of tomorrow 102
4.3.3 Overnight swaps and tom/next swaps 102
4.3.4 Hedging an FX forward via an FX spot and FX swap 103
4.3.5 Forward forward FX swap 104
4.3.6 Arbitrage between the FX swap market and the money
markets 105
4.3.7 Rolling over FX spot positions by using tom/next swaps 107
Non-deliverable forward 108
Precious Metals 109
Chapter 5
Futures 115
5.1 Role of a futures exchange and of a clearing house 115
5.1.1 Order types 116
5.1.2 Role of central counterparty 117
5.1.3 Margins 118
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guide to treasury in banking
5.2 5.3 STIR futures 118
5.2.1 Prices of STIR futures and implied forward rates 119
5.2.2 Fixing of the STIR futures settlement price on the expiry date 119
5.2.3 Daily result calculation and margin calculation 120
5.2.4 Use of STIR futures by companies 121
Arbitraging between FRAs and STIR futures 121
Chapter 6
Forward Rate Agreements 123
6.1
6.2 6.3
6.4 6.5 Contract data 123
The contract rate of an FRA 124
Settlement of FRAs 125
Use of FRAs by traders; trading and arbitrage 126
6.4.1 Straight forward trading in FRAs 126
6.4.2 Closing forward cash positions with FRAs 128
Use of FRAs by clients of the bank 129
Chapter 7
Interest Rate Swaps 131
7.1 7.2 7.3 7.4 7.5 7.6 7.7
7.8 7.9 8
Contract specifications and jargon 131
Settlement of an IRS 133
Overnight index swaps 134
Trading interest rate swaps 136
Arbitrage between IRS and FRAs or STIR futures 137
Applications of interest rate swaps for clients of the bank 138
7.6.1 Fixing the interest on loans with a floating rate 138
7.6.2 Fixing the floating rate of an investment / asset swap 140
7.6.3 Swap assignment 140
Basis swaps 141
Cross-currency swaps 142
Special types of interest rate swaps 143
contents
Chapter 8
Options 145
8.1 8.2
8.3 8.4 8.5 Option terminology 145
The option premium 148
8.2.1 Intrinsic value 148
8.2.2 Expectations value 150
8.2.3 Call put parity 153
8.2.4 Delta, gamma, theta, rho and vega: the ‘Greeks’ 154
Delta position and delta hedging 155
Synthetic FX forward 158
Interest rate options 158
8.5.1 Interest rate guarantees / caps and floors 158
8.5.2 Interest collar 161
8.5.3 Swaption 163
Chapter 9
Option Trading Strategies 165
9.1 9.2 9.3 Bull and bear spread 165
Straddle 167
Strangle 170
Chapter 10
Organization and Execution of Risk Management with Banks 173
Overview of banking risks 173
The central risk management organization of a bank 176
10.2.1 Asset and liability management committee 178
10.2.2 Credit risk committee 179
10.2.3 Market risk committee 180
10.2.4 Operational risk committee 180
10.3Limit control sheet 181
10.4New product approval process 181
10.1
10.2
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guide to treasury in banking
Chapter 11
Overview of the Basel Accords 183
11.1 11.2 11.3 11.4
Basel I 183
Basel II 184
11.2.1 Capital requirement for credit risk 185
11.2.2 Capital requirement for market risk 186
11.2.3 Capital requirement for operational risk 189
Basel III 190
11.3.1 General changes in solvency requirements 190
11.3.2 Leverage ratio 194
11.3.3 Liquidity requirements 195
Regulatory capital, economic capital and RAROC 195
Chapter 12
Market Risk for Single Trading Positions 197
12.1
12.2 12.3 12.4 12.5 12.6 Market risk sensitivity indicators 197
12.1.1 Value of one point / pip 198
12.1.2 Basis Point Value 198
12.1.3 The ‘Greeks’ 200
Value at Risk 204
Stress tests 205
Extreme value theory 206
Expected shortfall 208
Trading limits 208
12.6.1 Value at Risk limit 209
12.6.2 Nominal limits 209
Chapter 13
Consolidated Market Risk 215
13.1 13.2
13.3 13.4
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Full valuation method 215
Variance-covariance method 217
13.2.1 The standard normal probability distribution 218
13.2.2 The volatility of composed trading positions 219
13.2.3 The VaR of composed trading positions with the variance
covariance method 220
Monte Carlo analysis 221
Back tests 221
contents
Chapter 14
Interest Rate Risk 223
14.1 14.2 14.3 14.4
Definition of interest rate risk 223
Interest risk in the banking book and in the trading book 224
Interest rate risk measurement 226
14.3.1 Gap analysis / maturity method 226
14.3.2 The duration method 230
Hedge accounting 239
14.4.1 Fair value and amortized cost 239
14.4.2 The concept of hedge accounting 240
14.4.3 Fair value hedge 241
14.4.4 Cash flow hedge 241
14.4.5 Net investment hedge 242
14.4.6 Hedge accounting in practice 242
Chapter 15
Liquidity Risk 245
15.1
15.2 15.3 15.4
15.5
Availability risk and market liquidity risk 245
Causes of liquidity risk 246
Sources of liquidity 248
Liquidity risk management 251
Basel II minimum global liquidity standards 253
15.5.1 Liquidity Coverage Ratio 253
15.5.2 Net stable funding ratio (NSFR) – 2018 256
Chapter 16 Credit Risk 261
16.1 16.2 16.3 16.4
Types of credit risk 261
16.1.1 Debtor risk 261
16.1.2 Settlement risk or delivery risk 262
16.1.3 Replacement risk or pre-settlement risk 263
Factors that determine the amount of credit risk 264
Regulatory capital for debtor risk 267
Regulatory capital for counterparty credit risk 271
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guide to treasury in banking
Chapter 17
Credit Risk – Risk Mitigating Measures 275
Introduction 275
17.1 Counterparty limits 275
17.2 Covenants 276
17.3 Contractual netting / close-out netting 277
17.4 Collateral 277
17.5 Central counterparties 280
17.6 CLS 282
17.7 Credit default swap 286
17.8Securitisation 288
Chapter 18 Funds transfer pricing 291
18.1
18.2 Matched maturity funds transfer pricing 291
Application of the matched maturity funds transfer pricing method 292
Chapter 19
Operational Risk 295
Introduction 295
19.1
The cause-event-effect concept 295
19.2 Internal processes 297
19.2.1 Separation of duties 297
19.2.2 Internal controls 298
19.3
Human error 299
19.4
Computer systems 300
19.4.1 Confidentiality 300
19.4.2Integrity 300
19.4.3Correctness 301
19.4.4 Availability 301
19.5 External factors 302
19.6
Operational risk under the Basel rules 302
Index 305
12
Chapter 1
The Responsibilities
of Banks and of Their
Financial Markets
Division
Banks play an important role in the economy. The first reason for this is that they
are responsible for creating money. The second reason is that they are responsible
for executing the payment orders of their clients. These two activities are considered to be ‘utility functions’ which are crucial for the economy. These responsiblities are part of what is commonly referred to as commercial banking. Apart from
their utility functions, however, banks also perform other activities like acting as a
market maker in the financial markets, arranging securities issues and giving advice on mergers and acquisitions. The latter two activities are commonly referred to
as investment banking or merchant banking activities.
The financial markets division is often said to be the ticking heart of a bank. It is in
some ways comparable to the treasury department of a non-bank entity. This is because, just like every other treasury department, the financial markets division is
typically responsible for the bank’s cash management and for the management of
the bank’s financial risks.
1.1
Banking activities and the bank’s balance sheet
After a financial institution has been granted a banking license by its domestic central bank, it has several privileges over other financial institutions. First, the financial institution that is now referred to as ‘bank’ is allowed to hold an account with
the central bank, which enables transfers of money amounts in the domestic currency from its clients to market parties that hold an account with another bank.
Second, the bank is allowed to borrow money from the central bank (that acts as
the lender of last resort), provided that it has ample collateral. Finally, a financial institution with a banking license is allowed to ‘create money’. This activity is crucial
for the economy and also very favourable for a bank but, on the other hand, brings
about great risks.
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guide to treasury in banking
1.1.1
The process of money creation
Banks create money by granting loans to their customers without having attracted
funding for these loans. Although this may sound strange, it happens every day. In
fact, this is the core business of every commercial bank. Money is created by merely
making two entries in a bank’s ledger: the bank debits the asset item ‘loans’ for the
loan amount and, at the same time, it credits the liability item ‘current accounts’
for the same amount. As a result, the bank’s balance sheet total has increased on
both sides. The bank now has a new claim on its client, who has the obligation to
pay back the loan at some future date and at the same time the bank has a new obligation for the same amount since it has to transfer the money from the current account to another account at the client’s order or it has to pay a cash amount if the
client wants to withdraw his money, either at a bank office or at an automated money machine (ATM).
example
Susanne Bauer just signed the contract for a mortgage loan with her bank, Deutsche
Bank. The amount of the loan is EUR 300,000.00. Susanne already has a current account with Deutsche Bank Gronau, account number 3605681. The balance on this
account was EUR 2,500. Deutsche Bank Gronau now enters the following entries in
the ledger:
Mortgage loans + 300,000.00 / Current account 3605681: + 300000.
After these entries, Susanne’s account shows a balance of EUR 302,500 and the
money supply in the euro zone has just increased with EUR 300,000 as a result of
this loan. After all, before the mortgage loan contract was signed, the EUR 300,000
did not exist.
1.1.1.1 the consequences of money creation for the economy
For the economy as a whole, the creation of money is of crucial importance. Economic growth implies an increase of the total number of goods and services produced by the residents of a country in a given year, also known as the real gross
national product. To facilitate this growth, an increase in the money supply is required, i.e. an increase of the balances of the current accounts of the countries’
residents. If the money supply would not grow, it would simply be impossible for
producers in general to invest in their companies because there just is not enough
14
the responsibilities of banks and of their financial markets division
money in the economy to invest. Therefore, as a result, economic growth is fostered
by the money creating role of banks .
If consumers take up loans, this is normally also a source of economic growth. If
they use the borrowed funds to buy consumer goods, provided that the companies
have idle production capacity, the production increases until the production capacity is fully utilised. However, when demand starts exceeding supply, there is more
money available for every product. This leads to inflation. Inflation is in fact a form
of a so-called bubble. This is the result of an increase in the money supply that exceeds the growth of the real national product. Normally a bubble has the appearance of a rise of the prices of consumer goods i.e. inflation, however, a bubble can
take very different forms. For instance, a dramatic rise in the real estate prices or of
the related mortgage backed securities, or a dramatic rise of share prices or gold
prices.
It is the responsibility of a central bank to regulate the most commonly seen bubble, i.e. inflation. This is part of their monetary policy. Monetary policy is the targeted use of financial instruments and measures to influence the economy. Apart
from aiming at a stable price level, the monetary policy of central banks also has as
the objective to support a balanced economic growth. However, containing inflation is generally considered the most important goal for a central bank. This is why
central banks closely monitor the inflation in their monetary area. However, if they
would only intervene when the inflation rate deviates from the desired level, they
would be too late to correct it. Therefore, central banks monitor, amongst others,
the amount of liquidity in circulation in their currency area as an indicator that predicts the level of inflation.
When a central bank wants to curb inflation, it must follow a monetary policy
aimed at restraining lending. This policy works in an indirect way. First, the central
bank establishes that the commercial banks collectively have a shortage of money
in order to make sure that they need the central bank as a ‘lender of last resort’. In
addition to this, the central banks raises its interest rates and, because of the fact
the central bank acts as the ultimate supplier of liquidity, this rise influences the
interest rates that the banks charge each other. Moreover, if the inter-bank interest
rates change, the interest rates for client loans follow because the inter-bank interest rates act as the basis rate for these loans. As a result of the higher interest rates,
the demand for credit by companies and private clients is most likely to fall. On the
other hand, if a central bank wants to support economic growth, it normally lowers
its interest rates. Again, the inter-bank rates will follow and, as a result, commercial
interest rates will also decrease, leading to more loans to companies and private clients. This will generally lead to an increase in economic growth. However, spurring
economic growth is generally considered to be more difficult than containing inflation. Think of the analogy of holding your dog’s chain: when you pull it towards
15
guide to treasury in banking
you, the dog will automatically follow, but if you let the chain go, the dog will not
automatically run away.
1.1.1.2 the consequences of money creation for banks
The creation of money increases the net interest income of a bank. After all, for a
loan to its customers the bank charges an interest rate that is composed by the inter-bank rate for the corresponding term and a credit spread. On the other hand, the
interest that banks pay for balances on their clients current accounts is much lower.
And the difference between the two rates normally will not change a lot during the
term of the loan. The interest rate for most loans is fixed, and the interest rate on
current accounts is practically never revised. Thus, money creation is generally a
stable source of income for a bank. The part of the net interest income that is the result of money creation, therefore, is referred to as an interest ‘buffer’.
However, since ‘there is no free lunch in finance’, money creation must have some
disadvantages too. The first and most important disadvantage is the fact that money creation causes liquidity risk. After all, the bank’s clients are allowed to withdraw the money that is booked on their current account immediately. They are, for
instance, free to transfer the money immediately to another bank. If they decide to
do this ‘en masse’, a bank will not be able to fulfil its obligations and will go bankrupt. After all, a bank can not quickly sell all its assets in order to obtain the needed
cash amount. Examples of banks that collapsed because of a bank run were Northern Rock and the Dutch DSB Bank.
Another disadvantage of money creation is the fact that the client who took up the
loan may prove to be unable to repay the loan. This is called credit risk.
A way for banks to mitigate liquidity risk is to take up loans for (part of) the loans
that they grant to their clients. This is called funding. In this case, a bank only
runs a liquidity risk if the term of the loan exceeds the term of the funding. After
all, the funding must then be repaid earlier than the loan and the bank has to find
new funding. The credit risk of the bank is clearly not reduced by taking up funding. Since this kind of ‘financing’ loans is more expensive than through current accounts, it will reduce the net interest income of the bank. This is a general principle:
less risk leads to lower profits.
If banks finance their loans by taking up loans themselves, however, they may also
run another risk. If the interest term for both the loan and the funding is equal to
the contract term, this means that one of the contracts may have to be replaced earlier than the other and, as a result, will be repriced earlier. If the general level of interest rates at that moment has changed, the difference between the cost of funds
and the interest on the loan will change. This is referred to as interest rate risk.
16
the responsibilities of banks and of their financial markets division
1.1.2 Commercial banking, investment banking and the treasury function
Apart from creating money, banks have other important responsibilities. They are,
for instance, responsible for executing the payment orders of their clients. Next,
banks play an important role as a market maker for financial instruments. This
means that a bank is always willing to act as a counterparty for its clients if they
want to conclude transactions in financial instruments. The main advantage for the
clients is that they do not have to search for a counterparty themselves. This generally is true for every client that wants to make a transaction in a financial instrument, be it either a client that wants to invest in a deposit, needs a long term loan or
wishes to sell US dollars against euros or wants to hedge its interest risk. These are
all examples of commercial banking activities.
Apart from commercial banking activities, commercial banks also perform other
activities like arranging securities issues, give advice on mergers and acquisitions
and, last but not least, proprietary trading. These activities are commonly referred
to as investment banking or merchant banking. Investment banking activities are
generally considered more risky than commercial banking activities. This is not
true for arranging securities issues and supporting mergers and acquisitions however, since these activities are so-called fee driven activities. Proprietary trading,
however, is a very risky business and involves the opening of trading positions in financial instruments in order to take profit from favourable developments in rates or
prices. However, the rates and prices can also move in an unfavourable way which
results in a trading loss for the bank. This risk is referred to as market risk.
To fulfil its responsibilities, it is necessary for a bank to have access to the financial
markets. After all, if a client wants to invest in e.g. a dollar deposit, the bank has
to invest the dollars itself with another party. Therefore a bank needs access to the
money markets in all major currencies. Furthermore, for instance, a British client
may want to buy US dollars from a bank to pay an invoice from its US supplier. In
that case, this bank first needs to buy the US dollars itself in the currency market. Or
finally, think of a client that wants to issue securities. In this example it is convenient if the bank has access to the capital market in order to fine tune the issue by buying or selling the issued security during the first days after the issue date.
Banks also need access to the financial markets to obtain funding and to manage
their own risks. For instance, to reduce liquidity risk, a bank can decide to take
more deposits or to issue a bond instead of relying on current accounts as a source
of funding. For this reason, a bank needs access to the money market and the capital market. To reduce their interest rate risk, banks normally conclude interest rate
swaps. Therefore, they need access to the interest rate derivatives market. And to
reduce credit risk, banks may want to conclude credit default swaps, which necessitates their presence on the credit derivative market.
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guide to treasury in banking
The department that acts as the bank’s portal to the financial markets is, not surprisingly, the Financial Markets department of a bank. This department is mainly
responsible for the execution of the treasury function of the bank, i.e. cash management, funding and financial risk management. Figure 1.1 shows the central role of
the financial markets department of a bank.
Figure 1.1 The central role of Financial Markets
Commercial Banking
Investment Banking
Financial Markets /
Treasury
Banking Book
1.1.3
Trading Book
The items on a bank’s balance sheet
Most of a bank’s activities are reflected on its balance sheet. On their balance sheet,
banks normally make a distinction between the banking book and the trading book.
The banking book contains assets or liabilities that the bank intends to hold to their
maturity, such as corporate loans and mortgages. The trading book contains positions that the bank intends to hold for only a short term. The banking book items
are a reflection of the commercial banking activities and the trading book items
represent the investment banking activities.
18
the responsibilities of banks and of their financial markets division
Figure 1.2
Balance sheet of a bank
AssetsLiabilities
Cash and balances with central banks
2,791
Amounts due to banks
96,291
Short-dated government paper
1,809 Customer deposits and other funds
Amounts due from banks
80,837 on deposit
213,556
Loans and advances to customers
327,253 – Savings accounts 59,302
– Credit balances on customer
Debt securities
– accounts 60,090
– available-for-sale
16,106
– Corporate deposits 68,461
– held-to-maturity
21,970
– Other 25,703
Equity securities
Debt securities in issue
98,571
– available-for-sale
2,297
Other liabilities
80,983
– held-to-maturity
1,799
General provisions
1,029
Subordinated loans
21,413
Investments in group companies
28,252
Investments in associates
561
Total liabilities511,843
Intangible assets
1,375
Equipment597
Equity
Other assets
60,648
Total equity
34,452
Total assets546,295
Total equity and liabilities546,295
assets
Cash and Balances with Central Banks
This balance sheet item is the most important one on the asset side with respect
to liquidity. It includes the bank’s balances on central bank accounts, i.e. the balance on the current account that the bank holds with the central bank in the bank’s
home country and the balances of the current accounts with foreign central banks
or foreign subsidiaries that have their own banking license. The disadvantage of
this item is that it earns not much interest income.
Short-dated Government paper
This item includes short-term Government paper, for instance, US Treasury Bills
and UK Treasury Bills. In terms of liquidity these items are very important because
they can be sold very easily or given as collateral if the bank borrows money by concluding a repurchase agreement with the central bank.
Amounts due from Banks
This item includes all the money that is invested in deposits with other commercial
banks or that is lent out in repurchase agreements concluded with other banks. The
term of these contracts is normally very short, i.e. commonly from one day to one
week.
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guide to treasury in banking
Loans and Advances to Customers
This item shows the loans that are granted to the bank’s clients. It includes mortgage loans to private clients, money market loans to corporate clients, loans granted
for special projects et cetera. For all commercial banks, this is the largest item on
the asset side of the balance sheet.
Debt Securities and Equity Securities
This item includes the investment securities portfolios and the trading securities
portfolios. The investment portfolios are reported as ‘held to maturity’. This means
that the bank is planning to hold these securities until their maturity date. The
other part of this item is reported as ‘available for sale’. Although the bank may, in
principle, hold some securities until the maturity date, there is always a chance that
the bank wants to dispose of them. If the sold securities would have been reported
as ‘held to maturity’, the bank would be punished and is not allowed to report any
items in the held to maturity category for three years. To prevent this, banks record
most of the securities that belong to their investment portfolios at their market value as ‘available for sale’.
Other Assets
The most important component of this item is ‘Derivatives’ . Under this sub-item,
the market value of derivatives contracts with a positive market value is included.
Moreover, this item also includes amongst others the accrued interest of the bank.
liabilities
Amounts due to Banks
This item includes all money that is borrowed from other banks either through a
deposit or a repurchase agreement. The term of these contracts is normally short,
from one day to one week.
Customer Deposits and Other Funds on Deposit
This item shows all the money that clients of the bank have deposited with the
bank. Part of these funds have a fixed term, which means that the bank exactly
knows when it must repay the money. This is true for most of the corporate deposits
and for part of the balances on savings accounts. However, a substantial part of this
item is demandable, which means that the clients are allowed to transfer the balances without notice. This is true, for instance, for the entire item ‘credit balances
on customer accounts’, but also for parts of the balances on savings accounts and
even for a part of the corporate deposits, i.e. the overnight deposits and the callable
deposits. In terms of liquidity, this item is the most risky one for a bank. After all,
if, for instance, the clients of this bank would withdraw all their balances on current account, the bank in figure 9.2 would immediately need liquid assets for an
amount of 60 billion. At first sight, it is clear that this would impose an unsolvable
20
the responsibilities of banks and of their financial markets division
problem for this bank. After all, the total balance on its central bank account is only
2.8 billion and the bank only has 1.8 billion of high liquid securities that can be sold
immediately. Assuming that all the bank’s securities are eligible as collateral with
the central bank, the bank would also be able to borrow 41 billion from the central
bank. However, this would still be insufficient to deal with a bank run. After all, the
bank’s total liquid assets only amount to 44,6 billion. This not only applies for the
bank whose balance is shown in figure 9.2, but in general for all commercial banks.
Liquidity risk is therefore the most serious threat for commercial banks.
Debt Securities in Issue
Banks also issue securities themselves. An example of a short term security issued
by a bank is a certificate of deposit (also referred to as CD) or commercial paper (CP).
If they need more long term funding, banks can issue notes and bonds. Nowadays, as
a result of the fact that bank are not considered very creditworthy, banks are forced
to issue so-called covered bonds to obtain long-term funding. These are bonds that
give the holder the right to obtain a specific asset of the issuer in case of a default.
Other Liabilities
The item Other Liabilities has three important sub-items: ‘Derivatives’, ‘Trading Liabilities’ and ‘Accrued Interest’. The item ‘Derivatives’ contains the value of all derivatives with a negative market value. Under the item ‘Trading Liabilities’ the market
value of the short trading positions in financial values is reported, i.e. a short position in bonds.
Subordinated Loans (junior loans)
‘Subordinated’ means that these loans rank lower in the pay-out scheme when a
bankrupt bank is liquidated. For an investor, these subordinated loans are therefore
riskier in nature since the liquidation value of a bank is generally much lower than
the total outstanding claims on the bank. Examples of such loans are publicly issued capital debentures or privately placed loans.
1.2
The responsibilities of a bank’s financial markets division
A bank’s financial markets division is in some ways comparable to the treasury department of a non-bank entity. This is because, just like every other treasury department, the financial markets division is, amongst others, responsible for the bank’s
cash management and the management of the bank’s financial risks. In addition to
these normal treasury responsibilities, however, the financial mar­kets division has
several other tasks. As an example, it acts as a market maker for its clients and advises them on transactions in financial instruments. In order to be able to carry out
their role of market maker properly, banks often also take positions in financial instruments.
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guide to treasury in banking
In addition to these tasks that result from commercial banking, the financial markets division sometimes also arranges securities issues of its clients. This activity is
part of merchant banking or investment banking. Another merchant bank activity
is supporting clients with mergers and acquisitions. All tasks described here are executed at the financial markets division’s front office department.
1.2.1
Cash management
Cash management is the daily management of an organization’s current account
balances. European banks hold a euro account with the ECB (European Central
Bank) and foreign currency accounts with foreign commercial banks referred to as
correspondent banks. Banks also hold cash accounts at the organizations that register their securities, the custodians. The cash accounts that banks hold at other institutions are called nostro accounts. Banks hold multiple nostro accounts in every
currency.
In practice, one of the nostro accounts in each currency acts as a principal account.
For the own currency, this is the account at the central bank. The principal account
for a foreign currency is usually the account that the bank uses for having payments
in that currency processed. For instance, for US dollars, Bar­clays uses JP Morgan
Chase and for euro, United Bank of India uses Deutsche Bank, for this purpose. The
balances of the other nostro accounts are transferred to the principal account during the day. One of the employees in the dealing room, the fund manager, is responsible for ensuring that positive balances on the principal accounts earn interest by
investing them in the money market or that deficits are covered by attracting deposits. Banks make a daily forecast of the final balance of each principal nostro account. If a fund manager foresees that a surplus in a certain currency will occur by
the end of the day, he will try to invest this surplus on the money market gradually
during the day. If, on the other hand, he foresees a deficit, he will try to attract the
money during the day in order to cover this.
At the end of every trading day, the balance of each nostro account must be zero,
in principle. After all, a positive balance on a current account generates hardly any
interest income and high interest costs are associated with a negative balance. An
exception to this rule is the bank’s account at its national central bank. This is because most central banks require commercial banks to maintain a certain average
positive balance on their account, the minimal cash requirement. The fund manager must see to it that the balance at the central bank account is on average set at the
mandatory cash reserve over a given period.
Because the total, combined mandatory cash reserve of all banks is higher than
their combined balances at the central bank, the banks have a collective central
22
the responsibilities of banks and of their financial markets division
bank money deficit. The European Central Bank, for instance, gives the banks in the
euro area the opportunity to fund this deficit through refinancing transactions with
itself. The fund manager is responsible for determining to what extent he wants to
use this refinancing facility.
1.2.2
Attracting funding
Part of the money that banks lend to their customers is financed through the balances clients keep in current accounts or saving accounts. These balances are called
entrusted funds. Another part is financed on the financial markets by taking up
bank deposits or by issuing bonds. This is called interbank funding. The dealing
room is responsible for attracting this funding.
Some dealing rooms also function as an in-house bank. The dealing room then actually grants inter-company loans to business units that grant loans to their clients.
And when a business unit attracts a deposit, the dealing room functions as this
unit’s borrowing counterparty. The dealing room, in turn, then invests this balance
in the money market or in the capital market.
1.2.3
Execution of foreign exchange risk management
The fact that the foreign currency nostro accounts have a zero balance at the end
of each day as a result of the cash management activities does not mean that the
bank no longer has any foreign currency asset. After all, the foreign currency account balances have been invested in the money market. There are, therefore, still
foreign currency assets in the form of, for example, a deposit or short-term note like
a certificate of deposit.
A bank would run a currency risk if it did not have liabilities equal to these foreign currency assets. This is because the value of the bank’s assets will decrease
if foreign currency exchange rates decrease without there being an equal reduction in the bank’s liabilities. The foreign exchange trader must see to it that the
foreign currency assets and liabilities equal each other, with the exception of the
trade positions he wants to take himself. This is called foreign exchange risk management.
If a client of a German bank, for instance, wants to create a positive balance on his
US dollar account, he can withdraw money from his euro account, convert it into
US dollars and deposit it into his US dollar account. In this case, an obligation in US
dollars is created for the German bank. The foreign exchange dealer of this bank
must now buy US dollars himself and deposit these into the bank’s US dollar nostro
23
guide to treasury in banking
account. By doing so, he creates an asset that balances the US dollar obligation and,
as a result, the cur­rency position is again balanced.
It is important for the foreign exchange dealer to be kept informed about all changes in foreign currency claims and obligations of the bank that result from client
transactions. If the foreign exchange dealer is not well-informed, he cannot determine the bank’s exact cur­rency position and the bank may run a currency risk without knowing it.
The translation risk of a bank that may result from foreign takeovers by the bank
is managed separately, together with the strategic FX position that is managed by
ALCO.
1.2.4
Execution of interest rate risk management
If the ALCO finds that the bank should reduce or increase the interest risk, it will order the dealing room to effect interest rate swaps. Large banks have special departments set up in their dealing room for this very purpose. These departments are
often called Asset & Liability Management (ALM).
1.2.5
Proprietary trading
In a dealing room, trading also takes place at the risk and account of a bank. This is
called proprietary trading. The employees responsible for the proprietary trading of
a bank are called traders.
A position is an ownership or claim or a debt or obligation for which a party runs a
price change risk, also known as a market risk. The market risk of a bond trader that
has bought bonds is the risk that the bond price drops as the result of an increase in
the long term interest rate on the capital market.
A position can also result from the fact that banks operate as market maker for a
large number of instruments. A bank usually concludes a opposite transaction in
the market for every transaction it concludes with a client immediately. However,
sometimes this is not possible or prudent and the bank is (temporarily) left with an
open position.
24
the responsibilities of banks and of their financial markets division
1.2.6Sales
Sales involves the advising of clients on transactions in financial instruments and
the concluding of these transactions at the expense and risk of these clients with
the bank itself operating as counterparty. The front office employees that carry out
this task are called client advisors. Client advisors are not allowed to take a proprietary trading position. They merely act as an intermediary that passes a client’s position on to a trader at their bank or to the exchange.
The client advisor’s task is actually part of the account management of the bank.
The client advisor takes on the advisory and sales role for a specialized range of instruments, i.e. the instruments that are traded in the financial markets.
When giving advice on the use of financial instruments, client advisors should be
mindful of the level of professionalism of their clients. This level is determined by
the client’s level of knowledge, sophistication and understanding. One obligation is
that, prior to each transaction, a sales adviser should provide all necessary information reasonably requested by the customer so that the customer fully understands
the effects and risks of the transaction. The advice should also be given in good
faith and in a commercially reasonable manner. This is referred to as duty of care.
In many countries this duty of care is included in the applicable laws and/or regulations. These laws, however, differ substantially from jurisdiction to jurisdiction.
As a precautionary measure against future adverse allegations or assertions of
claims by the customer, many banks draw up a client folder and have it signed by
the client before entering into transactions. In this folder the client is asked to state
that
–
–
–
–
he understands the terms, conditions and risks of the traded instruments;
he makes his own assessment and independent decision to enter into
transactions and is entering into the transactions at his own risk and
expense;
he understands that any information, explanation or other communication by the bank shall not be construed as an investment advice or
recommendation to enter into that transaction except in a jurisdiction
where laws, rules and regulations (such as the Mifid directive by the EC)
would qualify the given information as an investment advice;
no advisory or fiduciary relationship exists between the parties except
where laws, rules and regulations would qualify the service provided by
the finan­cial market professional to the customer as an advisory or fiduciary relationship.
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guide to treasury in banking
1.2.7
Arranging securities issues
Organisations that have large financial requirements can choose to issue securities
themselves as an alternative to bank credit. Banks support those organizations in
their efforts to attract money. A bank that services an issue is called the arranger.
The arranger assists the issuer, for instance, in determining the issue price and represents the issuing institution towards the regulatory bodies and investors. An arranger always acts as issuing and paying agent.
The responsibility of an issuing and paying agent is to draw up a global note, deposit it with the central securities depository and apply for an ISIN code. The issuing agent is also responsible for compiling a prospectus, in the case of listed
securities, or a bond indenture, in the case of unlisted fixed-income securities. Both
documents contain the terms and conditions of security issued. A prospec­tus also
reveals comprehensive information about the issuing institution. These documents
must be approved by and deposited with the regulatory supervisor, such as the Financial Services Authority (FSA) in Great Britain. The issuing agent is also responsible for distributing the terms and conditions of the issue among investors. Finally,
the issuing and paying agent is responsible for draw­ing up the settlement instructions for the payments and for the securities transfers related to the issue and to the
coupons or dividends.
If a security is traded on an exchange, the arranger also acts as listing agent. In this
role, the arranger applies to the exchange for a listing on behalf of the issu­ing institution. The listing agent is also responsible for the following tasks:
–
–
–
–
reporting to and/or gaining approval for the listing from the supervisor;
registering stocks with the clearing institution;
placing a public announcement;
publicizing the result of the issue in the media.
In order to increase the placing power, an arranger often forms an issue syndi­cate.
This is a group of banks that jointly execute an issue. The arranging bank is called
the syndicate leader. Apart from the syndicate leader, there are a num­ber of parties
involved as dealer. They are allowed to buy the securities directly from the issuer
and sell them to their own clients.
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the responsibilities of banks and of their financial markets division
1.3 Concluding and processing transactions in financial
instruments
Financial instruments can be traded in different ways. The first way is through a
public market. This is a strictly organized market place where market parties can
conclude transactions in these instruments. Examples include exchanges and multilateral trading facilities. To trade on a public market, one has to be a member. Usually, only banks and dedicated trading companies are members. If a third party wants
to conclude a transaction on a public market, it needs a member to act on his behalf.
The member is then referred to as a broker. Sometimes banks net the orders of their
clients before they send them to a public market place. If they are allowed to do so
by the supervisor and if they do this on a large scale this is referred to as systemic
internationalization. The last way to trade financial instruments is to trade over-thecounter (OTC). In this case, two market parties enter into a transaction bilaterally.
Sometimes a market party uses the services of an intermediary to find a counterparty. This intermediary is referred to as a dealer broker or, more commonly, just as broker. In the professional market, the term brokers always refers to a dealer broker.
All transactions in financial instruments lead to a legal obligation to transfer money and/or securities. The process of fulfilling this obligations is referred to as clearing. The clearing obligations, however, are not necessarily bilateral obligations
between the transaction parties. If a transaction is concluded via an exchange, for
instance, a specific institution acts as the legal counterparty for both transacting
parties and takes the responsibility of the clearing the transaction towards each of
the transacting parties. This institution is referred to as a clearing house and it acts
as a central counterparty (CCP). As a result of the EMIR regulation in Europe and the
Dodd-Frank regulation in the US, in the future most over-the-counter transactions
will also be cleared through a clearing house instead of bilaterally.
1.3.1 Exchange and MTF
An exchange is a public marketplace where securities and/or derivatives are traded and where strict rules apply in relation to transparency, uniformity and safety.
An exchange is operated by an organization that holds a license, in some countries
granted by the Minister of Finance. In most countries, exchanges are no longer
hosted on a traditional ‘floor’ where traders shout in organized chaos to indicate
which transactions they want to conclude. Instead most exchanges are computer
systems in which market parties can indicate at what rates and volumes they wish
to conclude transactions. This process is referred to as placing an order. The computer systems are also referred to as a trading systems. The price of exchange traded
instruments is determined by supply, based on the orders that are inputted by the
members.
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guide to treasury in banking
Exchanges are required to provide information about the price of the most recent
transaction that has been concluded. They must also give insight in the trade volume. This is called post-trade transparency. In addition, exchanges must provide a
summary of the orders that have not yet been executed, i.e. the depth of the book.
In this respect, they must, for instance, indicate what the demand is for the five
rates that are immediately lower than the last traded rate and what the offers are for
the five immediately higher rates. This is referred to as pre-trade transparency. If a
company wants to have its shares traded through a public market place, it should
list its shares at an exchange. However, strict rules apply for companies which want
to get a listing. First, they should be of unquestionable financial status and reliability. Second they must publish their financial results on a regular basis, for instance
quarterly. If a company wants its shares to be traded on more than one exchange,
it should apply for a listing on each exchange that it wants its shares to be traded
on. There is a central counterparty (CCP) connected to nearly all exchanges. A CCP
stands legally between buyers and sellers of financial instruments. Each transaction
is broken down as a sale by the seller to the CCP and a purchase from the CCP by the
buyer.
A multilateral trading facility (MTF) is a public trading system that has to comply with fewer requirements than an exchange, as a result of which the expenses
and the charged fees are lower. The lower requirements are related to information.
MTFs nevertheless have a duty of transparency before and after trade. Examples of
MTFs are Chi-X and Turquoise. English, German, French and Dutch shares are traded on Chi-X. Turquoise also focuses on European equities. Shares can only be listed
on an exchange but once they are listed they can also be traded on multilateral trading facilities. Exchanges and MTFs are together referred to as the public market.
1.3.2 The OTC market
In the over-the-counter market (OTC market) transactions are concluded outside an
exchange or MTF. The OTC market is also known as the private market. Usually, one
of the parties involved in an OTC transaction is a bank. Most derivatives are traded in the OTC market, some are even traded exclusively over-the-counter, such as
interest rate swaps. A bank that has concluded an over-the-counter transaction, is
not required to publish the price of this transaction. However, according to EMIR
and Dodd-Frank every institution that exceeds a certain threshold, should report its
transactions to a special institution, a trade repository.
A major benefit of OTC contracts is that they can be customized. For every deal, the
negotiating parties can reach agreements on the volume, duration, price, market,
certain kinds of optionality’s, references to be used and legal aspects. A disadvantage of OTC contracts is that existing contracts are difficult to trade, i.e. there is no
28
the responsibilities of banks and of their financial markets division
secondary market. If a contract party wants to close his position in an OTC instrument, he can try to unwind the transaction with the existing counterparty or he
must find a counterparty to conclude an opposing OTC transaction.
A banks that wishes to conclude over-the-counter transactions with another professional party may sometimes engage the services of an inter-dealer broker, . Brokers
look for a party to act as the counterparty to a specific transaction. When concluding transactions, brokers do not act as a contracting party themselves but they only
play the role of intermediary. The deal is exclusively concluded between the principals: i.e. the party that has engaged the broker (the originating party) and the designated counterparty. The clearing obligations and, therefore the credit risk, lie with
the principals. Once a transaction is concluded, the broker sends a confirmation to
both contracting parties who should also exchange confirmations between themselves. They are two types of brokers: voice brokers and electronic brokers. The difference between the two is that a voice broker is a natural person whom a principal
informs by telephone of the transaction that he is willing to conclude whilst an ebroker is a computer system in which a trader can input his orders electronically.
As an extra service, voice brokers provide their clients with information about the
market conditions. They are able to do so because they are in contact with many
market parties and therefore have a good understanding of the market conditions
such as the liquidity and the sentiments in the market.
In the over-the-counter market banks act as a market maker. This is a party that
is always willing to quote prices for financial transactions. Market makers are
sometimes also called liquidity providers. Market makers make sure that all other
market parties, who are referred to as market users, are able to conclude the transactions that they want. One of the advantages for market makers is that they are always able to buy at the bid side of the market and sell at the offer side of the market.
This means that a market maker is earning the bid-offer spread. The risk, however,
is that a market maker may not be able to (immediately) conclude an opposite transaction after having concluded a transaction with a market user. This leaves him
with an open position and, as a result, he is faced with a market risk.
Transactions in the OTC market are often concluded by telephone, but increasingly
also through special electronic trading systems. Examples of over-the-counter trading systems are Reuters Eikon, EBS for foreign exchange transactions and Tradeweb
for fixed income transactions and interest rate swaps. Market players who are connected to these systems can conclude transactions directly with other affiliated
­parties.
Large banks, such as Goldman Sachs, BOA Merryl Lynch and Credit Suisse also act
as prime-brokers. The clients of prime brokers are hedge funds, pension funds and
other asset managers. One of the striking responsibilities of a prime broker is that he
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guide to treasury in banking
acts as a central counterparty between his client and the banks that the client concludes transactions with the executing banks. Each transaction between the client
and an executing broker will be split into two transactions: a transaction between
the client and the prime broker and a mirrored transaction between the prime broker and the executing bank. At the start of a prime-broker relationship, the prime
broker enters into an agreement with the client, i.e. the prime-broker agreement,
and with each executing bank, i.e. the give-up agreements. In these agreements,
the permitted transaction types, tenor limits, and credit limits are stated. The most
commonly used transaction types in a prime-broker relationship are cash equities
and exchange traded derivatives, however, every over-the-counter traded instrument may also be included in the prime-broker agreement. In addition to acting as
a central counterparty, prime-brokers often render other services such as securities
lending (in case the client wants to enter into a short position) and lending money
to buy securities (in case the client wants to enter into a long position).
1.3.3 Systematic internalization
When a bank enters a large number of securities orders from its clients into a dedicated system of its own in order to match them with other customer orders rather
than sending them to an exchange or MTF, this is referred to as systematic internalization. The bank acts as central counterparty for these transactions and, in order
to increase the liquidity in the system, the bank also acts as liquidity provider. The
difference with an exchange or MTF is that in the case of systematic internalization
the participants in the trading system are the clients of the bank whilst in the case
of an exchange or MTF the participants are the banks themselves.
Figure 1.3 shows the four different ways in which transactions in financial instruments can be concluded.
30
the responsibilities of banks and of their financial markets division
Figure 1.3 Different ways of concluding transactions
Client
Bank
Systematic
Internalization
Exchange
1.4
OTC
MTF
Settling transactions
Nearly all transactions in financial instruments lead to transfers of money and/
or securities. These transfers eventually take place at the organizations were the
clearing parties hold their money accounts or securities accounts. Money accounts
are held with commercial banks or central banks and securities accounts are held
with custodians or with central securities depositories. Parties that need to transfer
money or securities have to send settlement instructions to the organization where
they hold their accounts. Usually they use SWIFTNet for this purpose.
1.4.1 Money accounts and securities accounts
Private persons, companies and asset managers hold money accounts with commercial banks. Banks refer to these client accounts as loro accounts. Banks keep
track of the balances and mutations of the loro accounts in their own accounting
system. Banks, however, also hold accounts themselves. For the local currency, they
hold an account at the central bank of the country in which they have a banking license. All banks with a banking license in the euro area, for instance, hold a euro
account with the European Central Bank (ECB). They use this account to transfer
euro amounts to other banks with a ‘euro’ banking license.
In order to execute transfers in a foreign currency, a bank must have an account in
that currency. However, because a legal entity can have a banking license in only
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guide to treasury in banking
one country it can hold an account with only one central bank. In order to execute
payments in foreign currencies, banks must therefore open accounts with a foreign
bank that in turn holds an account at the central bank in that currency area. These
banks are referred to as correspondent banks or intermediary banks and the accounts are referred to as nostro accounts (from the account holder’s point of view).
If a bank with a French banking license, for instance, wants to be able to pay and collect amounts in US dollars, it should open a US dollar account with an US bank, e.g.
Bank of America.
Most banks do not only offer money accounts to their clients but also securities accounts. For this purpose, they have established subsidiaries that acts as a custodian. This is a company that registers securities and settles securities transactions
on behalf of its clients, for instance investment managers, investment funds, institutional investors, private investors and the financial markets divisions of banks.
Custodians in turn hold securities accounts with Central Securities Depositories.
Custodians can function as a clearing member, in which case they are sometimes
referred to as clearing custodians.
1.4.2 Sending settlement instructions
Settlement is the absolute transfer of money and/or securities as a result of transactions in financial instruments. Settlements take place at banks, central banks, custodians and central securities depositories or at specialized settlement institutions,
such as the CLS bank. The date on which the settlement takes place is referred to as
the settlement date or value date.
In order to withdraw a money amount or a number of securities from its own account and have it sent in favour of another account, a party must issue an order
to the institution at which it holds its account. This order is called a settlement instruction. Banks use SWIFTNet for this purpose. Settlement instructions for money amounts must always be sent to the settlement institution before a certain time
to ensure that the amount is transferred to the recipient’s account on the required
­value date and is able to invest the money in the money market. If this is the case,
this is referred to as good settlement value. The final time by which settlement instructions can be sent and still result in good settlement value is called the cut-off
time. The cut-off time for transfers in euros processed through TARGET, for instance, is 17:30 hours, for transfers processed through Euro1 it is 16:00 hours.
32
Chapter 2
Interest Calculations
and Yield Curves
Interest is the price paid for borrowing money. For the calculation of interest
amounts, different agreements or coventions apply. One of those conventions concerns the determination of the number of interest days in an interest period. Another convention concerns the number of interest payments that take place during
the period of the contract. These conventions are also important for calculating the
future value of an amount after an investment period and for the calculation of the
present value of a future cash flow.
Different interest rates apply for different periods. The relationship between the
term and the corresponding interest rate is represented by a yield curve. The shape
of a yield curve provides, amongst others, information about the market perception
regarding the interest rate development. The market perception is represented by
forward yields.
2.1
Calculation of interest amounts
Interest amounts are normally paid out in arrears and are calculated by using the
following equation:
Interest amount = Principal x interest rate x daycount fraction.1
Because interest rates are always presented per annum, an adjustment factor is applied to bring the interest rate in line with the term. This adjustment factor is called
the daycount fraction.
1
The equation to calculate coupon amounts should be entered in a HP financial calculator
as follows: COUP = NOM x C% x D / B. If, in an equation, a % character is added to a variable, this variable should be entered as a percentage: e.g. 4% = 0.04.
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guide to treasury in banking
The equation to calculate the daycount fraction is:
Daycount fraction =
2.1.1
number of days in a coupon period (tenor)
year basis
The duration of the coupon period
The start date of a coupon period is normally a fixed number of days later than the
(re)fixing date of the interest rate. The first coupon period, for instance, of a loan
starts when the nominal amount is transferred from the lender to the borrower.
With money market deposits, this is normally two working days after the closing of
the loan agreement (t+2). Exceptions are Great Britain and Switzerland, where the
coupon period starts on the trading date. With exchange traded bonds, the coupon
period normally starts after three working days (t+3). With an interest rate derivative the first coupon period also normally starts on t+2. If the interest rate is fixed
periodically during the term of a contract, the coupon period starts two working
days after the fixing date, with exceptions.
The end date of a coupon period is called the coupon date. On this date the coupon
is paid. The coupon dates of regular periods (1, 2, 3 months etcetera) normally fall on
the same day in the month as the start date. There are, however, exceptions to this
rule.
If the coupon date falls in a weekend or on a bank holiday, the coupon cannot be
paid on this date. This is because the central bank’s payment system is not operational on these days. The coupon date will then be adjusted to the previous or the
next business day according to the convention agreed upon in the market or in the
specific contract.
The most used conventions are ‘following’ and ‘modified following’. With the convention following, the coupon date will be postponed to the next business day. This
is also the case with the convention modified following with one exception, how­
ever. If the adjusted coupon date would fall in the next month, the coupon date is
then set on the previous business day. In the money market, the modified following
convention is normally used. This is also the case in ISDA agreements.
34
interest calculations and yield curves
Below are the maturity dates of the regular periods for trading day 13 April 2013.
perioddate
day
spot
15/4/2013Wed
1m
15/5/2013Fri
2m
15/6/2013Mon
3m
15/7/2013Wed
4m
17/8/2013
5m
15/9/2013Tue
6m
15/10/2013Thu
Mon
remark
15/8 is Sat
If the spot date falls on a month ultimo date, i.e the last trading day of a month, all
regular dates will in principle be set on a month ultimo date too. Additionally, the
modified following convention is applied. In this case, the convention is referred to
as end-of-month convention (EOM). The table below shows the matu­rity dates for
several regular periods for trading day 28 April 2013.
perioddate
day
remark
spot
30/4/2013Thu
1m
29/5/2013
2m
30/6/2013Tue
3m
31/7/2013
Fri
note: 31st
4m
31/8/2013
Mon
note: 31st
5m
30/9/2013Wed
6m
30/10/2013
Fri
Fri
31/5 is Sun
31/10 is Sat
If the coupon date of a contract is adjusted, the question is whether the coupon term
should be adjusted too. Again, two different conventions may be used: adjusted and
unadjusted. If the convention ‘adjusted’ is used, the number of the interest days is
adjusted to the new coupon date. If the convention ‘unadjusted’ is used, the number
of interest days stays unchanged.
The number of days in a coupon period is calculated by including the start date and
excluding the end date.
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guide to treasury in banking
example
A deposit starts on 4 April and ends on 23 May.
The number of interest days is 49: 27 (30-3) in April and 22 (= 23-1) in May.
2.1.2 Daycount conventions
There are different methods for calculating daycount fractions. These methods are
called daycount conventions. Which daycount convention applies depends on the
type of interest instrument traded and on the local market where this instrument is
traded. There are two types of daycount conventions. They differ in the way that the
number of days in a coupon period is calculated, the tenor. With the first type, the
number of days in each month is set at 30. With the second type, the actual number
of calendar days is calculated.
daycount conventions 30/360
With daycount convention 30/360, the number of interest days is calculated by setting each whole month that falls within the coupon period at 30 days, in prin­ciple.
The intervening ends of months dates are also set at 30. The year basis is always set
at 360.
The table below shows some examples of calculations of the number of days according to the 30/360 convention.
start date
end date
# days 30/360
1.
14-3-200914-9-2009180
2.
14-2-200914-4-200960
3.
28-1-200910-2-200912
4.
14-2-20095-3-2009 21
5.
14-2-20085-3-2008 21
1. There are two ways of calculating the number of interest days:
a. from 14-3 to 14-9 are six whole calendar months: 6 x 30 = 180 days.
b. Number of interest days in March: 30 - 13 = 17;
Number of interest days April to August: 5 x 30 = 150;
Number of interest days in September: 13;
Total: 180 interest days.
36
interest calculations and yield curves
2. Again there are two ways of calculating the number of interest days:
a. from 14-2- tot 14-4 are two whole calendar months: 2 x 30 = 60 days.
b. Number of interest days in February: 30 - 13 = 17;
Number of interest days in March: 30;
Number of interest days in April: 13;
Total: 60 interest days.
3. Number of interest days in January: 30 - 27 = 3;
Number of interest days in February: 9;
Total: 12 interest days.
4. Number of interest days in February 30 - 13 = 17;
Number of interest days in March: 4;
Total: 21 interest days.
5. Number of interest days in February: 30 - 13 = 17;
Number of interest days in March: 4;
Total: 21 interest days.
daycount conventions actual
With daycount conventions ‘actual’ the exact number of calendar days is calculated
for a coupon period. The year basis, however, can differ.
With daycount convention actual/360, for instance, the year is set at 360 days. This
daycount convention is used on the money markets in the euro area, in the US and
in Switzerland. With the daycount convention actual/365, the year is set at 365 days.
This is the case, for instance, in the UK money market and for CAD, AUD, NZD, SGD
and HKD.
example
A bank invests in a deposit with a principal of 20 million euros and an interest rate of
3.2%. The start date is 4 April and the end date is 23 May.
In order to calculate the interest amount, the number of interest days must first be
calculated. In April, 30 - 3 = 27 days are included (the first three days of April do not
count, April 4th does). In May 22 days are included (May 23rd does not count). The
total number of interest days, therefore, is 27 + 22 = 49 days.
The interest amount for this deposit is:
EUR 20,000,000 x 3.2% x 49/360 = EUR 87,111.11
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guide to treasury in banking
With the daycount convention actual/actual the number of days in a coupon period and the number of days in a year are both set at their actual number. In regular
years the year is set at 365 and in leap years at 366. This daycount convention is used
with most government bonds.
A deposit runs from 15 February 2008 (leap year) to 20. March. The table below
shows the daycount fractions according to the different daycount conventions.
daycount
# days in coupon
year basis
daycount fraction
360
34/360
conventionperiod
actual/ 360
(29-14)+19=34
actual/actual(29-14)+19=34366
34/366
actual/365
34/365
(29-14)+19=34365
special cases of the actual/actual convention
If part of a coupon falls in a leap year, with daycount convention actual/actual, the
daycount fraction is calculated by splitting up the coupon period in one part that
falls within the leap year and another part that falls within the regular year.
The following equation is used in these cases:
d
d
Daycount fraction = -----l- + -----r366 365
In this equation:
dl = number of days in the leap year
dr = number of days in the regular year
example
A German government bond with a nominal value of EUR 1,000 has a coupon of
4.5% with daycount convention actual/actual. The coupon date is 1 October. On 1
April 2008 an investor buys this bond. The daycount fraction for the expired period
is:
92
91
Daycount fraction = ------ + ------ = 0, 25205 + 0, 24863 = 0, 50068
365 366
38
interest calculations and yield curves
2.2
Interest rates for broken periods
If a money market instrument has a term that differs from a whole month, the expression broken period is used. In this case, the interest percentage to be used cannot be read directly from the normal yield curve but has to be matched with the
exact contract period. For this purpose, linear interpolation is used:
r b = r s + daycount fraction broken month × ( r l – r s )
In this equation
rb = broken rate;
rs = interest rate for adjacent standard period that is shorter than the broken period;
rl = interest rate for adjacent standard period that is longer than the broken period.
Given are the following interest rates:
period
end date
interest %
1 month
16-2-2009
2.57%
2 months
16-3-2009
2.97%
3 months
16-4-2009
3.04%
4 months
16-5-2009
3.11%
The interest rate for a deposit for the period 16 January to 3 April is determined using the 2 month interest rate and the 3 month interest rate:
r b = 2.97% + daycount fraction broken month × ( 3.04% – 2.97% )
The daycount fraction that is used in this equation depends on the relevant daycount convention.
The daycount conventions actual/360 and actual/365 both use the actual number
of interest days. These are 16 for March and 2 for April (the last day does not count).
After this, the number of days in the entire third month is determined. In this case
31. Here, the daycount fraction is thus 18/31 and the interest rate for the broken period is therefore:
r b = 2.97% + 18/31 × 0.07 = 2,97% + 0.041% = 3.011%
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guide to treasury in banking
With the daycount convention 30/360, each month is assumed to have 30 interest
days. The number of interest days for the deposit in the third month is now 15 + 2 =
17. The number of days for the entire third month is set at 30. Thus, the daycount
fraction is now: 17/30 and the interest rate for the broken period is:
r b = 2.97% + 17/30 × 0.07 = 2.97% + 0.0397% = 3.0097%
2.3
Converting interest rates for different daycount conventions
The amount of interest paid on a coupon date depends on the daycount convention
used. A deposit of EUR 100 million that runs from 15 March until 20 April yields
the following interest amounts for an interest rate of 5.00% with different daycount
conventions:
daycount
daycount fraction interest
interest amount
convention
calculation actual/360
36/360
EUR 100 mio x 5% x 36/360
EUR 500,000
30/360
35/360
EUR 100 mio x 5% x 35/360
EUR 486,111
It is possible to calculate how high the interest rate with daycount convention
30/360 must be in order to achieve the same interest amount as with daycount convention actual/360 and vice versa. The general equation for calculating the daycount convention 30/360 interest rate that is equivalent to a specific interest rate
with daycount convention actual/360 is:
number of days with daycount fraction actual/360
r 30/360 = ----------------------------------------------------------------------------------------------------------------------------- × r actual/360
number of days with daycount fraction 30/360
The interest rate with daycount convention actual/360 that corresponds to a specific interest rate for 30/360 can be calculated by rearranging this equation:
number of days with daycount fraction 30/360
r actual/360 = ------------------------------------------------------------------------------------------------------------------------------- × r 30/360
number of days with daycount fracrion actual/360
If these equations are applied to the table then the outcomes are:
35
r actual/360 = ------ × 0.05 = 0.0486 (equivalent to 0.05 with daycount convention 30/360)
36
and
40
interest calculations and yield curves
36
r 30/360 = ------ × 0.05 = 0.0514 (equivalent to 0.05 with daycount convention act/360)
35
2.4
Converting interest rates for different coupon frequencies
For interest rate instruments with a period of up to one year, it is common to pay
the whole interest amount at the end of the contract period. For interest rate instruments longer than one year, a periodic interest coupon payment generally takes
place during the term of the contract. The frequency for this can vary. In the euro
zone, the coupon frequency is usually annually while in the USA it is often semiannually.
For instruments issued on a zero coupon basis, a nominal amount is always paid at
the end of the period and at the beginning the present value of the instrument is
invested. With these instruments, no interim interest payments take place. This is
true irrespective of the term.
It is possible to calculate how high the interest rate for an annual coupon, the annual rate, must be in order to achieve the same yield as that for a semi-annual rate.
For this purpose, use is made of the fact that the future value of an investment with
a term of one year with an annual rate must equal the future value of an investment
for one year with a semi-annual rate. If this would not be the case, an arbitrage opportunity would exist. This is shown in the following equation:
1 + annual rate = ( 1 + 1/2 × semi-annual rate )
2
From the above equation, the equation can be derived with which the annual rate
can be calculated if the semi-annual rate is known:
2
annual rate = ( 1 + 1/2 × semi-annual rate ) – 1
A semi-annual rate of 5%, for instance, is equivalent to an annual rate of 5.0625%:
2
annual rate = ( 1 + 1/2 × 0.05 ) – 1 = 0.050625
The general equation for calculating the annual rate for a given interest rate for n
coupon payments per year is:
n
annual rate = ( 1 + 1/n × rate with n coupons a year ) – 1
Conversely, the semi-annual rate equivalent for a given annual rate can be calculated as follows:
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guide to treasury in banking
1
-2


semi-annual rate =  ( 1 + annual rate ) – 1 × 2


And, finally, the general equation for calculating the equivalent interest rate for n
coupon payments per year for a given annual rate is:2
1
-n


rate with n coupons a year =  ( 1 + annual rate ) – 1 × n


2.5
Present value and future value
The value of an invested amount increases over time. The amount achieved at
the end of an investment period is called the future value. The factor by which an
amount accrues to the future value during an investment period is called the accumulation factor.
Conversely, the amount that must be invested to achieve a specific future value
against a specific rate of interest can also be calculated. This amount is called the
present value. The factor by which a future value must be corrected in order to calculate the present value is called the discount factor.
For the determination of the present value and the future value, account needs to be
taken of the applicable daycount convention, of the fact whether there is single or
compounded interest and, finally, of the coupon frequency.
2.5.1 Future value with single interest
For contracts with a term of less than one year for which there is one single interest
payment on the maturity date of the contract (single interest), the future value can
be determined using the following equation:
Future value = Nominal value × ( 1 + interest rate × daycount fraction )
In this equation
2
The equation to convert an annual yield to a yield with more than one coupon per year
and vice versa should be entered in a HP financial calculator as follows:
42
YN% = ((1 + Y%) ^ 1/N - 1) x N
interest calculations and yield curves
1 + daycount fraction × interest rate
is the accumulation factor with single interest.
example
If a market party invests in a deposit of EUR 100 million for a period of three months
(90 days) at an interest rate of 5%, the future value is calculated as follows:
Future value = EUR 100 mio x ( 1 + 90/360 x 0.05 )
2.5.2 Present value with single interest
The present value of a cash flow that matures within one year with single interest is
calculated by rearranging the equation used to calculate a future value:3
Future value
Present value = -----------------------------------------------------------------------------------------------( 1 + daycount fraction × interest rate )
The factor
1
-----------------------------------------------------------------------------------------------( 1 + daycount fraction × interest rate )
is the discount factor with single interest.
example
The present value of a cash flow of EUR 100 million after three months at an interest
rate of 5.00% is:
EUR 100 mio
Present value = -----------------------------------------1 + 90/360 x 0.05
3
= EUR 98,765,432.10
The equation to calculate the present value from a future value and vice versa with
­simple interest should be entered in a HP financial calculator as follows:
FV = PV x ( 1 + D / B x Y%)
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guide to treasury in banking
2.5.3 Present value and future value with interim coupon payments and annual
coupon
For contracts that run for more than a year, interim coupons are generally paid.
Since these coupons can again be invested with interest, there is what is called a
compounded interest effect.
In general, the future value of a sum invested for n periods can be determined using
the following equation:
Future value = Nominal amount × ( 1 + interest rate )
n
In this equation
( 1 + interest rate )
n
is the accumulation factor with compounded interest with annual coupons.
example
An investor invests in a EUR 100 million deposit for a term of 2 years. The annual interest rate is 5.00%. If the investor is able to invest the coupon he receives after one
year against an interest rate of 5.00%, the future value after 2 years is:
Future value period 2 = (EUR 100 mio x (1+0.05)) x (1 + 0.05) = 100 mio × (1+ 0.05)
2
= 110,250,000
If we rearrange the above equation we find the general equation for calculating the
present value of a future cash flow that matures after n periods is:
Future value
Present value = --------------------------------------n
( 1 + interest rate )
In this equation
1
--------------------------------------n
1
+
interest
rate )
(
is the discount factor for compounded interest with annual coupons.
44
interest calculations and yield curves
2.5.4 Present value and future value with interim coupon payments and n coupons
per year
In order to calculate the future value and present value if there are multiple coupon
payments per year, for instance semi-annually or quarterly, the above equations
need to be changed somewhat.
The general equation for calculating the future value if there are n coupon payments per year is:
r n
Future value = Present value × ( 1 + ------- )
p/yr
In this equation
r
= annual interest rate with n coupons per year;
p/yr= number of coupon periods per year (2, 4 or 12);
n = total number of coupon periods during the term of the contract term.
example
For a deposit of EUR 100 million with a maturity of nine months, an interim coupon
is paid every three months. The interest rate is 5.00%. The future value after three
months is:
Future value 3 months = EUR 100 mio x (1 + 0.05 / 4) = EUR 1.012,500
The future value achieved after three months grows again during the following
three months with the same factor and, after that, once again. The future value after
nine months or three coupon periods is:
3
Future value 9 months = (100 mio × 1 + 0.05 / 4 ) = EUR103,797,070.31
From the equation for the future value with multiple coupon payments a year, the
equation to calculate the present value of a cash flow that matures after n coupon
periods with multiple coupon payments per year can be derived:4
4
The equation to calculate the present value from a future value and vice versa with compounded interest should be entered in a HP financial calculator as follows:
FV = PV x ( 1 + Y%/PYR)^N
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guide to treasury in banking
Future value
Present value = ------------------------------r n
( 1 + ------- )
p/yr
example
An investor knows that he will receive a cash flow of EUR 40 million after two years.
He uses a semi-annual rate of 6.00% to calculate the present value. The total term,
therefore, consists of 4 coupon periods and the present value is:
EUR 40 mio
Present value = ----------------------4- = EUR 35,539,481.92
 1 + 0.06
--------

2 
2.6
Yield and pure discount rate
In addition to deposits, negotiable securities (money market paper) are traded on
the money market. Often these are zero-coupon instruments. The return on these
short-term securities is often not paid as an interest coupon at the end of the period but consists of the difference between the price for which the security can be
purchased (price) and the nominal value (face value) that is repaid at the end of the
term. The return on these money market instruments can be expressed in two ways:
on the basis of a yield and on the basis of a pure discount rate
2.6.1 Yield
The price of many securities traded on the money market is calculated as the
present value of the face value of this security. If the remaining period for a money
market paper with a face value of EUR 100 million is, for instance, 91 days and investors require a return of 5.00% then the price that they would want to pay for this
security can be calculated using the following equation (single interest):
Face value
price (present value) = -----------------------------------------------------------------------------------------------( 1 + interest rate × daycount fraction )
The interest rate used to determine the price of a money market paper in this way is
also known as yield.
46
interest calculations and yield curves
In this case:
EUR 100 mio
EUR100 mio
price (present value) = ------------------------------------------- = ------------------------------- = EUR 98,751,887
1 + 0.05 × 91 ⁄ 360
1.102639
The yield is an annual percentage. When the yield is adjusted with the daycount
fraction and multiplied by the present value of a money market paper, the result
can be seen as the interest amount paid by the issuer for borrowing money.
2.6.2 Pure discount rate
Besides the yield, on the American and British money markets another measure
is used to indicate the return on a money market paper and to calculate the issue
price: the pure discount rate. Just as with the yield, the pure discount rate is an annual percentage. The pure discount rate (adjusted with the daycount fraction) is,
however, not multiplied by the present value of a money market paper to calculate
the interest amount, but by the future value or face value. The interest amount calculated in this way is called the amount of discount.
Amount of discount = future value x pure discount rate x daycount fraction
The price of a money market paper can be calculated by subtracting the amount of
discount of the face value as follows using the pure discount rate:
price = face value – amount of discount5
or
price = face value × ( 1 – pdr × daycount fraction)
example
A U.S. Treasury Bill with a term of 91 days has a face value of USD 50 million. The
pure discount rate is 4.25%. The price of this Treasury Bill is:6
price = USD 50 mio × ( 1 – 0.0425 × 91 ⁄ 360 ) = USD 49,462,847.25
5
The equation to calculate the price of a bill should be entered in a HP financial calculator
as follows: PRBILL = NOM x (1 - D/B x PDR%)
6
Use the PRBILL equation in your HP Financial Calculator:
NOM = 50,000,000, PDR% = 0.0425, D = 91, B = 360. Solve for PRBILL.
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guide to treasury in banking
2.6.3 Equations for converting the yield to pure discount rate and vice versa
The price of a money market paper can thus be calculated using the yield or ­using
the pure discount rate. The outcome must be the same for both calculations, otherwise there would be an arbitrage opportunity. By making use of this fact, an equation can be determined to convert a given yield into a pure discount rate and vice
versa.
face value
price = ----------------------------------------------------- = face value × ( 1 – dayc. fract. × pure discount rate )
1 + daycount fract. × yield
From this equation, the following equations that represent the relationship between pure discount rate and yield can be derived:7
yield
pure discount rate = ---------------------------------------------------------1 + daycount fraction × yield
and
pure discount rate
yield = ------------------------------------------------------------------------------------1 – daycount fraction × pure discount rate
If we apply the second equation to the U.S. Treasury Bill from the previous example,
we get
0,0430 =
0.0425
1 – 91/360 × 0.0425
The equivalent yield to a pure discount rate of 4.25% is 4.30%.
Note: if the yield and the pure discount rate are the same, the return on an investment is the highest if the price is calculated using the pure discount rate instead of
the yield.
7
The equation to convert a yield to a pure discount rate and vice versa should be entered in
a HP financial calculator as follows: PDR% = Y% / ( 1 + D / B x Y%)
48
interest calculations and yield curves
2.7 Yield curves
A yield curve, also called interest rate term structure, is a graphical representation of
the relationship between the (average) term of a given financial instrument and the
corresponding interest rates (yields) that are used in transactions with a debtor from
a single risk category. Thus, there are, for example, separate yield curves for government loans and for interest rate swaps between banks (the IRS curve).
There are different types of yield curves. The most common yield curve presents the
interest rates for periods that start on the spot date and concern instruments that
generate interim coupon payments. This curve is also called a spot coupon curve.
When the yield curve is discussed, it generally refers to this curve. Another important yield curve is the zero-coupon curve. This yield curve concerns instruments
that do not generate interim cash flows. The zero-coupon curve is used to calculate
the present value of single future cash flows for maturities longer than one year. A
forward yield curve presents a projection of the shape of a yield curve at a specific
moment in the future.
Generally, the interest rates for longer periods are somewhat higher than those for
shorter periods, i.e the yield curve is rising. This is explained by the liquidity prefe­
rence theory. According to this theory, investors require a higher return since they
have made their money available for a longer period. After all, they must postpone
their own expenditures and also they run a greater risk of not getting their money
back.
In practice, yield curves are generally rising. A rising yield curve is therefore often
called a normal yield curve. The yield curve generally rises more steeply for shorter periods than for longer periods: the yield curve ‘flattens’ out for longer terms
(flattening yield curve). Should the curve get steeper then this is called steepening.
However, this almost never occurs in practice.
Figure 2.1 contains the yield curve for Dutch State Loans (DSLs) and US Treasuries
for 29 January, 2010. This figure clearly shows a flattening pattern.
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guide to treasury in banking
Figure 2.1 Yield curves for DSL and US Treasuries
The fact that there is a difference between the rates for different terms is also partly
due to the fact that demand and supply conditions vary in different segments of the
yield curve. This is called the market segmentation hypothesis.
2.8 Forward rates
The shape of the yield curve can provide information about the expectation that the
market has about future interest rate developments. This is also called the pure expectations theory. If the rates for longer terms are higher than those for short periods,
this may indicate that the market expects a rise in interest rates. With a declining or
inverse yield curve, the money market interest rates are higher than the capital market rates. In this situation, market participants may expect interest rates to fall. With
a flat yield curve, interest rates for all periods are roughly the same. The (theoretical)
market expectations are reflected in the so called implied forward rates.
Forward interest rates are interest rates used for interest rate instruments for which
the term lies in the future. Examples of these include forward rate agreements and
forward start interest rate swaps. Forward interest rates can theoretically be calculated by using the interest rates for periods starting per spot, the spot rates.
50
interest calculations and yield curves
If the 6 month interest rate is, for example, 0.75% and the 12 month interest rate is
1.00%, it can theoretically be concluded that the market expects that interest rates
after six months will be higher than the current rates. For each period that starts in
the future, a forward interest rate can be determined, i.e. the implied forward yield.
2.8.1 Calculation of forward rates
A 6 month interest rate for a period that starts in three months time is referred to
as the ‘3 against 9’ or ‘3s v. 9s’ or a ‘3 x 9’ forward rate. The first number refers to the
start date of the forward period to which the forward rate refers (t = 3 months). The
difference between the two numbers refers to the term of the forward period (9 - 3 =
6 months), i.e. the underlying period.
When calculating the theoretical forward rate for a period of less than 1 year, use
is made of the fact that it should make no difference for an investor whether he invests an amount for an entire investment period in the money market against a
single interest rate or that he invests that amount for subsequent shorter periods
totalling the whole investment period. In the latter case he earns interim interest
revenues that can be invested again. The following equation shows this theorem:
(1 + ds/year basis × rs) × (1 + dfw/year basis × rfw) = 1 + dl/year basis × rl
In this equation
ds = days in the first investment period
dfw = days in the second investment period, the forward period
dl = days in the entire investment period
rs = interest rate for the first broken period
rfw = interest rate for the forward period
rl = interest rate for the entire investment period
example
Given are the following rates:
6 months (183 days) 5.4%
12 months (365 days) 5.8%
The break-even rate for the six month forward period after six months can be calculated as follows:
( 1 + 183/360 x 0.054) x ( 1 + 182/360 x rfw) = ( 1 + 365/360 x 0.058)
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guide to treasury in banking
The left hand side of the equation shows the future value of a principal sum of 1
(euro) after six months (183 days) with an interest rate of 5.4%, that is reinvested for
six further months (182 days) against the forward yield (rfw). The right hand side of
the equation shows the future value of a principal sum of 1 (euro) invested for the total period of one year (365 days) with an interest rate of 5.8%. The two values must
be the same, otherwise arbitrage would be possible. The unknown variable from the
equation is rfw, i.e. the 6s v 12s forward rate. This rate can be calculated as follows.
1.02745 × (1 + r fw × 182 ⁄ 360 ) = 1.0588056
and, therefore,
1.0588056
r fw =   -------------------- – 1 × 360 ⁄ 182 = ( 1.0352 – 1) × 360 ⁄ 182 = 0.06036 = 6.036%
  1.02745 

The general equation used for determining a forward rate on the money market is:8
1 + r × d ⁄ year basis
r fw =   -----------l--------l------------------------ – 1 × year basis ⁄ d fw
  1 + r S × d S ⁄ year basis

In this equation
rfw = forward yield;
rs = interest rate for the period until the start date of the forward period;
ds = number of days until the start date of the forward period;
dfw = number of days in the forward period;
rl = interest rate for the period until the end date of the forward period;
dl = number of days until the end date of the forward period;
yb = year basis.
Forward rates can also be viewed from a more conceptual perspective. If an amount
is invested with interest, it grows over time. The extent to which the amount grows
is given by the accumulation factor. For a six month rate of 5.4%, an amount invested for 183 days, for instance, grows with an accumulation factor of 1 + 183/360
x 0.054= 1.0275. And for an annual rate of 5.8%, an amount invested for 365 days
grows with an accumulation factor of 1 + 365/360 x 0.058 = 1.0588. This is shown in
Figure 2.2.
8
The equation to calculate an implied forward rate from two money market cash rates
should be entered in a HP financial calculator as follows:
52
Y%FW = (( 1 + DL / B x Y%L) / ( 1 + DS / B x Y%S) - 1 ) x B / ( DL - DS)
interest calculations and yield curves
Figure 2.2 Calculation of the 6s v 12s forward rate
Figure 2.2 also shows that an amount, invested during the forward period from
183 days to 365 days, grows with the accumulation factor of 1.0588056 / 1.02745 =
1.0352. In order to derive a (forward) interest rate from this accumulation factor,
this factor must first be reduced by the number ‘1’ and then corrected with the inverse value of the daycount fraction. After all, the accumulation factor of 1.0352 was
realized in only 182 days, i.e. 365 – 183.
The 6s v 12s forward rate can be calculated as follows:9
1.0588058
6s v 12s forward rate =  -------------------- – 1 × 360
----- = 0.06036
 1.02745
 -182
2.8.2 Strip forwards
As we have seen, an implied forward rate can be derived from two spot rates. From
a three month and a six month spot rate, for instance, a 3s v 6s forward rate can be
derived.
9
Use the Y% FWMM equation to calculate the 6s v 12s forward rate: DL = 365, DS = 183, B =
360, Y%L = 0.0580, Y%S = 0.0540. Solve for Y%FWMM.
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guide to treasury in banking
rate
# days
3 month spot rate
2.55
91
6 month spot rate
2.61
183
3s v 6s forward rate
2.65
92
The six month spot rate is actually made up of the three month rate and the 3s v 6s
forward rate. The six month and nine month spot rate, in turn, can then be used to
derive the 6s v 9s forward rate:
rate
# days
6 month spot rate
2.61
183
9 month spot rate
2.67
273
6s v 9s forward rate
2.75
90
The nine-month spot rate is actually made up of, respectively, the three month spot
rate, the 3s v 6s forward rate and the 6s v 9s forward rate respectively.
Continuing this reasoning, the nine month spot rate and the twelve month spot rate
can be used to derive the 9s v 12s forward rate. The twelve month spot rate and the
fifteen month spot rate can then be used to derive the 12s v 15s forward rate and so
on.
The two year interest rate for an interest rate swap (IRS rate) can therefore also be
considered as a combination of the following subsequent rates, i.e. a ‘strip’ of forward rates:
3 month spot rate 2.55
3s v 6s forward rate
2.65
6s v 9s forward rate
2.75
9s v 12s forward rate
2.90
12s v 15s forward rate
3.00
15s v 18s forward rate
3.20
18s v 21s forward rate
3.30
21s v 24s forward rate
3.40
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interest calculations and yield curves
Figure 2.3 shows how the two years rate is made up of subsequent three month forward rates.
Figure 2.3 Strip of three month implied forward rates
For a rising yield curve, the first rate of the strip (in this case the three month Euribor) is lower than the level of the long interest rate. The final rate in the strip then lies
above the level of the long interest rate. For an inverse yield curve, the reverse is true.
calculating a spot rate from a shorter spot rate
and a strip forward rates
The one year rate in the previous section can be calculated by using the following
formula (assume that the fourth quarter has 92 interest days):
1yr rate =
(( 1+91/360 x 0.0255)x(1+92/360x0.0265)x(1+90/360x0.0275)x(1+92/360x0.0290) -1) x 365/360 =
0.0274 = 2.74%
In interest calculations, however, often more periods are involved. The equation
below can be used for the calculation of compounded interest for ‘n’ successive
­periods:
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guide to treasury in banking
Compounded interest rate
= ( ∏ ( 1 + di / year basis x ri) - 1 ) x year basis / total number of days10
The character ∏ in the equation is a Greek letter that indicates the product of similar terms, here the accumulation factors for the successive periods. ∏ ( 1 + di / year
basis x ri), therefore, gives the accumulation factor for the whole period. We have
already seen that an accumulation factor can be converted to an interest rate by subtracting 1 and adjusting the answer by the inverse of the daycount fraction. This is
done in the remainder of the equation.
example
The following rates are given:
3 month EURIBOR (91 days): 1.76%
3s v 6s FRA (92 days): 1.82%
6s v 9s FRA (90 days):1.84%
The 9 months rate implied by these rates can be calculated as follows:
Compounded rate = ((1+ 91/360 x 0.0176) x (1+92/360 x 0.0182) x (1+90/360 x
0.0184) -1) x 360/273 = 0.0181 = 1.81%11
10 The equation to calculate a compounded interest rate for a maximum of 5 periods should
be entered in a HP financial calculator as follows: Y%COMP = ((1+D1/BxY%1) x (1+D2/
BxY%2) x (1+D3/BxY%3) x (1+D4/BxY%4) x (1+D5/BxY%5) -1) x B / (D1+D2+D3+D4+D5)
11 Use the Y%COMP equation in your HP Financial Calculator: D1 = 91, D2 = 92, D3 = 90, D4
= 0, D5 = 0, Y%1 = 0.0176, Y%2 = 0.0182, Y%3 = 0.0184, B = 360, Y%4 and Y%5 need not to
be filled in. Solve for Y%COMP.
56
Chapter 3
The Money Market
The money market is the market in which interest related financial transactions
with a short term take place. Traders normally only consider transactions with
a term shorter than one year as money market transactions. The most important
function of the money market is to enable parties with temporary liquidity surpluses to give short-term loans to parties that are short of money. The lenders receive
a compensation for this, the money market interest. The traditional financial instruments on the money market are deposits, money market paper and repurchase
agreements. The majority of money market instruments are concluded over-thecounter.
In many countries, the regulatory bodies make a distinction between professional
players and non-professional players. When non-professional players do business
with professional players they are protected by supervisory laws which stipulate
that the professional players have a duty of care towards their non-professional
­clients. For example, in the UK the FSA has set the dividing line for money market
transactions for non-professional customers (retail clients) at transactions of less
than GBP 100,000.
3.1 Domestic and Euro money markets
Each currency has its own money market in which transactions are concluded
in the local currency. These money markets are called local money markets. The
country of domicile of the market parties is not relevant in this respect. For example, if a British company issues commercial paper in USD in the United States, then
this is a local commercial CP since it is issued in the US. And if, for instance, a US
citizen invests in a EUR denominated deposit in Frankfurt, then this is a domestic
deposit.
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guide to treasury in banking
If, on the other hand, a party performs a transaction in a currency outside the country where the currency is the local currency, then the word euro is added to this
transaction. If a UK company, for example, issues a CP denominated in US dollars
in the UK, then this is a eurodollar CP. And if a US company invests in a USD deposit
with a Singaporan bank, this is referred to as a eurodollar deposit. This deposit is
not subject to the cash reserve requirements of the Fed, but to the cash reserve requirement of the central bank of Singapore.
The inter-bank transfers that are the result of both, transactions in the domestic or
the euro market are always cleared via the central bank of the relevant currency. A
transfer of US dollars for instance between a German Bank and a Japanese bank in
London, is ultimately cleared via the Federal Reserve bank in New York.
3.2 Deposit
A deposit is a loan for a fixed term at a fixed interest rate. The party that lends the
money benefits from a higher interest rate than that is paid on a current account.
Regular terms for deposits are 1,2 and 3 weeks and 1 to 12 months. The minimum period for a deposit, however, is only one day. Examples of deposits with a term of one
day are overnight deposits, tom/next deposits and spot/next deposits – starting today, tomorrow or spot respectively. Generally, no collateral is requested for a deposit. The British regulator, the FSA, uses the terms straight deposit or clean deposit for
uncollateralized deposits. Some deposits have an undetermined period to maturity;
they can be ended at the request of the lender. A call deposit, for example, is payable
on demand (with a cut-off time of 12.00). And a notice deposit can be demanded after one or two days. ­
A deposit is not tradable and can, in principle, not be redeemed before the maturity
date. If a depositor wants his money back before the maturity date, the bank pays
the lower of the two, the fair value, i.e. the present value of the sum of the principal and the interest amount or the book value, i.e. the nominal amount plus the accrued interest until the moment that the deposit is cancelled.
example
An investor has invested in a deposit with a nominal amount of 20 million euro, a
term of 49 days and an interest rate of 3.2% (actual/360). If the investor would not
terminate the deposit early, the redemption amount would be:
EUR 20M x (1 + 49/360 x 0.032) = 20,087,111.11.
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the money market
After 20 days, however, the depositor wants to cancel his deposit. The remaining
term, therefore is 29 days. At that moment, the yield for a period of 29 days is 3.4%.
The book value of the deposit is:
EUR 20M (1 + 20/360 x 0.032) = EUR 20,035,555.
The fair value of the deposit is:
EUR 20,087,111.11/ (1 + 0.034 x 29/360) = EUR 20,032,245.02.
The bank thus pays the fair value.
The penalty fee for cancelling the deposit can be calculated as follows:
EUR 20,033.333.33 – EUR 20,032,245.02 = EUR 1,088.31.
example
If, at the time of cancelling the deposit, the interest rate would have been lower than
the deposit contract rate, e.g. 2%, the bank would pay back the book value of the deposit, since this value is now lower than the fair value.
Book value: EUR 20M x (1 + 20/360 x 0.03) = 20,033,333.33.
Fair value: EUR 20,087,111.11 / (1 + 0.02 x 29/360) = 20,054,800.60.
This means that the investor is not profiting from the decrease in interest rates.
3.3 Money market paper
Money market paper is a negotiable fixed income security with a short term. The
maximum term for money market paper in the euro money market is, for instance,
two years. The nominal value (face value) of money market paper is always a multiple of one million. It is therefore only suitable for large investors.
Money market paper is issued under an issuing or lending programme. This means
that a borrower can issue interest-bearing securities up until a specific maximum
amount without the need to draw up a separate prospectus each time. The utilization of a lending programme by the issuing institution is called drawing on the
programme. Banks advise the issuing institutions in the setting up a lending programme. With the issue of money market paper, the bank plays the role of broker/
intermediary. The bank sells the money market paper to investors by order of the issuer. In this capacity, the bank runs no credit risk. That risk is for the purchaser of
59
guide to treasury in banking
the money market paper. Nor do banks provide a placement guarantee. If no investors can be found, the issuer must offer a higher yield or seek finance in another way.
Since the investor takes the credit risk, it is important that he has access to good information about the creditworthiness of the issuing organization. To satisfy these
information requirements, more and more issuers of money market paper are applying for a rating from one of the well known rating agencies such as Standard &
Poor’s, Moody’s and Fitch IBCA. These institutions assess organizations with regard
to their creditworthiness and record this assessment in a letter-number combination: the rating. It is often stated in a treasury charter of investing institutions that
it may only invest in securities with a specific minimum rating level, for example, at
least A1-P1 (for both Standard & Poor’s and Moody’s, this means a good short-term
rating).
The following types of money market paper exist.
– commercial paper;
– Treasury Bill;
– certificate of deposit;
– Bank bills / bankers’ acceptances.
3.3.1 Commercial paper
Commercial paper is a type of money market paper that can be issued by all kinds of
market parties. However, the issuing institutions are usually companies or local or
regional government authorities.
Commercial paper is issued on a zero-coupon basis. This means that the investor
buys the commercial paper at a price that is equal to the present value of its face
value. The price of a commercial paper is calculated by using the equation of the
present value. The interest rate used in this equation is also referred to as yield. The
yield is usually stated as a spread against the prevailing money market benchmark
(LIBOR or EURIBOR). At maturity, the investor receives the face value of the commercial paperback.
rate of return in the event of a premature sale
If an investor sells a commercial paper during the term, the yield that he has
achieved during the investment period is calculated by determining the difference
between the present value of the paper on purchase and the present value on sale.
This difference is then expressed as a percentage of the present value on purchase
(the amount invested). This percentage needs to be converted to an annual percentage by multiplying it by the inverse of the daycount fraction for the term of the in60
the money market
vestment. The following equation is used to calculate the yield of an investment in
commercial paper:12
price – purchase price year basis
Rate of return = sale
------------------------------------------------------- × -------------------- × 100%
purchase price
period
example
An investor buys a newly issued commercial paper with a face value of EUR
50,000,000, a yield of 5% and a term of 91 days. The issue price is:
EUR 50,000,000 / ( 1+ 91/360 x 0.05) = EUR 49,375,942.9413
One month later, the investor decides to sell the commercial paper. The current yield
is 4.5% and the remaining term is 61 days. The sale price is:
EUR 50,000,000 / ( 1 + 61/360 x 0.045) = 49,621,635.0314
The investor has made an annual return of:
(49,621,635.03 - 49,375,942.94) / 49,621,635.03 x 360 / 30 x 100% = 5.97%15
3.3.2
Treasury Bills and bank bills
A Treasury bill or T-Bill is a money market paper issued by the American or British
central government. UK Treasury Bills are issued at the present value of the nominal amount, and US Treasury Bills are issued against a price that is based on the
pure discount rate. During the period to maturity, the price of the Treasury Bill is
also determined by the pure discount rate method. At the end of the period Treasury Bill is redeemed at face value.
12 The PV equation can be used for this purpose. The sales price must be entered as FV and
the purchase price must be entered as PV.
13 Use the PV equation in your HP Financial Calculator to calculate the issue price:
FV = 50,000,000, D = 91, B = 360, Y% = 0.05. Solve for PV.
14 Use the PV equation in your HP Financial Calculator to calculate the sale price:
FV = 50,000,000, D = 61, B = 360, Y% = 0.045. Solve for PV.
15 Use the PV equation in your HP Financial Calculator to calculate the annual return:
FV = 49,621,635.03, PV = 49,375,942.94, D= 30, B = 360. Solve for Y%.
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guide to treasury in banking
UK Treasury Bills are issued via a weekly tender organized by the DMO (Debt Management Office). This tender is non-competitive which means that all allocations
are made against the same yield, including those for subscribers who tendered
against a lower yield. The terms are 1, 3, 6 and 12 months. The settlement of transactions in UK Treasury Bills takes place at Crestco (formerly CMO, Central Money Markets Office) which is part of Euroclear.
U.S. Treasury Bills are also issued weekly with terms of 3 and 6 months. The 12
month U.S. Treasury bill is however issued on a monthly basis. Between the time of
the auction and the actual settlement date, US Treasury Bills are traded on the WI
(When Issued) market.
A bank bill or banker’s acceptance is a money market paper issued by a non-bank
which is, however, guaranteed by a bank. Companies in the United States use bank
bills to pay their suppliers. The price of a bank bill is calculated on the basis of the
pure discount rate. At the end of the period, a bank bill is redeemed at face value. If
the bill is not guaranteed by a bank, it is referrred to as a bill of exchange.
3.3.3
Certificate of deposit
A certificate of deposit (CD) is a money market paper that is issued exclusively by
banks. As opposed to the other forms of money market paper, CDs are sometimes
issued at face value and, at the maturity date, the face value amount plus the interest payment is paid back. So, as with a deposit, a coupon is then attached. If a CD
is traded before maturity, the price is equal to the present value of the sum of the
principal plus the coupon at maturity. Other CDs, however, are issued at the present
value and are repaid for the nominal amount and they resemble com­mercial paper.
The price of a coupon bearing CD during the term can be calculated by using the following equation:16
NOM × ( 1 +
Price =
1+
original term
year basis
remaining term
year basis
× coupon rate )
× current yield
16 The equation to calculate the price of a coupon bearing CD during its term should be entered in a HP Financial Calculator as follows:
62
PRICECD = NOM x ( 1 + DT / B x C%) / ( 1 + DR / B x Y%)
the money market
example
A coupon bearing certificate of deposit has an original term of 91 days and a face value of USD 50,000,000. The coupon rate is 5%. The maturity amount is:
50,000,000 x ( +
91
360
x 0.05 ) = 50,631,944
The price of this certificate of deposit after 30 days and a current yield of 4% is:17
USD 50,631,944.40
Price = --------------------------------------- = USD 50,291,082.66
1 + 0.04 × 61/360
In the UK, all banks and building societies with a banking licence are allowed to issue certificates of deposit. The term of a British CD varies between three months
and five years. CDs with a term of more than one year bear an annual coupon. The
settlement of transactions for UK CDs takes place via Crestco. The term for an American CD varies between 14 days and 10 years.
The characteristics of the various forms of money market paper are summarised below.
instrument
yield/pdr
amount paid back
issuer
at maturity
Commercial Paper
Yield
Face value
Miscellaneous
Commercial Paper US
Pure discount rate
Face value
Miscellaneous
Treasury Bill Pure discount rate
Face value
US/UK
Federal Government
Bank bill (bill of exchange)
Pure discount rate
Face value
Corporates
Certificate of deposit
Yield Face value + Coupon
Banks
or Face Value
17 Use the PRICECD equation in your HP Financial Calculator to calculate the issue price of
the CD:
NOM = 50,000,000, DT = 91, DR = 61, B = 360, C% = 0.05, Y% = 0.04. Solve for PRICECD.
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guide to treasury in banking
3.4 Repurchase agreements
A repurchase agreement (REPO) and a sell/buy back are both forms of short term
loans in which securities (usually bonds) are provided as collateral. The borrower
of the money is called the repo seller and the money lender the repo buyer. The
repo buyer thus enjoys a double protection against credit risk: double indemnity. This is because two parties must default before he suffers a loss. If the collateral is in a different currency than the money amount, the transaction is called a
cross-currency repo. Since a repo is conceptually nothing more or less than a loan,
a coupon is paid at maturity. And because the repo is traded on the money market,
money market daycount conventions are used: actual/360 or actual/365. Figure
3.1 shows the transfers as a result of a repo at the start date and at the maturity
date.
Figure 3.1
If the transaction in figure 3.1 is initiated by the repo seller stating ‘I repo’, he acts
as a market user. The repo buyer now acts as a market maker and is able to quote
the rates stating ‘I reverse in bonds’. His ask rate refers to the rate he wants to receive for lending money and his bid rate refers to the rate he is willing to pay for
borrowing money. If this quote is 1.75% - 1.77%, this means that the repo seller can
borrow money from the repo buyer at a rate of 1.77%.
The economic ownership of the collateral remains with the repo seller. However,
during the period of the agreement, the lender is the legal owner of the collateral. If the repo seller is unable to fulfil his repayment obligation, the repo buyer
can dispose of the collateral in order to compensate for his credit loss. Most repos
are concluded under a SIFMA/ICMA Global Master Agreement.
The maximum term for a repo is 1 year. The largest volumes occur, however, within
a period of 2 weeks, most of which is tom/next or spot/next. For many repos, the
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the money market
maturity date is fixed; such repos are called term repos. In addition, there are also
callable repos which can be redeemed early.
the use of repos by central banks
Repurchase agreements are also widely used by central banks in the execution of
their monetary policy. The refinancing transactions of the European Central Bank
are, for example, repos which the ECB uses to temporarily lend money to commercial banks.
The Federal Reserve Bank in the United States also uses repos to influence money market liquidity: system repos and matched sales repos. With system repos the
Fed increases the liquidity on the money market by temporarily lending money to
the commercial banks (comparable with the refinancing transactions of the ECB).
Matched sales or system reverse repos are repos that the Fed uses to temporarily
drain money from the money market by borrowing from the commercial banks.
The Fed also uses customer repos. These are repos concluded with other central
banks to make US dollars temporarily available to them.
3.4.1 Initial and maturity consideration
The amount transferred at the beginning of a repo is called the initial consideration. The initial consideration is related to the value of the collateral. For bonds, this
is the dirty price, thus including accrued interest. The amount paid back on maturity is called the maturity consideration. The maturity consideration is equal to the
initial consideration plus a coupon based on the repo rate.
example
A money market dealer repos out 20,000,000 3.75% Dutch State Loans (DSL) with a
clean price of 98.64. The coupon date of the bonds is 15 July and the start date of the
repo is 20 August (not a leap year). The dealer is quoted 1.75% - 1.77% for a term of
14 days.
The daycount convention of DLS is actual/actual. This means there are 17 + 19 = 36
days accrued.
The initial consideration of this repo is 20,000,000 x ( 0.9864 + 36/365 x 0.0375) =
19,801,972.60
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guide to treasury in banking
The maturity consideration of this repo is 19,801,972.60 x ( 1 + 14/360 x 0.0177) =
19,815,602.9618
Often, repo buyers employ a haircut, also known as initial margin to the collateral.
The repo buyer than offers less cash than the value of the collateral. The initial consideration is then calculated using the following equation:
initial consideration = dirty price bonds x 100 / (100 + initial margin)
example
If the repo buyer in the previous example employs a margin of 2.5%, the initial consideration of the repo would be:
19,801,972.60 x 100/102,50 = 19,318,997.66
During the term of the repo the value of the claim is constantly compared to the
value of the collateral. This is referred to as marking to market the repo. If the value
of the collateral is too low to cover the claim, then the repo buyer asks the seller to
transfer more bonds. This is called daily margining.
3.4.2
General and special collateral
For repos concluded within the context of of the liquidity management of the bank,
general collateral (GC) is frequently used. The collateral used for a GC repo consists of government bonds of particular countries. In a master agreement it is stated which government bonds are eligible e.g. Dutch bonds, German bonds, French
bonds et cetera. The specific bond used as collateral is then not important and the
repo seller is allowed to substitute between different government bonds, as long as
they are on the list of eligible bonds.
In some cases, however, the repo buyer will set specific requirements for the collateral. This is called special trading. The reason for the repo is then a requirement for
a specific bond, for example, to meet the delivery commitment as a result of entering into a short position or to meet a delivery commitment for bond futures. The
bond in question is referred to as ‘special’.
18 Use the PV equation in your HP Financial Calculator to calculate the maturity consideration: PV = 19,801,972.60, D = 14, B = 360, Y% =0.0177. Solve for FV.
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the money market
Some parties hold on to these special securities in the expectation that other parties
will want to borrow them in a repo transaction. This is called icing or putting stock
on hold.
3.4.3
Transfer of collateral
For most repos, the collateral is transferred directly from the securities account of
the repo seller to the securities account of the repo buyer. These repos are called deliver-out or delivery repos. With these repos, a coupon payment during the term of
the repo is immediately transferred from the repo buyer to the repo seller.
A tri-party repo is a variant of a deliver-out repo in which a joint custodian is
brought in for the transfer of the securities and cash between the contract parties.
This custodian must conclude a separate bilateral agreement with both parties. The
right of disposal over the collateral passes ultimately from the repo seller to the
repo buyer.
In a tri-party repo, the custodian takes over the collateral management from the
contract parties. It performs the collateral administration and is responsible for the
calculation and execution of the necessary margin payments. The custodian is also
able to net the contracts which considerably reduces the number of transfers for the
contract parties. Finally, the custodian is responsible for settling any coupon payments.
For some repos, the collateral is not transferred to the account of the repo buyer.
This is the case, for instance, for the refinancing transactions of the ECB. These repos are referred to as hold in custody (HIC) repos. A hold in custody repo is a repo
in which the repo seller holds the collateral within its own securities account. This
­account is intended specially for holding the collateral of repo buyers. The repo seller, however, holds the right of disposal for the securities. HIC repos offer less security to the buyer than delivery repos. This is because the buyer has to make sure that
the collateral is transferred to his account when the seller has defaulted. With HIC
repos, also there is a chance that the seller may use the securities in more than one
repo transaction. This is referred to as double dipping.
3.4.4
Sell/buy back
An alternative for a repurchase agreement is a sell/buy back contract. Economically,
sell/buy back contracts can also be seen as borrowing money using securities as collateral. The most important difference between a repo and a sell/buy back is that for a
sell/buy back transaction, any coupons or dividend payments are not transferred im67
guide to treasury in banking
mediately to the repo seller, but are settled at the maturity date. Another difference
is the fact that a sell/buy back transaction consists of two separate contracts. A sale
of bonds at the start date and a purchase of the same bonds at the maturity date. This
means that the substitution of collateral with sell/buy back contracts is not possible.
If the seller wants to substitute the collateral, the contract must be re-negotiated.
The risk with a sell buy back transaction is that during the term the value of the collateral may change dramatically, leaving one of the parties with a heavily under-collateralized position. To prevent this, in the master agreement parties ususally agree
a so called repricing arrangement. This means that if the market value of the collateral stated as a percentage of the nominal contract amount ceases to be within a
pre-agreed range, then the contract will be unwound and will be replaced by a new
contract which is in accordance with the current market conditions. This means
that the value of the collateral is set at the same level as the principal of the loan. If
a haircut was applied in the original contract, this will also be the case for the new
contract.
3.5 Trading on the money market
Trading on the money market takes, amongst other things, place by borrowing
money for a specific term and investing it for another term. Traders may use deposits and certificates of deposit to borrow money and may use deposits and all kinds
of money market paper to lend money. In this respect, borrowing money is referred
to as opening a long cash position and investing money is referred to as opening a
short cash position.
If a trader expects money market interest rates to fall, he invests money for a relatively long period, e.g. six months, and borrows money for a shorter period, e.g.
three months. He has now created a short forward cash position in the 3s v 6s. This
position is shown in figure 3.2.
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the money market
Figure 3.2 Short forward cash position (3s v 6s)
After three months, the money market trader has to take another deposit to close
his position, for instance, another three month deposit. The implied forward money market rate at the moment of opening the position is the break-even rate for this
position. The break-even rate for a spot forward cash position can be calculated by
the following equation:
1 + r × d ⁄ year basis
r fw =   -----------l--------l------------------------ – 1 × year basis ⁄ d fw
  1 + r S × d S ⁄ year basis

In this equation
rfw = forward yield;
rs = interest rate for the period until the start date of the forward period;
ds = number of days until the start date of the forward period;
df = number of days in the forward period;
rl = interest rate for the period until the end date of the forward period;
dl = number of days until the end date of the forward period;
yb = year basis.
Figure 3.3
Break-even position of a deposit trader
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guide to treasury in banking
A trader will only take a forward cash position if he expects that the future spot in­
terest rate will differ from the actual implied forward rate. If he expects that the
­future spot interest rate will be higher than the actual implied forward rate, he will
open a long forward cash position and if he expects that the future spot interest rate
will be lower than the implied forward rate, he will open a short forward cash position.
example
A trader expects Euro money market interest rates to fall after six months (i.e. he
expects the future spot interest rate to be lower than the actual implied forward rate
for that period). He therefore opens a short cash position in the 6s v 12s by taking a
deposit for 6 months and investing the money in a 12-month deposit.
The actual interest rates are:
6 months:
1.25 - 130 (182 days)
12 months:
1.35- 1.40 (365 days)
The implied forward rate is: ((1 + 365/360 x 0.0135) / ( 1 + 182/365 x 0.0130) – 1)
x 360 / 183 = 0.0139 = 1.39%19.
If, after six months, the actual six month interest rate would be lower than the breakeven rate of 1.39%, the trader realizes a profit. The actual 12 month rate that the trader realizes for the two successive six-month borrowings is a compounded rate that is
composed of the successive six month rates.
If the actual six month rate after six months will be 1.32%, the trader’s compounded
funding rate can be calculated as follows:
Compounded funding rate = (( 1 + 0.0130 x 182/360) x ( 1 + 0.0132 x 183/360) - 1 ) x
365/360 = 0.0131 = 1.31%20.
Since the interest rate on his investment was 1.35%, the trader now realizes a profit
of 4 basis points over one year over the principal amount.
19 Use the Y%FWMM equation in your HP Financial Calculator to calculate the break-even rate
(Y%FW): DL = 365, B = 360, Y%L = 0.0135, DS = 182, Y%S = 0.0130. Solve for Y%FWMM.
20 Use the Y%COMP equation in your HP Financial Calculator to calculate the twelve month
spot interest rate: D1 = 182, B = 360, D2 = 183, D3 = 0, D4 = 0, D5 = 0, Y%1 = 0.0130, Y%2 =
0.0132, Y%3, Y%4 and Y%5 need not to be filled in. Solve for Y%COMP.
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the money market
3.6 Money market benchmarks
Each day, about 40 of the major banks from the Euro money market – the so-called
panel banks – set a EURIBOR (Euro Interbank Offered Rate) for specific periods up
until one year. Each of the panel banks forwards the rates that it has observed in the
market to the European Money Markets Institute (EMMI). This is a European umbrella organization formed by national associations representing banking national
interests. The EURIBOR rates are set each day at 11.00 for 1, 2 weeks and 1, 2, 3, 6,
9, 12 months. The EMMI calculates the EURIBOR rates for each separate period by
calculating the average of the rates forwarded by the panel banks where the lowest
and the highest three rates are excluded from the calculation. In setting the rates,
the panel banks themselves base their own rates on the interest rates of the European Central Bank (ECB) and on their expectations about changes in the ECB interest rates for the coming year. During the credit crisis, they also included a liquidity
premium in the rates they communicated.
In addition, a benchmark rate for the overnight rate is determined each day - the
EONIA (European overnight index average). The EONIA is set at 18.00. At the end
of each trading day, the same 40 banks that form the Euribor panel forward all data
about deposits made with a term of one day that they have concluded with other
banks on the past trading day. The EMMI calculates the average rate for all these
transactions weighted according to size.
Both the EURIBOR and the EONIA rates concern loans (deposits) without collateral. In addition to EURIBOR, the EMMI also sets the EUREPO index and the EONIA
SWAP INDEX based on data from the same panel banks. The EUREPO index is an index of rates for interbank repos (collateralized lending). The EONIA SWAP INDEX is
an index that indicates the rates banks use when they conclude EONIA swaps.
The credit exposure for repos and for EONIA swaps is much lower than that for a
regular deposit. Ater all, with a deposit, the bank that lends out the money can lose
the entire principal while, with a repo, they may keep the collateral and, with an
EONIA swap, they can only lose a net interest amount. Under normal market conditions, the EUREPO rates and the EONIA SWAP INDEX will not differ much from
the EURIBOR rates. The exposure for (unsecured) deposits is indeed greater but the
chance that a bank does not repay a deposit is small under normal market circumstances. During the credit crisis between 2007 and 2009, however, big differences
did appear between the EURIBOR rates, on the one hand, and the EUREPO rates and
the EONIA SWAP INDEX rates on the other hand. The reason for this was that during this period banks no longer trusted each other and demanded a considerable
credit spread for uncollateralised deposits.
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In a similar way, each day at 11.00 AM the British Bankers Association sets reference rates for five different money markets: the LIBOR or London Interbank Offered
Rate. For each of these five currencies a separate panel has been set up consisting
of at least eight banks that play an important role in the money market for the currency in question. Furthermore, when selecting the panel, the BBA also considers
reputation and knowledge of the banks.
The table below shows the ten currencies for which a LIBOR is fixed.
currencyiso-code
Pound sterling
GBP
US dollar
USD
Japanese yen
JPY
Swiss franc
CHF
EuroEUR
EURIBOR, EONIA and LIBORs are benchmarks. Amongst other things, they are
used as the reference for fixing the interest rate for financial instruments with a
floating interest rate condition. Furthermore, they are used as historical material to
show the development of money market interest rates over time.
However, the rates are not tradable – banks are not obliged to use them when concluding transactions. Each bank has its own money market rates which it publishes via data suppliers such as Thomson Reuters. Unlike the benchmark rates, these
rates fluctuate constantly during the course of a trading day.
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Chapter 4
Foreign Exchange
The foreign exchange market (FX market) is the market on which different currencies are traded against one another. The rate at which this happens is called the
exchange rate or FX rate. Various instruments are used on the FX market, including FX spot transactions, FX forwards, and FX swaps. All of these instruments are
­traded over-the-counter.
4.1
FX spot rates
With most FX transactions, the currencies are traded at the current market exchange rate and settlement takes place on a standard delivery date, usually two
business days after the transaction date. These transactions are called FX spot transactions. The current market exchange rate is called the FX spot rate.
For certain currency pairs, the settlement of spot transactions takes place after only
one business day. This is the case, for instance, for currency transactions between
US and Canadian dollars. Sometimes the value date for one currency is different
from that of another currency. This may be the case, for instance, when a currency
from an Islamic nation is traded for a currency in a Western country and the delivery date is near the weekend.
4.1.1 Exchange rates
The exchange rate between two currencies is given by using an FX quotation. An
exchange rate expresses the value ratio between two currencies as a number. The
currency mentioned first in an FX quotation is called the trade currency or base currency (the traded good) and the second currency is called the counter currency or
quoted currency (the currency in which the price of the base currency is expressed).
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In FX quotations, currencies are expressed by their ISO-codes. ISO stands for International Standardization Organization. Figure 4.1 shows a table with the ISO-codes
of some of the most important currencies.
Figure 4.1 ISO Currency codes
currencyiso-code
EuroEUR
US-dollarUSD
Pound sterling
GBP
Japanese yen
JPY
Canadian dollar
CAD
Australian dollar
AUD
New-Zealand dollar
NZD
Hong Kong dollar
HKD
Singapore dollar
SGD
Koran won
KRW
Danish krona
DKK
Swedish krona
SEK
Norwegian krona
NOK
Swiss franc
CHF
South African rand
ZAR
Mexican peso
MXN
Israeli shekel
ILS
There are international conventions regarding which currency is the base currency
and which is the price currency in an FX quotation. The euro is always quoted as the
base currency against other currencies: EUR/USD, EUR/GBP, EUR/JPY, EUR/CHF etc.
The British pound and the other currencies of the Commonwealth are base currency in all exchange rate quotations except in those cases where the euro is the counter currency. The US dollar is the base currency in most exchange rate quotations
with the exception of euro and the currencies of the Commonwealth:
USD/JPY; USD/CHF; USD/CNY, however,
EUR/USD; GBP/USD; AUD/USD.
Exchange rate quotations for which these rules are properly applied, are referred to
as direct quoted FX rates. If these rules are not applied, for instance in the case of
GBP/EUR, the quotation is called an indirect quoted FX rate.
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foreign exchange
4.1.2
Bid rate, ask rate and two way prices
In most exchange rate quotations, one unit of a currency is expressed in a number
of units of another currency. For example, when the EUR/USD spot rate is 1.5000
then this means that 1 Euro has the same value as 1.5000 US dollars.
example
On 12 October 2009, the euro-dollar trader at ING Bank buys 10 million euros at spot
from the euro-dollar trader at Deutsche Bank. The spot rate is 1.3425.
On 14 October 2009 (= spot value date), ING Bank must transfer an amount of USD
13,425,000 to Deutsche Bank. Deutsche Bank must, in turn, transfer an amount of
EUR 10,000,000 to ING.
Just as with all prices in the financial markets, there are bid and ask rates for the FX
spot rate. These two prices together are called a two-way price. The difference between the bid and ask rate is called the spread.
For example, when a market maker quotes the following two-way prices for EUR/
USD: 1.3530 - 1.3532, this means that he is prepared to buy 1 euro for 1.3530 US dollars and to sell 1 euro for 1.3532 US dollars. The table below contains the amounts
that this market maker is willing to exchange for an amount of EUR 10,000,000
and for an amount of USD 10,000,000.
action market taker bid/ask
spot rate
action market maker
eur/usd
sell EUR 10 mio
bid
1.3530
sell USD 10 mio x 1.3530 = USD 13,530,000
buy EUR 10 mio
ask
1.3532
buy USD 10 mio x 1.3532 = USD 13,532,000
sell USD 10 mio
ask
1.3532
buy EUR 10 mio / 1.3532 = EUR 7,389,891
buy USD 10 mio
bid
1.3530
sell EUR 10 mio / 1.3530 = EUR 7,390,983
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guide to treasury in banking
Figure 4.2 shows a Thomson Reuters page with the FX spot rates of the contributing
banks.
Figure 4.2 4.1.3
FX spot quotations
Big figure and points/pips
Currency traders know fairly precisely what the level of an exchange rate is. When
they quote each other a price, it is therefore not necessary to supply all the digits for
an exchange rate. Generally they limit themselves to the last two digits. These digits are called the points or pips of an exchange rate. The remaining digits are called
the ‘big figure’. For example, for a USD/CHF FX spot rate of 1.2389 - 1.2391, 1.23 (really only the ‘3’) is the big figure and there are 89 pips for the bid rate and 91 pips for
the ask rate. A market maker would then only quote: 89-91. If, later, the USD/CHF
two-way FX rate is 1.2398 - 1.2400, he will then quote 98-00 and calls this 98 ‘to the
figure’. For a USD/JPY spot rate of 82.45, for instance, the big figure is 82 and the
number of pips is 45.
Currency traders often express the risk in their position as a value of one point. The
value of one point indicates how much the value of an FX position changes if the FX
spot rate changes by 1 pip/point.
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foreign exchange
4.1.4 Cross rates
Not every currency pair is traded as often as others. Mexican pesos, for example, are
commonly traded against US dollars but much less frequently against euros. There
is therefore an interbank market for USD/MXN but not for EUR/MXN. If a client
wants to conclude an FX spot transaction with a bank in EUR/MXN, the bank will
need to conclude two spot transactions on the interbank market in order to offset
this transaction – one in EUR/USD and one in USD/MXN. The exchange rates for
currency pairs that are not directly traded are called cross rates. They are calculated
by using the FX rates for standard currency pairs in which the bank concludes the
transactions to offset the transaction.
In order to calculate cross rates, it is easiest to consider the rates as mathematical
expressions. Thus, for instance, EUR/USD expresses 1 euro divided by ‘x’ US dollars.
And USD/MXN expresses 1 US dollar divided by ‘x’ Mexican pesos.
The EUR/MXN cross rate can then be calculated as the following mathematical
product: EUR/USD x USD/MXN. In this mathematical product, USD appears once
above the line and once below the line and is thus cancelled out.
Suppose that the two-way FX spot rates for EUR/USD and USD/MXN are as follows:
bidask
EUR/USD1.3550
1.3552
USD/MXN13.15
13.17
To determine whether we must use the bid rate or the ask rate from the two relevant
currency pairs, we apply some straightforward reasoning: the bid rate is low and
the ask rate high. This practical idea can always be used as a rule of thumb to avoid
complicated reasoning.
This straightforward reasoning leads to the following conclusion:
–
–
The bid rate for EUR/MXN is calculated by using the bid rate for EUR/USD
and the bid rate for USD/MXN, therefore, bid rate EUR/MXN = 1.3550 x
13.15 = 17.82.
The ask rate for EUR/MXN is calculated by using the ask rate for EUR/USD
and the ask rate for USD/MXN, therefore, ask rate EUR/MXN =
1.3552 x 13.17 = 17.85.
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The question of whether the bid or ask rates must be used, can also be reasoned out
by considering the actions that the bank needs to take to offset its position. If a market user requests a EUR/MXN bid rate, this means that he wants to sell euros to the
bank against Mexican pesos. The bank must first sell these euros against US dollars.
Since the bank now acts as a market user, he will get the EUR/USD bid rate. Next,
the bank must sell the US dollars against pesos. The bank acts once again as a market user and gets the USD/MXN bid rate.
the cross currency is the base currency in both fx quotations
CHF/NOK is traded via EUR/CHF and EUR/NOK. Here,the base currency for both
the currency pairs is the same. The cross rate CHF/NOK is calculated by dividing the
EUR/NOK rate by the EUR/CHF rate:
EUR ⁄ NOK
CHF ⁄ NOK = -------------------EUR ⁄ CHF
In this equation, EUR, which is the ‘cross currency’ can be found once under the
(horizontal) line and once above the (horizontal) line and is thus cancelled out. The
NOK appears once under a (diagonal) line and remains there (as a denominator).
The CHF appears twice under a line: once under the horizontal line and once under
a diagonal line. Mathematically, this places CHF above the line (as a numerator).
Suppose that the two-way FX spot rates EUR/CHF and EUR/NOK are as follows:
bidask
EUR/NOK8.8100
8.8150
EUR/CHF1.5169
1.5171
To determine whether the bid or ask rates must be used, the rule of thumb is once
again applied: the bid rate is low and the ask rate is high, thus
EUR ⁄ NOK bid
8.8100
CHF ⁄ NOK bid = -------------------------- = ------------- = 5.8071
EUR ⁄ CHF ask
1.5171
and
EUR ⁄ NOK ask
8.8150
CHF ⁄ NOK ask = -------------------------- = ------------- = 5.8112
EUR ⁄ CHF bid
1.5169
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foreign exchange
The question of whether the bid or ask rates must be used, can again also be reasoned out by considering the actions that the bank needs to take to offset its position. If a client requests a CHF/NOK bid rate, this means he wants to sell Swiss
francs to the bank against Norwegian crowns. The bank must now first sell these
Swiss francs against euro; the bank must therefore buy euro. Because the bank is
acting here as a market user, it gets the EUR/CHF ask rate. After this, the bank must
sell the euro against Norwegian crowns. The bank is once again a market user and
gets the EUR/NOK bid rate.
4.1.5
Spot trading positions
Traders with banks take positions in foreign exchange. They take a long position
in one currency if they expect that the FX rates will move in favour of this currency
and take a short position if they have the opposite view. Normally, a trader’s position is the result of a number of different transactions. In order to calculate the average price of an FX position, the following equation can be used21:
Average rate = Σ ( pi x ri) / Σ pi
Where
pi
= number of trade currency bought or sold in transaction ‘i’
ri
= price of transaction ‘i’
example
A trader has concluded the following transactions:
Purchase of 5,000,000 euro against US-dollars: FX rate: 1.3500
Sale of 3,000,000 euro against US-dollars: FX rate 1.3520
Purchase of 4,000,000 euro against US-dollars: FX rate: 1.3485
The overall position of this trader is 6,000,000 long euro and the average rate of this
position is
Average rate = (5,000,000 x 1.3500 - 3,000,000 x 1.3520 + 4,000,000 x 1.3485) /
(5,000,000 - 3,000,000 + 4,000,000) = 1.3480
21 The equation to calculate the average price of an FX position should be entered in a HP
Financial Calculator as follows: AVRATE = (P1xR1+P2xR2+P3xR3) / (P1+P2+P3)
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guide to treasury in banking
All trading positions are valued on a daily basis. For this purpose, valuation rates
are used that are imported from the systems of data suppliers such as Thomson
Reuters. The value of a position is calculated by comparing the average rate of the
position with the valuation rate. The value of a spot position can be calculated by
using the following equation:22
Position value = (rv - Σ ( pi x ri) / Σ pi) x Σ pi
In this equation, rv is the rate used for valuation.
example
The end of day FX spot rate used for valuation is 1.3524. The value of the above FX position can be calculated as23:
Position value = (1.3524 - 1.3480) x (5,000,000 - 3,000,000 + 4,000,000) =
USD 26,400
4.2 FX forward
An FX forward contract, also known as an FX outright contract, is a contract in
which two parties enter into a reciprocal obligation to exchange a certain amount of
a currency at a certain period in the future for a predetermined amount in another
currency. The rate that is used is called the FX forward rate. The FX forward rate is
largely based on the FX spot rate.
Because settlement only takes place after some time in the case of an FX forward,
the FX spot rate is adjusted. The level of the adjustment is based on the difference in
the interest rates for the two currencies involved and is represented by using swap
points. One swap point for EUR/USD, for instance, is equal to 0.0001. Swap points
are the translation of a difference in interest rates between two currencies into the
difference between the FX spot rate and the FX forward rate.
22 The equation to calculate the value of an FX position should be entered in a HP Financial Calculator as follows: POSVAL = (RVAL – (P1xR1+P2xR2+P3xR3) / (P1+P2+P3)) x
(P1+P2+P3)
23 Use the POSVAL equation in your HP Financial Calculator to calculate the value of the
position. RVAL = 1.3524, P1 = 5,000,000, R1 = 1.3500, P2 = -3,000,000, R2 = 1.3520, P3 =
4,000,000, R3 = 1.3485. Solve for POSVAL.
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example
An ING Bank euro-dollar trader concludes an FX forward with the Deutsche Bank
euro-dollar trader on 12 May, 2013 and buys 10,000,000 euro for US dollars with the
delivery date being 14 May, 2014 (one year after the spot date). The EUR/USD cash
rate is 1.3475 and the swap points amount to -130. The EUR/USD FX forward rate is
thus 1.3345.
On 14 May, 2014 ING Bank must transfer an amount of 13,345,000 US dollars to
Deutsche Bank and Deutsche Bank must transfer an amount of 10,000,000 euros
to ING Bank.
4.2.1 Theoretical calculation of an FX forward rate
The FX forward rate can theoretically be calculated by calculating the future values
of one unit of the trade currency and of the corresponding amount of units of the
quoted currency, both on the forward delivery date. The future value in the quoted
currency should then be divided by the future value in the trade currency.
In figure 4.3 the FX forward rate is theoretically calculated for a EUR/USD FX forward contract with a term of 91 days. The FX spot rate EUR/USD is 1.2500, the three
months euro interest rate is 2% and the three month US dollar interest rate is 1%.
Figure 4.3 Theoretical calculation of the three month forward rate EUR/USD
The future value of 1.2500 USD (quoted currency) after three months is:
Future value of USD 1.2500 = 1.2500 ×  1 + --91
---- × 0.01 = USD 1.25316

360
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guide to treasury in banking
The future value of one euro (base currency) after three months is:
Future value of EUR 1 = 1 ×  1 + --91
---- × 0.02 = EUR1.005056

360
The theoretical FX forward rate is calculated by dividing the future value in the
quoted currency by the future value in the trade currency:
1.25316
Forward FX rate = ----------------- = 1.246856
1.005056
The general equation to theoretically calculate an FX forward rate is24:
In this equation rq is the interest rate of the quoted currency and rb is the interest
rate of the base currency, both for the term of the FX forward contract.
In the above example, the FX forward rate is EUR/USD 1.2469 (rounded) where the
FX spot rate is EUR/USD 1.2500. The difference between the FX forward rate and the
FX spot rate is -0.0031, or 31 swap points.
4.2.2 Swap points, premium and discount
If the FX spot rate and the swap points are given, the FX forward rate can be calculated by adding or subtracting the swap points to or from the FX spot rate. The question is whether the swap points should be added to or subtracted from the FX spot
rate. This depends on whether the in­terest rate for the base currency is higher or
lower than that for the quoted currency.
Depending on the differences in interest rates between the currencies, there are three
possibilities:
–
the interest rate for the base currency is lower than that for the quoted
currency: The forward rate is then higher than the spot rate. The base
currency is said to trade at a premium
24 The equation to calculate an FX forward rate should be entered as follows in a HP Financial Calculator: FXFW = SPOT x (1+D/BQ x Y%Q ) / (1+D/BB x Y%B)
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foreign exchange
–
–
the interest rate for the base currency is higher than that for the quoted
currency. The forward rate is lower than the spot rate. The base currency is
said to trade at a discount
the interest rates of both relevant currencies are equal. The forward rate is
the same as the spot rate and this is called parity.
If only the swap points are known and not the interest rates, the method of quotation can be used to determine whether there is a premium or discount. Just as with
any other price, there are bid and ask rates for swap points. For example:
eur/usdbid
ask
1 month
18
20
2 months
28
30
3 months
40
42
6 months
70
72
9 months
104
106
12 months
128
130
In the table above, the bid rates for the swap points are lower than the ask rates. In
this case, there is a premium and the swap points must be added to the FX spot rate.
For a forward bid rate, the bid rate for the swap points must be added to the bid rate
for the FX spot rate. And for a forward ask rate, the ask rate for the swap points must
be added to the ask rate for the FX spot rate.
If the two-way FX spot rate is, for example, 1.2500 - 1.2502, the following FX forward
rates apply.
eur/usdbid
ask
1 month
1.2518
1.2522
(1.2500 + 0.0018)
(1.2502 + 0.0020)
2 months
1.2528
1.2532
3 months
1.2540
1.2544
6 months
1.2570
1.2574
9 months
1.2604
1.2608
12 months
1.2628
1.2632
Figure 4.4 indicates that, in the case of a premium, the FX forward rate is higher the
further into the future the value date lies.
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Figure 4.4 FX forward rates when the base currency trades at a premium
Sometimes, the bid rates of the swap points are higher than the ask rates. This is
shown in the table below.
eur/jpybid
ask
1 month
16
14
3 months
40
38
12 months
128
124
If this is the case, there is a discount and the swap points must be subtracted from
the FX spot rate. Bid points must be subtracted from the FX spot bid rate and ask
points must be subtracted from the FX spot ask rate.
If the two-way FX spot rate is, for example, 140.50 - 140.52, the following FX forward
rates apply.
eur/jpybid
ask
1 month
140.34
1.4038
(140.50 - 0.16)
(140.52- 0.14)
3 months
140.10
140.14
12 months
139.22
139.28
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Figure 4.5 indicates that, in the case of a discount, the FX forward rate is lower the
further into the future the value date lies.
Figure 4.5 FX forward rates when the base currency trades at a discount
4.2.3 Forward value dates and corresponding FX forward rates
FX forwards are over-the-counter traded instruments. This means that they can be
concluded for any amount and for any period. However, the FX swap points are normally only set for the standard periods: 1, 2, 3, 6 and 12 months. When determining
the dates for these standard periods, the modified following convention is used. If
the spot date is an ultimo date then the end-of-month convention is applicable for
the standard periods.
As an example, the maturity dates for the regular periods based on the modified following convention for trading day 15/4/2009 are shown below.
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perioddate
day
remark
spot
17/4/2013Fri
1 month
18/5/2013
Mon
2 months
17/6/2013
Wed
3 months
17/7/2013
Fri
6 months
19/10/2013
Mon
17/10 is Saturday
12 months
19/4/2014
Mon
17/4 is Saturday
17/5 is Sunday
As an another example, the EOM dates for trading day 28 April 2009 are shown in
the following table.
period
value date
day
remark
spot
30/4/2013Thu
1 month
29/5/2013
Fri
2 months
30/6/2013
Tue
3 months
31/7/2013
Fri
31/7 is last business day
6 months
30/10/2013
Fri
31/10 is Saturday
12 months
30/4/2014
Fri
31/5 is Sunday
In reality, however, it frequently happens that the value date for an FX forward contract does not fall exactly on a standard date. Such a date is called a broken date or
cock date. To determine the number of FX swap points that belong to a particular
value date, interpolation is used. For this purpose, the following equation can be
used:
fp b = fp s + daycount fraction broken period × ( fp l – fp s )
In this equation
fpb = swap points broken period;
fps = swap points for the adjacent standard period that is shorter than the broken period;
fpl = swap points for the adjacent standard period that is longer than the broken period.
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The EUR/USD swap points for spot 15/1/2013 are given below:
period
value date
# days
forward points
bid
ask
1 month
16-2-2013
32
5
8
2 months
16-3-2013
601013
3 months
15-4-2013
901720
6 months
15-7-2013
181
51
54
12 months
15-1-2014
365125130
If a market user wants to conclude an FX forward in which he sells US dollars
against euro on 8 April 2009, the swap points are calculated as follows:
fpb = 13 + 23/30 × ( 20 – 13 ) = 13 + 5.37 = 19 (rounded upwards)
As a market user he is buying the euro and, therefore, he gets the ask rate for the
swap points. The value date, 8 April, lies between the regular periods of two months
(16 March) and three months (15 April). As a starting point for the above calculation
the swap points for 8 April are taken: 13 swap points.
Next, the daycount fraction is calculated for the period from 16 March to 8 April.
The number of interest days for this period is 23 and the number of days for the
whole month is 30. The day count fraction is thus 23/30. This daycount fraction is
then applied to the difference between the swap points for the regular three month
period and the regular two month period (20 - 13 = 7). The outcome (23/30 x 7 = 5.37)
is then added to the swap points for the adjacent shorter period: 13 + 5.37 = 18.37.
Since it is an ask rate and there is a premium, the market maker will round this outcome upwards.
Figure 4.6 shows a Thomson Reuters screen with the regular forwards points for
EUR/CHF. At the bottom of the screen, a tool for calculating forwards points for broken dates is added.
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guide to treasury in banking
Figure 4.6 Forward points for regular and broken dates
4.2.4 FX forward cross rates
To calculate FX forward cross rates, the following steps must be undertaken:
1. Determine the way in which the FX spot cross rate would have been calculated.
2. Apply this calculation method to the FX forward rates of the regular
currency pairs
A trader is asked to give his FX forward bid rate for EUR/MXN when the following
rates apply:
spot rate
bid
ask
EUR/USD1.3550
1.3552
USD/MXN13.15
13.17
and
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1 month
bid
ask
swap rate
EUR/USD0.0012
0.0010
USD/MXN0.10
0.20
1. The FX spot bid rate for EUR/MXN would have been calculated by multiplying the spot bid rate EUR/USD by the spot bid rate USD/MXN.
2. The FX forward cross rate is calculated in the same way - thus by multiplying the FX forward bid rate EUR/USD by the FX forward bid rate USD/MXN.
FX forward bid rate EUR/USD = 1.3538 (discount)
FX forward bid rate USD/MXN = 13.25(premium)
FX forward bid rate EUR/MXN = 1.3538 x 13.25 = 17.94
As a second example, we will calculate an FX forward ask price for CHF/NOK when
the following prices are known:
bidask
EUR/NOK8.8100
8.8150
EUR/CHF1.5169
1.5171
and
6 month
bid
ask
swap rate
EUR/NOK0.44
0.45
EUR/CHF0.0015
0.0013
1. The FX spot ask rate CHF/NOK would have been calculated by dividing the
FX spot ask rate EUR/NOK by the FX spot bid rate EUR/CHF.
2. The forward cross rate is calculated in the same way – thus by dividing the
FX forward ask rate EUR/NOK by the FX forward bid rate EUR/CHF.
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FX forward ask rate EUR/NOK = 9.2650 (premium)
FX forward bid rate EUR/CHF = 1.5154 (discount)
FX forward ask rate CHF/NOK = 9.2650/ 1.5154 = 6.1139.
4.2.5 Value tomorrow and value today FX rates
Sometimes, the delivery for an FX transaction takes place on a date before the spot
date; on the trading day itself (value today) or on the next trading day (value tomorrow). These dates are called ex ante dates. Settlement value tomorrow is always possible while settlement value today is only possible if the payment systems of the
central banks of the relevant currencies are still operational on the trade date.
A EUR/USD FX transaction concluded by a dealer in Europe can, in principle, be
settled same day value. However, the transaction must be concluded before the
TARGET2 cut-off time. TARGET2 is the euro inter-bank payment system. If the
transaction must be settled via the CLS Bank, however, settlement same day value
is no longer possible. This is because transactions that are settled value today via
the CLS Bank, must be adviced to the CLS Bank before 6.30 am CET. A EUR/JPY FX
transaction concluded between a German dealer and a US dealer can never be settled same day value. After all, the Japanese Central Bank closes at 07.00 CET.
A USD/MXN FX transaction can be settled same day value by a bank in the euro
area or in the UK. Both the United States and Mexico are in a later time zone which
leaves plenty of time for sending settlement instructions. Settlement via the CSL
Bank is, however, still not possible because, in that case, the transaction must once
again be delivered before 7.00 am.
Just as for FX forward contracts, the FX rates for value today or value tomorrow FX
transactions differ from the FX spot rates. Swap points are also used with these
transactions and thus discount and premiums apply.
ex ante rates in the case of discount
In case of a discount, the FX rate is lower the further into the future a value date lies.
This also applies for ex ante value dates. In the case of a discount, the FX rates for ex
ante value dates are higher than the FX spot rate. After all, the spot date is further
into the future than the ex ante date, i.e. today or tomorrow. This is shown in figure
4.7.
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Figure 4.7 FX rates before the spot when the base currency is trading at a discount
For a discount, a two-way price for value tomorrow (tom/next points) is, for example, 5 - 4. For an ex ante FX rate value tomorrow, these swap points must be added to
the FX spot rate. Following the rule that a bid rate must always be as low as possible,
the lowest number of points (4) must be added to the FX spot bid rate. And since an
ask rate must be as high as possible, in order to calculate the value tomorrow ask
rate the highest number of points (5) must be added to the FX spot ask rate.
example
The two way spot rate GBP/USD is 1.2500 - 1.2502 and the two way price for tom/
next points is 3 - 2.5.
The indirect quotation indicates that the GBP is trading at a discount.
The FX bid rate GBP/USD value tomorrow is 1.2500 + 2.5 = 1.25025.
The FX ask rate GBP/USD value tomorrow is 1.2502 + 3 = 1.2505.
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For an FX rate value today, a quotation is required for both the tom/next swap points
and the overnight swap points. Such a quotation is given below:
forward points
bidask
tom/next swap
3
2.5
overnight swap
2
1.5
total5
4
For a GBP/USD spot rate of 1.2500, the overnight bid rate GBP/USD is 1.2500 +
0.0004 = 1.2504 and the overnight ask rate is 1.2502 + 0.0005 = 1.2507.
ex ante rates in the case of premium
A premium can be recognised by a ‘normal’ quotation. This rule is applied consistently for ex ante dates. If there is a premium, this means that the FX rate is higher
the further into the future a value date lies. This also applies to value dates for the
spot; for a premium, the FX rates for value dates before the spot are lower than the
FX spot rate. This is shown in the figure 4.8 below.
Figure 4.8 92
FX rates before the spot when the base currency is trading at a discount
foreign exchange
For a quote for the tom/next swap points of , for example, 0.5 - 1, the value tomorrow rates are thus lower than the FX spot rate. If the two way spot rate is 1.3500 1.3502 then the FX bid rate EUR/USD value tomorrow is 1.3500 - 1.0 = 1.3499 and the
FX ask rate EUR/USD value tomorrow is 1.3502 - 0.5 = 1.35015.
For an FX rate value today, a quote is needed for both the FX swap points tom/next
and for the overnight FX swap points:
forward points
bidask
overnight swap
0.75
1.25
tom/next swap
0.5
1
total1.25 2.25
For a two way price for FX spot EUR/USD of 1.3500 - 1.3502, the overnight bid rate
would be EUR/USD 1.3500 - 0.000225 = 1.349775 and the overnight ask rate 1.3502 0.000125 = 1.350075.
4.2.6 Time option forward contracts
A variant of the FX forward contract is a time option forward contract or delivery
option contract. This is an FX forward contract where the customer may choose,
within a specific period – the underlying period – when the settlement must take
place. This period can come into effect on the spot date or at a specific moment in
the future. The length of the underlying period is generally limited, e.g. up to three
months. If, on the maturity date, the full amount of the contract still has not been
settled, a close out takes place via a reverse spot transaction, an offsetting transaction, or the contract is rolled over by means of an FX swap.
The FX rate for a time option forward contract is the, for the customer, least favourable of the FX forward rates for the start date of the underlying period and the FX
forward rate for the end date of the underlying period.
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guide to treasury in banking
example
A client concludes a time option forward contract in which, for the period between
six and twelve months, he must purchase a total amount of EUR 50 million against a
pre-determined rate.
At the moment when the contract is concluded, the following FX forward rates for
EUR/USD apply:
Six month FX forward ask rate EUR/USD: 1.4590
Twelve month FX forward ask rate EUR/USD: 1.4520
The bank sets the contract rate at 1.4590.
If, after twelve months, the client has only used the time option forward contract to
purchase 40 million euro, he must now either perform a close out FX spot transaction in which he sells 10 million euro at spot against the applicable spot rate or he
must conclude an FX swap in which he sells 10 million euro per spot and buys them
back on a later date against the current FX forward rate.
4.2.7
Offsetting FX forwards
Sometimes, an import or export transaction is cancelled. If a company has entered
into an FX forward contract to fix the FX rate for the payment in foreign currency
related to this transaction, this FX forward contract will be superfluous. The company will then probably want to undo the FX forward. This can be done by concluding a reverse FX forward for the same amount and with the same value date. This is
called closing out or offsetting the FX forward contract. In contrast to stock market
transactions, where offsetting leads to the unwinding of the original contract, the
two opposing FX forward contracts continue, in principle, to co-exist.
example
A French company has concluded an import contract with an American supplier
for a value of USD 2 million. The expected payment date is 10 October. In order to
hedge the FX risk, the importer has concluded an FX forward contract with its bank
in which he buys the US dollars against a EUR/USD forward rate of 1.5200. On 8 September, the importer hears that the supplier has gone bankrupt and that the delivery
will therefore not take place. The payment of USD 2 million on 10 October will therefore also not take place.
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foreign exchange
Since the importer has already entered into an obligation to purchase the US dollars
from the bank, he now has an unwanted long position in US dollars. To close this
long position, the importer must conclude a reverse FX forward contract in which it
sells USD 2 million value 10 October.
Suppose that on 8 September, the EUR/USD spot rate is 1.5385 and the one month
premium is 0.0015. The one-month FX forward rate is therefore 1.5400.
With the settlement of the two FX forward contracts on 10 October, the following
transfers are carried out in the bank accounts of the importer:
USD account: debit 2,000,000 and credit 2,000,000
Euro account: debit 1,315,789.47 (2,000,000 / 1.5200)
and credit 1,298,701.30 (2,000,000 / 1.5400)
On balance, the two transactions result in the debiting of the euro account of the importer with an amount of EUR 17,088.17.
4.2.8
Valuation of an FX forward contract
An FX forward contract is valued first by calculating the individual present values
of the two future cash flows using the current market in­terest rates, after which the
present value for the foreign currency is converted at the prevailing FX spot rate to a
present value in the local currency. Finally, the balance of the two opposing present
values is calculated.
example
The cash flows on 10 October of the FX forward contract in the previous example are
USD 2,000,000 and EUR 1,315,789.47. On 8 September, the one month EURIBOR is
2.00% and the one month USD LIBOR is 3.17%. The present values of the two cash
flows can be calculated as follows:
EUR 1,315,789.47 / ( 1 + 30/360 x 0.02) = EUR 1,313,600.14 negative
USD 2,000,000 / ( 1 + 30/360 x 0.0317) = USD 1,994,730.59 positive
Converted against the FX spot rate of 1.5385, the counter value of the US dollar cash
flow in euro is USD 1,994,730.59 / 1.5385 = EUR 1,296,542.47.
The value of the FX forward contract is thus EUR 1,296,542.47 -/- EUR 1,313,600.14 =
-/- EUR 17,057.67.
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guide to treasury in banking
4.2.9 Theoretical hedge of an FX forward via FX spot and deposits
In the inter-bank market, FX forward transactions are not commonly concluded. This
means that a bank that has concluded an FX forward transaction with a client usually
cannot offset it directly with another bank via a reverse FX forward transaction.
If, for instance, a British bank concludes an FX forward with a client in which, in 3
months, the bank will sell an amount of EUR 10 million against US dollars with an
FX forward rate of EUR/USD 1.2469, this bank now has a short position in euros. To
offset this short position, the bank must buy an amount of EUR 10 million per spot
against an FX spot rate of, for instance, 1.2500. The FX position of the bank is now
closed. After all, the bank has purchased an amount of EUR 10 million and sold an
amount of EUR 10 million and both the ‘purchase price’ and the ‘selling price’ for
the euros are fixed.
However, a new issue arises. The bank now has a liquidity position in both currencies. It will receive an amount of 10 million euro per spot that does not need to be
transferred to the client’s account until after three months. Thus, it has temporary
excess liquidity in euro. Furthermore, the bank has a temporary liquidity shortage
in US dollars: on the spot date, it must deliver the US dollars to the market party
from which it purchased the euros, however, it will only receive the US dollars from
the client in three months’ time.
The bank can theoretically close the liquidity positions in both currencies by investing the euro in the money market for three months and simultaneously taking a US
dollar loan for three months. The costs and revenues associated with this will depend on the interest rate differential between euro and US dollars. In practice, however, the bank will not do this and it will offset the opposing liquidity positions by
using an FX swap.
4.3 FX swaps
An FX swap is an OTC FX derivative contract with a short term, in which two parties
enter into a reciprocal obligation to exchange a certain amount of two currencies
on the spot date at the FX spot rate and to reverse this exchange in the future at the
FX forward rate. The exchange at the beginning of the term is called the short leg or
near leg, the exchange at the end of the term is called the long leg or far leg.
If the first exchange of an FX swap normally takes place on the spot date, this exchange is also called the spot leg of the FX swap. The reverse exchange on the forward date is then called the forward leg.
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foreign exchange
For the price for the spot leg in an FX swap, the spot mid-rate is often taken. However, a market maker can choose the level of the spot rate in agreement with the
­client, as long as he stays within the bid-ask spread of the FX spot rate. In the example below, the mid rate is used.
example
A client wants to conclude an FX swap in which he sells 10 million euro per spot
against US-dollars and then, 1 month later, he wants to buy them back. The spot rate
is 1.2500 – 1.2504. The quote for the one month swap points is 18 – 20.
The bank now ‘buys and sells’ the euro in one month against US-dollars and uses
the following rates in this FX swap: 1.2502 and 1.2522. However, the following calculations of rates are also allowed for this transaction: 1.2500 – 1.2520 and 1.2504
– 1.2524.
A special form of FX swaps are so-called IMM swaps. These are FX swaps where the
maturity dates are the same as the maturity dates for IMM futures.
The ‘price’ of an FX swap where the first exchange takes place on the spot date
are the FX swap points that correspond with the contract period of the transaction.
eur/usdbid
ask
1 month
18
20
2 month
28
30
3 month
38
40
6 month
70
72
12 month
128
130
If a market maker buys the base currency in the forward leg (sells and buys the base
currency), he will use the bid rates of his swap points quotation. A market maker
uses his ask rate when he sells the base currency in the forward leg (buys and sells
the base currency).
points ‘my favour’ and points ‘against me’
If the market maker who has provided the above prices concludes an FX swap in
which he purchases the euros at spot and sells them for future delivery (buy and
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sell), for him the sale price is higher than the purchase price. This is because the
euro is trading at a premium. In jargon: the points are in his favour. This can also
be explained by looking at what is actually happening in this FX swap: the market
maker is in fact borrowing euro and is lending US-dollars for the term of the FX
swap. Because the euro is trading at a premium, this means that the euro interest
rates are lower than the US-dollar interest rates. The market maker, therefore, borrows at the lower interest rate and lends at the higher interest rate. This means he is
earning the interest rate differential. This is reflected in the fact that the points are
his ‘favour’.
example
As a market maker, an FX swap trader buys and sells euro against US-dollars in three
months at the prices in the above table. The current EUR/USD spot rate is 1.2500.
The position of the dealer is shown in figure 4.9 below.
Figure 4.9
In the picture it is clear that the points for the dealer are ‘in his favour’. After all,
at the maturity date he receives more US-dollars than he ‘invested’ at the start
date; USD 1,254,000, corresponding with an FX forward rate of 1.2540 versus USD
1,250,000 corresponding with an FX spot rate of 1.2500.
For the client in the above example, the points are said to be against him. After all,
he is borrowing US-dollars at a high interest rate and is lending euro at a lower interest rate.
theoretical calculation of swap points
As we have already seen, swap points can be considered as an interest rate differential expressed as a difference between the FX spot rate and the FX forward rate. This
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means that if we know the interest rates of the traded currencies, we should be able
to calculate the swap points theoretically. To find this ‘implied swap rate’, we can
use the following equation:25
Swap points =
– spot rate
To calculate the ask price for the three month FX swap points we need the 3 month
euro and 3 month US-dollar interest rates:
Euro:
US-dollar
2.00 - 2.05
3.22 - 3.27
(91 days)
(91 days)
We can determine whether we should take the bid or the ask side by again looking
at what is actually happening in the swap. The market maker in the previous example borrows euro and lends US-dollars. This means he will use his bid price for borrowing 3-month euro and his ask price for lending 3-month US-dollars in order to
calculate the swap points26:
3 months swap points = 1.2500 ( 1 + 91/360 x 0.0327) / ( 1 + 91/360 x 0.020) – 1.2500 =
0.0040
4.3.1 Unmatched principal swaps and matched principal swaps
In the inter-bank market, usually the nominal amounts differ for both currencies
in the spot leg and in the forward leg. The amounts that are exchanged in the spot
leg are typically equal to the present values of the amounts that are exchanged in
the forward leg. This is shown in figure 4.10 where in the near leg the principal
amounts are exchanged and in the far leg the principal amounts plus interest are
exchanged (i.e. EUR interest rate is 2% and USD interest rate is 4%).
25 The equation to calculate the swap points should be entered in a HP financial calculator
as follows: SWAP = SPOT x (1+D / BQ x Y%Q) / (1+D / BB x Y%B) – SPOT
26 Use the SWAP equation in your HP Financial calculator to calculate the swap points:
SPOT =1.2500, Y%Q = 0.0327, D = 91, BQ= 360, Y%B = 0.02, BB = 360. Solve for SWAP.
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Figure 4.10 Unmatched principal swap
EUR 10M
spot
Trader
Market User
rate = 1.2500
Market User
rate = 1.2562
USD 12,500,000
EUR 10,050,000
time
90d
Trader
USD 12,625,000
The reason that unmatched principal swaps are preferred by traders is that they
leave the trader with a closed FX position. The FX position of an FX swap trader
can be determined by adding the present values on the spot date of all (future) cash
flows as a result of his transactions. If we would do this for the unmatched FX swap
in figure 4.10, then it becomes clear that the FX swap does not result in an open FX
position. Both the NPVs in EUR and in USD are zero. This means that the trader is
not exposed to changes in the EUR/USD FX rate.
currency
period
cashflow
pv cash flow
pv calculation
EUR
Spot
- 10,000,000
- 10,000,000
90 days
+ 10,050,000
+ 10,000,000
10,050,000 /
(1 + 90/360 x 0.02)
EUR NPV
0
USD
Spot
+ 12,500,000
+ 12,500,000
90 days
- 12,625,000
- 12,500,000
12,625,000 /
(1 + 90/360 x 0.04)
0
USD NPV
This also means that for an unmatched principal FX swap, the spot rate that is used,
is not relevant, The convention, however, is to take the spot mid rate.
Clients of banks, however, prefer to have the principals in one of the currencies the
same in both legs. These type of swaps are referred to as matched principal swaps.
In the FX swap that is shown in figure 4.11 the nominal amounts in EUR are the
same in the near leg and in the far leg.
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Figure 4.11 Matched principal swap
EUR 10M
spot
Trader
Market User
spot: rate = 1.2500
USD 12,500,000
EUR 10M
time
90d
Trader
Market User
USD 12,562,000
T = 90d:
rate = 1.2562
Unlike unmatched principal swaps, matched principal swaps result in an open FX
position. This is shown in the table below. As a result of the FX swap, the trader
holds a short EUR position for an amount of 9,850,249 - 10,000,000 = 49,751 EUR
and a long USD position for an amount to 12,500,000 – 12,437,624 = USD 62,376.
currency
period
cashflow
present value
EUR
Spot
- 10,000,000
- 10,000,000
91 days
+ 10,000,000
+ 9,950,249
pv calculation
10,000,000 /
(1 + 90/360 x 0.02)
- 49,751
EUR NPV
USD
Spot
+ 12,500,000
+ 12,500,000
91 days
- 12,562,000
- 12,437,624
12,562,000 /
(1 + 90/360 x 0.04)
USD NPV
+ 62,376
Since by concluding a matched principal swap the trader is opening an FX position,
the choice of the spot FX rate is now very important. If the trader sells the base currency in the spot leg, then he is opening a short position in the base currency. This
is because the present value of the amount that is traded in the spot leg is always
greater than the present value of the same amount that is traded in the far leg. As
a consequence the trader has to use the ask rate of the spot quotation if he acts as a
market maker. If the trader buys the base currency is the spot leg, then he is opening a long position in the base currency and, therefore, he has to use the bid rate of
the spot quotation if he acts as a market maker.
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4.3.2 FX swaps out of today / out of tomorrow
FX swaps out of today / out of tomorrow are FX swaps where the first leg is before
the spot date and the second leg is after the spot date. For these FX swaps, the swap
points for the period before the spot date and for the forward period must be added.
The following quotations for swap points are given:
overnight0.5
1
tom/next0.75
1.25
3 months 25
28
6 months
45
50
Based on these prices, the swap points for a 3 month FX swap out of tomorrow are:
two-way price 3 months fx swap out of tomorrow
tom/next0.75
1.25
3 months 25
28
25.7529.25
And the swap points for a 6 month FX swap out of today are:
two-way price 6 months fx swap out of today
overnight0.5
1
tom/next0.75
1.25
6 months 45
50
46.2552.25
4.3.3 Overnight swaps and tom/next swaps
Often, market parties may want to conclude FX swaps for periods that fall entirely
before the spot date. An overnight swap (o/n swap) is an FX swap where the first leg
falls on the current trading day and the second leg on the next trading day. The first
leg of a tom/next swap (t/n swap) falls on the next trading day and the second leg on
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the spot date. It is easiest to take the FX spot mid rate for the first leg. The FX rate
for the second leg can then be determined in the normal way: with a premium, the
swap points are added to the first rate and, for a discount, they are subtracted.
example
The following quotes are given:
forward points
bidask
overnight swap
0.75
1.25
tom/next swap
0.5
1
total1.25 2.25
Here, the bid rates are lower than the ask rates. The trade currency therefore is trading at a premium. The FX rates for dates that lie further into the future are thus higher than those for earlier dates.
A market user who wants to conclude a tom/next swap in which he is buying euro
value tomorrow and selling them per spot will be quoted 1.5000 and 1.50005 respectively if the spot rate is 1.5000.
4.3.4 Hedging an FX forward via an FX spot and FX swap
A bank that concludes an FX forward contract, always hedges its currency position
via an opposing FX spot transaction. As we have seen, the bank can theoretically
cancel out the liquidity positions that originate from this combination of transactions by concluding two opposing deposits. However, in practice, it will use an FX
swap for this purpose.
If a bank, for instance, concludes a 3 month EUR/USD FX forward contract in which
it sells 10 million euro to a client, it will immediately conclude an FX spot transaction in which the bank itself purchases 10 million euro. It also concludes an FX
swap in which it sells and buys euro against US dollars for three months.
Suppose that the FX spot mid rate is 1.2502 and the quotation for the FX swap points
is 38 - 40. For the FX swap that the bank concludes in the market, it acts as market
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user. Since it is purchasing euro in the far leg, the bank is quoted the 3 month ask
rate for the swap points: 40. Figure 4.12 shows the FX forward transaction with the
­client, the reverse FX Spot deal and the FX swap that the bank has concluded to offset the FX forward contract.
Figure 4.12
4.3.5 Forward forward FX swap
A forward forward FX swap is an FX swap where the first leg takes place on a date
later than the spot date. Forward forward swaps are typically client transactions.
Corporate clients may want to use a forward forward swap to extend an FX forward
transaction with a value date that lies in the future. Banks hedge forward forward
swaps by concluding two opposite FX swaps. For instance, a three month forward
forward FX swap starting after six months is hedged by a six months FX swap and
an opposite nine months FX swap.
An FX forward forward bid rate is calculated by subtracting the ask rate of the short
term FX swap points from the bid rate for the longer term FX swap points. An FX
forward forward ask rate is calculated by subtracting the bid rate for the short term
FX swap points from the ask rate for the longer term FX swap points. Examples of
two-way prices for various forward forward swaps are shown in the table below:
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foreign exchange
eur/usdbid
ask
1 - 3 months
18
22
(38-20) (40-18)
3-6 months
30
34
(70-40)(72-38)
6-12 months
56
(128-72)(130-70)
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example
A client wants to conclude an FX swap in which he buys 10 million euro in one
month against USD and sells them 2 months later. He therefore has to sell and buy
EUR/USD in one month and buy and sell EUR/USD in three months.
The spot rate is quoted 1.2500 - 1.2504.
The one month swap points are quoted: 18 - 20
The three month swap points are quoted: 38 - 40
The rates employed in the FX swap are
1 month ask rate EUR/USD 1.2522 (1.2502 + 0.0020)
3 month bid rate EUR/USD 1.2540 (1.2502 + 0.0038).
The price for the forward forward swap is 18 points in favour of the client.
4.3.6 Arbitrage between the FX swap market and the money markets
When an organization has a funding requirement in its own currency, it can consider concluding a synthetic loan to lower its interest costs. This can be done.by
concluding a loan in another currency and by using an FX swap to convert the cash
flows from this loan into its own currency. In theory, this does not help the organization much; the interest rate differential between the loans in the two currencies
is after all included in the FX forward rate used in the far leg of the FX swap. This
is called the interest rate parity theorem. However, in practice, the implied interest differential in the FX swap points often differs slightly from the FX swap points
that should theoretically apply based on the differences between the money market
interest rates in the relevant currencies. This is because the money market works
differently than the market for FX swaps. In such cases, arbitrage opportunities can
arise. Making use of such opportunities is called covered interest arbitrage.
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example
A French organization wants to issue commercial paper with a term of 30 days. The
funding requirement is 8 million euro. The organization investigates whether it
would be more favourable to arrange the financing by means of a synthetic commercial paper via US dollars instead of euro.
The one month interest rate for commercial paper in euro is 3.6%. The one-month
US dollar interest rate for commercial paper is 5.6%, the EUR/USD FX spot rate is
1.2500 and the one month EUR/USD trades at a premium of 22 points.
The issue price of a commercial paper with a face value of USD 10 million can be calculated as follows:
USD 10 mio
price = ------------------------------------- = USD 9,953,550.10
1 + 30 ⁄ 360 × 0.056
Figure 4.13 shows the cash flows for the synthetic US dollar loan. The company sells
the US dollar proceeds of the CP issue in the spot leg of the swap at the spot rate of
1.2500 and receives a euro amount of 9,953,550.120 / 1.2500 = 7,962,840.08 euro. In
the far leg the company buys the face value of the CP issue from the bank at the forward rate of 1.2522 and pays 10,000,000 / 1.2522 = 7,985,944.74 euro.
Figure 4.13 Synthetic short term euro loan
The interest rate that the organization pays in the above strategy can be calculated
as follows:
Interest costs in euro = EUR 7,985,944.74 - EUR 7,962,840.08 = EUR 23,104.66.
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The interest costs as a percentage of the principal amount can be calculated as follows:
EUR 23,104.66 / EUR 7,962,840.08 * 100% = 0.00290%
Interest rate on annual basis: 0.00290 * 360/30 = 3.48%
(Note that the term was 30 days).
If the organization had issued commercial paper in euro, the interest rate would
have been 3.6%.
The arbitrage opportunity for the organization in the above example arises because
the FX swap points in the FX swap differ from the theoretical FX swap points that
can be calculated based on the interest rate differential between the euro and the
US-dollar. The following equation can be used to calculate the theoretical FX swap
points that correspond with the interest rate differential between the US dollar
commercial paper (5.60%) and the euro commercial paper (3.6%):
1.2500 ×  1 + --30
---- × 0.056

360
Forward points = FX forward - FX spot = --------------------------------------------------- – 1.2500 = 0.00208
1 + --30
---- × 0.036
360
The number of FX swap points according to the market is 22 while, theoretically,
they should be only 20.8. This is the reason for the above arbitrage opportunity. If
the FX swap points in the market had been lower than the theoretically calculated
FX swap points, arbitrage would not have been possible. In that case, the organization should have issued the commercial paper in euro or should have investigated
whether or not there was an arbitrage opportunity in another currency.
4.3.7 Rolling over FX spot positions by using tom/next swaps
A spot trader who wants to keep an open position must roll this over each day using an FX swap. The trader waits for the next trading day and then concludes a tom/
next swap. The reason for this is that a spot trader often waits to make the decision
on whether or not to take his position overnight until the end of the trading day.
If he then still wishes to conclude a spot/next swap, he would most probably get
a bad price. He therefore issues a stop loss order to one of his colleagues in a later
time zone and waits until the following morning when he will conclude a tom/next
swap.
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example
At the end of a trading day, a London FX trader holds a long GBP/USD position
against an average rate of 1.4490. He decides to roll over his position for a day. He issues a stop-loss order to his colleague in New York and goes home.
At the beginning of the next day, it turns out that the stop-loss order was not executed. He therefore concludes a tom/next swap in which he sells the GBP per tomorrow
and buys them back per spot.
If the GBP/USD is trading at a discount, he achieves an interest benefit from the FX
swap After all, the GBP rate is then higher than the USD rate and the FX swap can be
seen conceptually as an investment in an overnight GBP deposit and a drawn overnight US dollar deposit. The points in the tom/next swap are therefore ‘in his favour’. This is advantageous for his result.
example
The average purchase price for the GBP bought by a trader is 1.4490. He decides to
roll over his position for a day. The quote for the tom/next swap points is 0.0002 0.000015.
The trader sells and buys GBP (buys and sells euro). Therefore, he gets the bid rate of
0.00015 (in his favour!). As a consequence, the average cost decreases by the number of tom/next swap points.
The average purchase price is now adjusted with the swap points:
1.4490 - 0.00015 = 1.448850.
4.4 Non-deliverable forward
A non-deliverable forward or NDF is an OTC instrument that is traded on the FX
market in which the difference between the contract FX rate and the spot FX rate
on the fixing date is offset on the settlement date. A non-deliverable forward (NDF)
is used to hedge FX risks in currencies for which there is no market in ordinary FX
forward contracts. This is the case, for instance, for a number of Asian currencies
such the Chinese yuan, the Indian rupee, the Indonesian rupiah, the Korean won,
the Philippines’ peso and the Taiwanese dollar.
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foreign exchange
You could say that an NDF is an FX forward contract with cash settlement instead of
physical delivery. In theory, the rate for an NDF is determined in the same way as the
FX forward rate for an ordinary FX forward contract.
The difference between the contract rate and the FX spot rate on the fixing date is
paid out in the ‘hard’ currency. In the case of an USD/TWD contract, for instance,
the settlement takes place in US dollars.
example
A Spanish importer concludes a three-month NDF in EUR/CNY to hedge himself
against an increase in the Chinese yuan. This means he buys the CNY and sells the
euro. The contract size is CNY 100 million and the contract rate is 9.45. On the contract fixing date, the EUR/CNY FX spot FX rate is 9.25.
The settlement amount is calculated as the difference between a notional purchase
of CNY at the contract rate and a notional sale of CNY at the FX spot rate on the fixing date:
‘Purchase’ CNY 100 million at 9.45: EUR 10,582,010.58
‘Sale’ CNY 100 million at 9.25: EUR 10,810,810.81
On balance, the importer receives an amount of EUR 228,800.23.
4.5 Precious Metals
Besides financial derivatives, departments of the Financial Markets division of
banks are also increasingly involved in the trading commodity derivatives. Commodity derivatives are instruments which are derived from cash commodity
transactions. The most common variants are forward contracts and options. Commodities are increasingly being used by companies to hedge the price risks with
raw materials and energy carriers. Banks perform the role of market maker and as
a consequence they are more or less forced to take trading positions in these instruments. Within commodities, a special place is taken by precious metals. These include gold, silver and platinum. The ISO codes for the major precious metals are
given in the table below.
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type
iso code
GoldXAU
SilverXAG
PlatinumXPL
PalladiumXPD
Gold and silver are, amongst others, traded on the London Gold and Silver Fixing.
This is a trading platform where buyers and suppliers can deposit their orders via
its members: Barclays Capital, HSBC, Deutsche Bank, Scotiabank and Sociéte Generale.
The gold price is fixed twice each day at 10.30 and 15.00. This is done by means of
telephone discussions between the members. Transactions between the members
are concluded at the fixing price. Before the members begin to trade between themselves, they net their orders internally. Therefore, each member submits only one
net order for each fixing. Because there are only five members, there is no need for
a central counterparty.
The fixing of the price of silver is done in the same way. The only difference is that,
for silver, there is only one fixing per day, at 12.00 and that there are only three
members: Deutsche Bank, HSBC and Scotiabank.
Gold and silver are traded in bars and coins. In the professional market, however, normally only bars are traded. To protect the market parties from buying gold of an inferior quality, The London Bullion Market Association (LBMA) has set definitions for
standard bars of gold and silver. These requirements refer to the weight of a bar and,
more important, to the composition of the bar, i.e. the percentage of pure gold. If a
bar complies with the requirements, the bar is said to qualify for ‘Good D
­ elivery’.
According to the LBMA, the standard weight for a gold bar is approximately 400
fine troy ounces (usually between 350 and 430 troy ounces) and the standard weight
for a silver bar is 1,000 troy ounces. A troy ounce is 31.1035 grams.
A gold bar that qualifies for good delivery must contain between 995.0 and 999.9
grams of gold per kilo and a silver bar must contains 999.0 to 999.9 grams of silver
per kilo.
The gold price is and the silver price is stated per troy ounce and is always quoted
in US dollars. Although gold and solver are commodities, a gold trade does not involve the physical transfer of the bars. In stead, a trade is executed by transferring
an amount of gold from the gold or silver account of the seller from the gold or sil110
foreign exchange
ver account from the buyer. Therefore, a trader who wants to trade precious metals
or an investor who wants to invest in a precious metal must open an account. For
the London market, this is the LOCO account.
Non-professional investors normally buy coins. For gold, the following coins are
used by non-professionals:
coin
grams of gold per kilo
UK Sovereign
916.7
US Gold Eagle
916.7
SA Kruger Rand
916.7
Canadian Maple Leaf
999.9
Australian Kangaroo 2013
999.9
example
The gold price is quoted 1,412.50 – 60 to you. You want to buy 5,000 troy ounces of
gold. You have to pay 1,412.60 x 5,000 = 7,063,000.
If, for instance, USD/JPY is quoted 98.53 – 55, a Japanese buyer would have to pay
1,412,60 x 5,000 x 98.55 = 696,058,650.
gold swaps and forwards
Some parties have a temporary need for gold, for instance, because of a delivery obligation as a result of entering into a short position. They can then conclude a gold
interest rate swap. A gold interest rate swap is comparable to a repurchase agreement. At the start date, gold is delivered against the spot price instead of securities
and, on the maturity of the contract, the gold is returned for a sum equal to the principal amount plus an interest coupon. Gold interest rate swaps are always denominated in US dollars. Figure 4.14 shows a diagram of a gold interest swap.
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Figure 4.14 Gold interest rate swap
The price used for the second leg of the gold interest rate swap is the so-called gold
forward rate. This is thus equal to the spot price plus interest. This price is, of course,
also used when a party wants to buy gold for future delivery. The gold forward rate
is calculated in accordance with the general formula for forward prices:
Forward Rate = Spot Rate + Cost of carry -/- Direct yield of the traded value
Because the direct yield on gold is zero, the forward rate is determined by adding
the rate for the gold interest rate swap to the spot rate.
The interest rate for a gold interest rate swap is lower than that for an uncollateralised deposit. With the gold, the party providing the money in a gold interest rate
swap is after all receiving valuable collateral. This party can invest the principal
amount at the higher interbank deposit interest rate (LIBOR) and thereby make an
interest profit. In the example below, the trader lends gold (and borrows money) at a
gold swap interest rate of 2% and then lends out the money at an interbank deposit
rate of 5% leading to an interest profit of 3%. This is shown in figure 4.15.
Figure 4.15 Interest arbitrage through a gold interest rate swap
The benchmark for the interest rate used for lending out gold via a gold interest rate
swap is GOFO. GOFO stands for gold forward rate. GOFO is an ask rate for gold and,
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foreign exchange
therefore, a bid rate for US dollars and is fixed at 11.00 for 1, 2, 3, 6 and 12 months by
a panel of at least six banks.
In general, GOFO is positive. The forward price of gold is then higher than the spot
price. This is called contango.
gold lease
It is also possible to borrow gold without having to simultaneously transfer a sum of
money. This is called gold lease. The fee for lending gold is comparable to the interest profit made by a party who borrows gold in a gold interest rate swap and invests
it in a deposit. Figure 4.16 shows a diagram of a gold lease transaction.
Figure 4.16 Gold lease
In this gold lease contract, the trader lends gold directly and requires a fee of 3%.
The benchmark for gold lease transactions is the gold mid-market lease rate. This
benchmark is not determined directly by a panel of banks but is derived from two
other benchmarks: GOFO and LIBOR. To derive the gold mid-market lease rate from
these two benchmarks, two aspects need to be taken into account:
1. GOFO is a bid rate for money and LIBOR is an ask rate
2. The spread between the bid and ask price for GOFO is 25 basis points and,
for LIBOR, it is 12.5 basis points
Taking these two aspects into account, the gold mid-market lease rate can be calculated using the following formula:
Gold mid-market lease rate = (GOFO + 12.5 basis points) -/- (USD LIBOR- 6.25 basis points)
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example
The 2 month GOFO fixing is 2.75% and the 2 months LIBOR fixing is 2.50%. The gold
mid-market rate can be calculated as follows:
(2.75% + 0.125%) - (2.50% - 0.0625%) = 2.8750% - 2.4375% = 43.75 basis points.
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Chapter 5
Futures
A financial future is an exchange traded financial instrument in which two parties
enter into a reciprocal obligation to buy or deliver a certain value at a certain future
point in time at a predetermined price (physical delivery) or to offset the difference
between the price or interest rate that is agreed upon in the futures contract and the
actual price or interest rate at that point in time (cash settlement).
Bought futures contracts can be sold to the exchange and sold futures contracts can
be bought back from the exchange at any time during their lifetime. This is referred
to as closing the futures contract or offsetting it. If a party closes a futures contract,
the original contract becomes void. The last date on which trading may take place is
called the expiry date. Just before the expiry date of a future with a physical delivery
obligation, the market parties usually close their futures positions in order to avoid
physical delivery.
Because financial futures are exclusively traded on stock exchanges, they have
standardized conditions. In the case of most futures, only a limited number of series are traded. Contract sizes are also standardized. Parties that want to conclude
a futures contract need only indicate how many contracts they would like to sell or
buy.
5.1 Role of a futures exchange and of a clearing house
Futures are always traded on an exchange. This means that only members of the
exchange can trade directly in futures. Members can indicate the prices at which
they would like to conclude contracts, i.e. they can place an order. Non-members
must involve a member to get their transactions concluded. The member then fulfils the role of broker. Brokers charge a commission for each transaction that they
conclude on behalf of their clients. Sometimes they charge a separate fee if the cus115
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tomer buys and sells simultaneously, as is the case with strategies like spreads and
butterflies. This is referred to as a round trip commission.
One of the major benefits of trading via an exchange is the high market liquidity.
The liquidity of an exchange is indicated in two ways. The first way is the open interest, which is the total number of outstanding contracts at the end of the trading
day, both long and short. The second way is the volume which is the total number of
concluded contracts on a trading day. Buy and sell transactions are taken individually.
example
At an exchange the following transactions are concluded:
1.
A buys 10 futures contracts from B (both parties open a position)
2.
C buys 20 futures contracts from D (both parties open a position)
3.
A sells 10 futures contracts to E (A closes its position and E opens a position)
4. B buys 5 futures contracts from C (B and C both close their position partially)
The open interest may change with every transaction:
transaction
a
b
c
d
e
1
10 long
10 short
open interest
20
2
10 long
10 short
20 long
20 short
60
3
0
10 short
20 long
20 short
10 long
60
5 short
15 long
20 short
10 long
50
4
The trade volume for this trading day = 2 x 10 + 2 x 20 + 2 x 10 + 2 x 5 = 90 contracts.
5.1.1 Order types
Members of stock exchanges can use various types of orders on an exchange. A
non-exhaustive list is presented below:
Name Description
Market order An order that must be executed against the next market
price
Limit order An order that must be executed as quickly as possible
once a specific (favourable) price level has been reached
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Stop loss order Stop limit order Good until cancelled order
Fill or kill order Scale order 5.1.2 An order that must be executed as quickly as possible
once a specific unfavourable price level has been reached
An order that must be executed as quickly as possible
once a specific unfavourable price level has been reached
but which is cancelled automatically if the price hits a
more unfavourable level before being processed
An order that is applicable for as long as it is not revoked
by the instructing party
An order that must be executed for the full order
amount in one go or that otherwise will be cancelled
An order where for each previously agreed price change,
a specific quantity must be purchased or sold
Role of central counterparty
If the trading system of an exchange has executed two orders against each other
then a clearing institution acts as central counterparty (CCP). One example of a
clearing house is LCH.Clearnet. For each exchange transaction, a CCP concludes
two contracts simultaneously. The selling exchange member sells the traded instrument to the clearing house and the buying exchange member buys it from the clearing house. The advantage of this is that the CCP can cancel out the transactions it
has concluded with each party so that, at the end of the trading day, for each party
and for each traded financial instrument, only one quantity to deliver or to be received can be calculated and then finally, based on the transactions for all instruments combined, one sum of money to be paid or received can be calculated. This is
referred to as netting.
In order to be able to participate in this process, exchange members must also be
a member of the clearing house. Members who do not wish to do so, must ensure
that their transactions are then included together with the transactions of members who are indeed members of the clearing house. For this, they must enter into
a separate agreement with these other members. Exchange members who are also
members of the clearing house are called clearing members. Clearing members
who also forward transactions from non-clearing members into the clearing process are called general clearing members (GCM). Clearing members who only clear
their own transactions are called individual clearing members (ICM).
In some cases, the same instrument is traded on different exchanges. This is true,
for instance, for the Eurodollar future that is traded on, amongst others, the SGX in
Singapore and on the CME in Chicago. CME and SGX have an agreement that contracts that are concluded on one of these exchanges can be offset on the other exchange. This is called fungibility.
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5.1.3 Margins
The central clearing house carries the risk that the clearing members might be unable to meet their obligations. Therefore, it takes a risk mitigating measure, i.e. the
required margin. There are two kinds of margins: the initial margin and the variation margin. The initial margin is a cash deposit that the clearing house requires as
a collateral on the moment of concluding a futures contract. This amount must be
transferred to an account that a clearing member holds with the CCP, i.e. the margin account. After a contract has expired, the clearing member is allowed to transfer the initial margin from its margin account to its own account with the central
bank or a correspondent bank. This also happens if the clearing member closes his
position early. The amount of initial margin is based on the volatility and the market liquidity of the underlying value.
Variation margin or margin calls refers to the the daily settlement of profits and
losses of a futures contract. At the end of each trading day, the closing price for a
futures contract is determined. If the closing price is higher than the closing price
from the previous day, then the clearing member who has for instance bought a future has made a profit. The clearing house then credits the margin account of the
clearing member. If the closing price has decreased, however, the clearing house
asks the clearing member to transfer extra money to its margin account (‘to make a
margin call’), and immediately debits the margin account of this member in favour
of a clearing member whose position was at a gain that day. On the expiry date of a
futures contract, only the result for the final day is settled.
Sometimes an exchange only asks a member to pay a variation margin if the balance on the margin account would become lower that a certain pre-agreed percentage of the initial margin. This level is referred to as maintenance margin. If this
level is breached, however, then a margin payment is required to set the balance on
the margin account exactly at the level of the initial margin again.
5.2 STIR futures
A money market future or short term interest rate future (STIR future) is an exchange listed future contract where the price is based on the forward interest rate
for an underlying period of one or three months (30/90 days, year basis 360). The
cycle for money market futures is March, June, September, December, coded with
the letters Z, H, M and U respectively. The table below contains examples of money
market futures.
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futures
contractvalue
exchange
Short Sterling
GBP 500,000
ICE
3m US / Eurodollar
USD 1,000,000
ICE, CME, SGX 3m Euribor
EUR 1,000,000
ICE, EUREX, CME
3m EuroSwiss
CHF 1,000,000
ICE, CME
3m EuroYen
JPY 100,000,000
CME, TFX
1m EONIA
EUR 3,000,000
ICE
The contract term of STIR futures can be up to ten years. Every cycle of four quarterly expiries is called a sequence. The different sequences are sometimes referred
to by a colour code. The futures contracts of the first sequence are, for instance,
called whites. The futures in the second sequence are called red and the next ones
green.
5.2.1 Prices of STIR futures and implied forward rates
The price of a STIR future is quoted as 100 -/- the (implied) forward rate. Thus,
the price goes up if the forward interest rate for the underlying period goes
down. A party that wants to speculate on a fall in the interest rate or wants to
hedge against a fall must therefore buy a STIR future. And a party that wants to
speculate on a rise in the interest rate or wants to hedge against a rise must sell
a STIR future. This is exactly the reverse then with an FRA. If the price of a STIR
future is known, the implied forward rate for the underlying period can also be
calculated.
example
In January, the price of the Mar Eurodollar future is 98.87. This means that the implied forward rate 2s vs 5s at that moment is 1.13%.
5.2.2 Fixing of the STIR futures settlement price on the expiry date
During the lifetime of a STIR future, the price is continuously determined via by
supply and demand. However, at the expiry date the fixing price is determined by
the exchange. For futures contracts on NYSE Liffe, this is done on the last trading
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day at 11.00 AM. The fixing price is called the Exchange Delivery Settlement Price
(EDSP) which is calculated as 100 -/- fixing of the underlying benchmark, e.g. USD
LIBOR or EURIBOR.
5.2.3 Daily result calculation and margin calculation
Each day, traders calculate the value of all their futures transactions. The clearing
house also does this in order to determine the size of the daily settlement of the variation margin. A concept that this is often employed in this respect is the ‘value of
one point movement’. This is the change in the value of a futures position as a result
of a 0.01 change in the futures price. The value of one point for a Eurodollar contract is, for instance, 1,000,000 x 90/360 x 0.0001 = 25 US dollar. The table below
shows the value of one point for five STIR future contracts.
contract
contract value
calculation of value
value of
of one point one point
Short Sterling
GBP 500,000
GBP 500,000 x 90/360x 0.0001
GBP 12.50
Eurodollar
USD 1,000,000
USD 1,000,000 x 90/360x 0.0001
USD 25.00
Euribor
EUR 1,000,000
EUR 1,000,000 x 90/360x 0.0001
EUR 25.00
EuroSwiss
CHF 1,000,000
CHF 1,000,000 x 90/360x 0.0001
CHF 25.00
EuroYen
JPY 100,000,000
JPY 100,000,000 x 90/360x 0.0001
JPY 2500.00
Once the value of one point is known, it is easy to determine the amount of the daily
margin call.
example
A dealer has 10 Eurodollar contracts purchased at a price of 98.45. After one day, the
price has risen to 98.75. The value of one point movement is:
10 x USD 25 = USD 250.00
Because the price has changed by 30 points, his result is:
USD 250.00 x 30 = USD 7,500 positive.
The clearing house will transfer this amount to the trader’s bank account.
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If, a day later, the price falls to 98.64 (a decrease of 11 points) the daily result is USD
250.00 x 11 = USD 2,750 negative.
The clearing house will debit the trader’s account for this amount.
5.2.4 Use of STIR futures by companies
Companies may use STIR futures for hedging short-term interest rate risks. If a
company, for instance, has a short forward cash position in the period three to six
months, it can sell a STIR future to hedge its risk. If the price of the 3s v. 6s STIR future is, for instance, 95.50, by selling the future the company has ensured that the
financing costs (without credit spread) are fixed at a level of 4.5% (30/360):
If the EDSP on the expiry date is exactly 95.50, no settlement takes place on account
of the STIR future. For a loan, however, the company must pay the market rate of
4.5% at that moment.
If the EDSP on the expiry date is, for instance, 94.50 then, under the futures contract, the company receives the difference between 95.50 and 94.50 (thus 100 ticks
or 1% on an annual basis) over the size of the futures contract. Since the company
must pay the market rate of 5.5% for a loan, its interest costs, on balance, are 4.5%.
If the EDSP on the expiry date is, for instance, 96.50 then, under the futures contract, the company pays the difference between 96.5 and 95.5 (thus 100 ticks or –1%
on an annual basis). Since the company must pay the market rate of 3.5% for a loan,
its interest costs, on balance, are again 4.5%.
5.3 Arbitraging between FRAs and STIR futures
A market party who has sold an FRA with a specific underlying period, could hedge
this by selling a STIR future with the same underlying period. This hedge is not always perfect because futures contracts are only available for standardized periods
and for standard amounts. Furthermore, the development of the prices for STIR
futures can differ from the development of the FRA rates. This is called basis risk.
Finally, the day count convention for FRAs and STIR futures is different. The imperfection with regard to the term can be eliminated by concluding so called IMM
FRAs. These FRAs have the same underlying period as STIR futures.
The fact that the FRA and STIR futures rates can differ somewhat from each other
may open the possibility of arbitrage.
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example
It is 20 February. The Mar-Jun Euribor future is trading at 96.35. The 2s v 5s FRA is
now trading at 3.62-3.64 (converted to daycount convention 30/360). A trader can
arbitrage by buying an FRA at 3.64 (which is similar to selling a future at 96.36) and
buying the Mar-Jun future. If he holds his position until the maturity date of both
contracts, he will realize a profit of 1 basis point.
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Chapter 6
Forward Rate
Agreements
A forward rate agreement (FRA) is an over-the-counter interest rate derivative traded on the money market in which two parties enter into a mutual obligation to settle the difference between an interest rate specified in the contract and the level of
a reference interest rate on the fixing date where this rate differential is applied to
a fixed principal sum, the notional amount. FRAs are often concluded under standardized conditions, for instance, the FRABBA terms (where BBA stands for British
Bankers’ Association).
6.1
Contract data
In an FRA contract (contract for difference according to the Bank of England), the
following transaction details are recorded:
–
–
–
–
–
–
–
the notional amount
the reference interest rate, the rate against which the contract is fixed
generally EURIBOR or LIBOR
the contract interest rate: i.e. the rate compared on the fixing date with the
reference rate
the fixing date: the date when the settlement amount for the FRA is determined
the settlement date: the date on which the parties settle the interest rate
differential
the underlying period; the period over which the interest rate differential
is calculated
who the buyer is and who the seller is
The buyer of an FRA is the party that receives the settlement amount from the other
party if the reference interest rate on the fixing date is higher than the FRA contract
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rate. The seller receives the settlement amount from the buyer if the reference interest rate is lower than the contract rate on the fixing date.
There are two relevant terms for FRAs: the contract term and the underlying term.
The contract term runs from the contract date to the settlement date. The underlying term starts at the settlement date and ends at the maturity date of the underlying period. The contract term of a ‘6s vs. 9s’ FRA, for instance, is six months and the
underlying term is three months.
example
The relevant dates of a ‘6s vs. 9s’ FRA contract that is concluded on the 1st of March are:
Contract date: 1 March
Fixing date: 1 September
Settlement date: 3 September
Maturity date: 3 December
For an FRA on the local British money market, the fixing date and the settlement
date are the same. The FRA is thus fixed on the settlement date and not on a separate
fixing date.
Since FRAs are over-the-counter traded instruments they can be tailor-made. The
parties in the above example could therefore also agree to let the underlying period
start on, for instance 15 September instead of 3 September. The FRA is then referred
to as a 6s v 9s FRA ‘over the 15th’. The underlying period of this FRA then starts on
15 September and ends on 15 December. The FRA contract rate will be adjusted accordingly.
6.2 The contract rate of an FRA
The contract rate of an FRA can theoretically be derived from interest rates for cash
instruments. The following equation can be used for this purpose27.
1 + r × d ⁄ year basis
r f =   -------------l--------l-------------------------- – 1 × 360 ⁄ d f
  1 + r s × d s ⁄ ( year basis )

27 This is the Y%FW equation in your HP financial calculator.
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forward rate agreements
where:
rk = interest rate for the period until the forward period start date;
dk = number of days until the forward period start date;
rf = forward yield;
df = number of days in the forward period;
rl = interest rate for the period until the forward period maturity date;
dl = number of days until the forward period maturity date.
example
On 18 May the following interest rates apply for value 20 May:
1 month
1.24 (20 June, 31 days)
2 months 1.34 (22 July, 63 days)
3 months 1.44 (20 August, 92 days)
The bid and ask a rate for a CHF 1s v 2s FRA are:
FRA rate28 = ((1 + 63/360 x 0.0134) / (1 + 31/360 x 0.0124) - 1) x 360/32 =
0.0144 = 1.44%
6.3
Settlement of FRAs
The amounts involved in the settlement of an FRA are calculated on the FRA contract fixing date. Settlement takes place on the corresponding spot date, which in
most cases means two workings days later (t+2), with the exception of FRAs traded
in GBP. The calculation of the FRA settlement amount takes place in three steps:29
1. On the fixing date, the reference interest rate is compared with the contract
interest rate.
2. The difference in interest rates is calculated as an amount over the underlying term and over the notional amount.
3. Because the settlement date is at the start of the underlying period in stead
of at the maturity date of the underlying period of the FRA, the settlement
28 Use the Y%FW equation in your HP financial calculator to calculate the forward rate:
DL = 63, B = 360, Y%L = 0.0134, DS = 31, Y%S =0.0124. Solve for Y%FW.
29 The equation to calculate the settlement amount of an FRA should be entered in a HP financial calculator as follows: FRASET = (NOM x (FIX% - FRA%) x D/B) / (1+ D/B x FIX%).
This settlement amount is seen from the point of view of the buyer of the FRA.
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amount is discounted using the money market reference rate that corresponds with the underlying period as the discount rate.
example
Two parties have concluded a ‘4 vs. 7’ FRA. Maturity is in four months and the reference interest rate is the three-month EURIBOR. The contract interest rate is 3.75%.
The contract notional is EUR 5,000,000. On the fixing date, the three-month EURIBOR is fixed at 3.95%.
This FRA is settled as follows30:
1. The difference between the contract interest rate and the reference interest rate
is calculated 3.95% – 3.75% = 0.20%.
2. The interest differential is converted to an interest amount over the underlying
term and over the notional amount of EUR 5,000,000:
EUR 5,000,000 x 91/360 x 0.20% = EUR 2,527.78.
3. This amount is discounted by using the three-month EURIBOR rate of 3.95%.
In this case, the settlement amount is: 2,527.78/(1 + 91/360 x 0.0395) = EUR 2,502.79.
On the settlement date, the seller has to pay EUR 2,502.79 to the buyer.
6.4 Use of FRAs by traders; trading and arbitrage
Traders can use FRAs in various ways for trading and arbitraging purposes including straight forward trading and closing forward cash positions.
6.4.1 Straight forward trading in FRAs
If a money market trader expects an interest rate rise, he buys an FRA. If he expects
a fall in interest rates, he sells an FRA. If a money market trader wants to close a
­single FRA position, he concludes an offsetting FRA with the same notional and underlying term. Since an FRA is an over-the-counter product, this does not have to
30 Use the FRASET equation in your HP financial calculator to calculate the settlement
amount of this FRA: NOM = 5,000,000 , FIX% = 0.0395, FRA% = 0.0375, D = 91, B = 360.
Note that the outcome of the equation is seen from the point of view of the buyer of the
FRA. Solve for FRASET.
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take place with the same counterparty. Both FRA contracts will continue to exist
until the maturity date and will be settled on the same settlement date. The (unrealized) trading result, however, has been fixed at the moment that the trader has
closed his position and will be shown in his profit and loss report.
example
It is 15 March and a money market trader expects that the central bank will raise its
official rates within six months. This rise, however, is not reflected in the current
spot interest rates. The trader decides to buy a 6s v 9 s FRA with a contract rate of, for
instance, 3.0%. The underlying period runs from 17 September to 17 December. After three months the central bank has indeed raised its interest rates and the trader
now wants to close his position. He sells an 3s v 6s FRA, which has the same underlying period as the original FRA contract, i.e. from 17 September to 17 December. The
contract rate for this FRA is now, for instance, 3.45%.
As a result, the trader has locked in a profit of 0.45% over the notional amount for
the underlying period of the FRA. The unrealized profit will be shown immediately
in the trader’s profit and loss account but will only be materialized at the settlement
date of the FRA contracts.
anticipating changes in the shape of the short term yield curve
If a trader expects that the shape of the short term yield curve is going to change,
he can anticipate by selling FRAs with a short contract term and buying FRAs with
a longer contract term or vice versa. This is called spread trading. Since the trader
now has two opposing FRAs, the risk is lower than when he is only buying or selling. After all, parallel changes in the yield curve do not influence the value of his
position. The table below shows the different ways in which a trader can perform a
spread strategy.
market vision
strategy
curve steepens
(or changes from inverse to normal)
sell FRA with short term
buy FRA with longer term
curve flattens
(or changes from normal to inverse)
buy FRA with short term
sell FRA with longer term
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6.4.2 Closing forward cash positions with FRAs
Money market traders often enter into a forward cash position by concluding two
opposite deposits with different terms. Figure 6.1 shows a money market position
which was originally opened as a 3s v 6s short cash position.
Figure 6.1
The trader who holds the above position can close his position after three months
by taking a three months deposit. However, if he wants to close the position earlier,
e.g. after one month, he theoretically needs to take a forward deposit with a term of
three months starting after two months. Forward deposits, however, are not traded
in the inter-bank money markets. As an alternative, the trader can buy a 2s v 5s FRA
in order to close his position. After all, by concluding an FRA, a forward interest rate
is fixed. Figure 6.2 shows the closed position. Note that the bought FRA is shown as
a fictitious taken deposit. After all, after two months the trader has to take a three
months deposit. The effective rate of this deposit will equal the FRA rate (assuming
that the trader is able to realize an interest rate of EURIBOR or US-LIBOR flat!).
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forward rate agreements
Figure 6.2 Closing of a forward cash position by using an FRA
The compounded interest rate to be paid for the total period can be calculated by the
following equation:
Compounded interest rate = ( ∏ ( 1 + di / year basis x ri) - 1 ) x year basis / total number of days
example
A trader has taken a three months Euro deposit (91 days) at a rate of 1.20% and has
invested the money in a six month Euro deposit (183 days) at a rate of 1.30%. After
one month he wants to close his position. At that moment, the 2s v 5s FRA is quoted
1.33 - 1.35% .
If he closes his position, the interest costs for the total period of 183 days are:
Compounded interest rate =
( (1 + 91/360 x 0.012) x ( 1 + 92/360 x 0.0135) - 1) x 360/183 = 0.0128.
By concluding the FRA, the trader has now locked in a profit of 2 basis points over
the total period of six months.
6.5 Use of FRAs by clients of the bank
Companies generally use FRAs to fix the interest rate for a future short-term liquidity shortfall. For this reason, they buy FRAs. If a company has bought an FRA to
hedge its interest rate risk, it will always pay a fixed rate, no matter what will happen to the short term interest rates. The overall fixed rate to be paid can be calculated by using the following equation:
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Effective interest rate = FRA contract rate + credit spread
example
It is 15 March and in four months’ time, on 15 July, a company will be faced with a
liquidity shortfall of EUR 5 million that will last for three months. The ‘4s v 7s’ FRA
ask price is 3.75%. The company can borrow at EURIBOR with a credit spread of 30
basis points. If the company concludes an FRA, the overall interest rate for the future
period will be:
3.75% + 0.30% = 4.05%.
After all, for each fixing of the three month EURIBOR on the fixing date of the FRA
contract above the contract rate of 3.75%, the company will receive the difference between the fixing rate and 3.75%. This compensates for the fact that the bank uses the
actual higher EURIBOR rate as the base rate for the three month loan.
For instance, if on 13 July the 3-month EURIBOR fixing for value 15 July is 3.95%, the
overall interest rate for the company is
3.95% + 0.30% -(3.95% - 3.75%) = 4.05%.
For each fixing of the three month EURIBOR on the fixing date lower than the contract rate of 3.75 %, the company must pay the difference between the fixing rate and
3.75 %. This compensates for the fact that the bank uses the actual lower EURIBOR
rate as the base rate for the three month loan. For instance, if on 13 July the 3-month
EURIBOR fixing for value 15 July is 3.40%, the overall interest rate for the company is
3.40% + 0.30% -(3.40% - 3.75%) = 4.05%.
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Chapter 7
Interest Rate Swaps
An interest rate swap (IRS) is an OTC interest rate derivative contract in which two
parties enter into a reciprocal obligation to exchange interest payments in the same
currency during an agreed period of time without exchanging principals. Interest
rate swaps are often used to change the interest rate conditions of a financial instrument, usually from fixed to floating or vice versa.
IRS terms vary from one to fifty years. The notional amounts differ from 100,000
to 100 million or even more. The reference rate for the floating interest coupon of
an IRS in euro is usually the three or six-month EURIBOR rate. For IRS contracts in
other currencies, this is usually a LIBOR rate.
The fixed IRS rate is determined by supply and demand on the IRS market and usually follows the market interest rate for government bonds with a spread. The fixedinterest is usually set for the entire term of the IRS. In some cases, both interest
rates are floating. This is the case, for instance, for an IRS in which a three-month
EURIBOR is exchanged for a one-year EURIBOR. An IRS involving the exchange of
two floating interest rates is called a basis swap.
7.1 Contract specifications and jargon
The following transaction data is recorded in an IRS contract:
–
–
the notional amount
the reference rate for the floating interest rate and the daycount convention (e.g. EURIBOR or LIBOR, actual/360)
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–
–
–
the contractual interest rate; the level of the fixed interest rate and the
daycount convention
the term and any possible repayment schedule
who the buyer is and who the seller is, i.e. the fixed rate payer and fixed
rate receiver
If parties regularly enter into financial contracts, a framework agreement is often
concluded. For IRS contracts, this is a BBAIRS general master agreement, drawn up
by the British Bankers’ Association or an ISDA general master agreement. An ISDA
agreement regulates the following items:
–
–
–
–
–
–
–
definitions regarding the instruments and the settlement (terms and
conditions and payment procedures)
applicable law
procedures for cancellation
the extent to which bilateral contracts can be transferred to other parties
(assignment)
who is authorised to enter into transactions
what information the parties must provide for the other parties and how
frequently this must happen
how transactions must be confirmed.
For the party that pays the fixed rate in an IRS, the swap is a payer’s swap. For the
party that receives the fixed rate, the same IRS is a receiver’s swap. Sometimes the
terms buying or selling an IRS are used. As usual, the general rule with regard to
buying and selling in financial markets applies: a buyer profits from an increase in
the price determining parameter and a seller profits from a decrease in the price determining parameter, in this case the fixed interest rate. The buyer of an IRS is thus
the party who pays the fixed rate because he profits from a rise in interest rates.
Figure 7.1 shows a diagram of an IRS. The buyer pays the fixed interest coupon and
the seller pays the floating interest coupon.
Figure 7.1 132
Interest rate swap
interest rate swaps
7.2 Settlement of an IRS
Both the fixed and floating coupon in an IRS are normally paid in arrears. The frequency for the floating coupon is usually quarterly or semi-annually. Except for
Great Britain, two days prior to the expiry of each floating coupon period, the new
floating coupon rate is set for the next coupon period. The fixed coupon is generally paid at the end of each year. Often, on the payment date of the fixed coupon,
the amount of the fixed coupon is netted against the floating coupon that is due
on the same date (payment netting). This is a standard arrangement for an ISDA
contract.
All interest rate fixings and coupon payments of an IRS are recorded in an event
calendar. The table below shows the event calendar for a receiver’s IRS with a contract term from 15/7/2013 until 17/7/2016 for which the reference interest rate is the
six-month EURIBOR. The IRS is concluded under an ISDA framework agreement,
therefore, the fixed coupon is netted against the last floating coupon of the year.
dateevent
13/7/2013
Fixing 6 month EURIBOR
Coupon period 15/7/2013 - 15/1/2014
13/1/2014
Fixing 6 month EURIBOR
Coupon period 15/1/2014 - 15/7/2014
15/1/2014
Paying of floating coupon
Coupon period 15/7/2013 - 15/1/2014
13/7/2014
Fixing 6 month EURIBOR
Coupon period 15/7/2014 - 15/1/2015
15/7/2014
Receiving of net amount of fixed coupon of 1st year and floating
coupon for coupon period 15/1/2014 - 15/7/2014
13/1/2015
Fixing 6 month EURIBOR
Coupon period 15/1/2015 - 15/7/2015
15/1/2015
Paying floating coupon
Coupon period 15/7/2014 - 15/1/2015
15/7/2015
Receiving of net amount of fixed coupon of 2nd year and floating
coupon for coupon period 17/1/2015 - 15/7/2015
In ISDA framework agreements it is sometimes agreed that coupon payments
should be fully synchronised. This means that the coupon frequency for the fixed
leg is set to be the same as that for the floating leg and that the fixed rate is converted to the daycount convention of the floating rate (actual/ 360). The fixed rate must
then be adjusted in two ways:
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–
–
7.3 from annual coupon to semi-annual or quarterly coupon
from 30/360 to actual/360.
Overnight index swaps
An overnight index swap (OIS) is an OTC interest derivative in which two parties undertake to exchange interest payments in the same currency without the exchange
of principal sums while the floating coupon is based on an overnight interest rate
index. The following transaction data must be recorded in an OIS contract:
– notional amount
–term
– level of the fixed interest rate
– reference rate for the overnight interest rate
– fixed interest daycount convention
– who the buyer is and who the seller is; the fixed rate payer and fixed rate
receiver.
Overnight indices for euro are EONIA, determined by the European Banking Federation, and EURONIA, determined by the WMBA (Wholesale Markets Brokers’
Association). The difference between the two is that EURONIA is concerned with
transactions concluded via brokers in London and that EONIA is concerned with
the overnight transactions of the EURIBOR panel banks.
The overnight index for Pound Sterling is SONIA (Sterling overnight index average)
that is determined by the WMBA, for CHF it is the CHF tom / next indexed swap rate
(TOIS) and for the US the overnight reference rate is the Fed funds rate.
Both the fixed coupon and the floating coupon for an OIS are paid in arrears using
payment netting. For contract terms shorter than one year, there is only one cash
flow that is due at the end of the term. For contract terms over one year, the net
settle­ment takes place on an annual basis. The diagram below shows when this net
amount is settled in the various money markets.
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interest rate swaps
currency
settlement date
GBP
maturity date (M)
JPY, EUR
M+1
US, CHF
M+2
The level of the floating coupon is calculated by using compounded interest. The interest amount for the floating leg is calculated using the following equation.
Interest amount = nominal x ( ( 1 + 1 ⁄ yb × r 1 ) × ( 1 + 1 ⁄ yb × r 2 ) × ... – 1 ) × yb ⁄ days total
example
On Monday, a trader sells an OIS swap in euro with a notional of EUR 100 million.
The fixed rate is 0.95%. The EONIA fixings are
dayfixing
Monday0.95%
Tuesday0.98%
Wednesday1.01%
Thursday1.02%
Friday1.04%
The floating coupon can be calculated as follows:
EUR 100 mio x ((1+1/360 x 0.95) x (1+1/360 x 0.98) x (1+1/360 x 1.01) x (1+1/360 x
1.02) x (1+3/360 x 1.04)-1) = EUR 19,668.07.
The amount of the fixed coupon is EUR 100 mio x 7/30 x 0.0095 = EUR 18,472.22.
The net amount to be paid by the trader at the maturity date on Tuesday (M+1) is:
EUR 19,688.07 - EUR 18,472.22 = EUR 1,195.85.
In the above example, the Friday fixing rate is multiplied by a factor 3/360 in stead
of 1/360. This is because the Friday fixing rate applies for the whole weekend.
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7.4 Trading interest rate swaps
Interest derivative traders trade, amongst others, in IRS contracts. They speculate
on future developments of the long term interest rate. If an interest derivative trader expects an interest rate rise, he buys an IRS. If he expects a fall in interest rates,
he sells an IRS.
If an interest derivative trader wants to close a single IRS position, he will conclude an offsetting IRS with the same notional and remaining term. Since an IRS
is an over-the-counter traded instrument, this does not have to take place with the
same counterparty. Both IRS contracts will continue to exist until the maturity date,
which, for instance means, that the coupon payments of both contracts will actually
continue to take place during the remaining term of the contracts. The (unrealized)
trading result, however, was fixed at the moment that the trader has closed his position and will immediately be shown in his profit and loss report.
example
An interest derivative trader expects a rise in interest rates. He, therefore buys a ten
year IRS with a fixed interest rate coupon of 3.0%. After three months the ten year
interest rate has indeed risen. Based on the current market conditions, the trader
has now changed his opinion and thinks that the long term interest rate will not rise
any further. He will now close his position by selling an IRS for the remaining term:
9 years and 9 months. The fixed rate for this IRS is 3.35%.
The trader now has locked in a profit of 0.35% for the remaining term of the IRS contracts. This unrealized profit will be shown immediately in the trader’s profit and
loss account but will only be materialized during the remaining term of the IRS contracts: each year the trader will receive a fixed coupon of 3.35% over the nominal
amount while he only has to pay a fixed annual coupon of 3.00%.
During the three months that the trader held an open position, he also realized an
interest result. This is because he had to pay the fixed rate of 3% and was receiving
the three month reference rate.
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interest rate swaps
anticipating changes in the shape of the irs curve
An IRS can be regarded as a strip of FRAs, each with the same contract rate, the IRS
rate. If a trader expects that the shape of the IRS curve is going to change, he can
anticipate this by taking a position in specific forward periods. If he thinks that the
long term interest rates will rise while the short term rates will stay the same or may
even fall (and thus that only the forward yields that lie in the far future will rise), he
must buy only FRAs with a long term. If he choses to buy an IRS with a long term,
however, he would buy all the composing FRAs in the IRS and not only the ones that
lie the most in the future. Therefore, he also simultaneously has to sell an IRS with
a shorter term. By doing this, he has a closed position in the short term FRAs and a
long position in the FRAs with the longer terms. If after some time he proves to be
right and the long term forward yields have indeed risen, he may close his position
by buying the short term IRS and selling the long term IRS.
7.5 Arbitrage between IRS and FRAs or STIR futures
An IRS with a short term can be constructed synthetically by a strip of FRAs or STIR
futures. For instance, a synthetic payer’s swap can be composed of a strip of purchased FRAs or a strip of sold STIR futures. The interest rate for a synthetic IRS can
be calculated from the rates for the successive FRAs or STIR futures. For a strip of
STIR futures, however, the future prices must first be converted to implied forward
yields. The rate for a synthetic IRS with a term of up to one year can theoretically be
calculated by using the following equation:
Compounded interest rate = ( ∏ ( 1 + di / year basis x ri) - 1 ) x year basis / days total
where:
r1 = LIBOR/EURIBOR
r2 .. rn = FRA contract rates or implied future interest rates
di = number of days in the underlying periods
days total
= term of the synthetic swap in days
The price of the synthetic swap is compared to the actual IRS rate to determine if an
arbitrage opportunity exists.
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example
For December, the following rates are known
rate
# days
3 month EURIBOR
2.23% (2.26% bond basis)
91
MAR Eurodollar future
97.65
90
JUN Eurodollar future
97.52
90
SEP Eurodollar future
97.34
90
DEC Eurodollar future
97.23
90
1 yrs IRS (bond basis)
2.49 - 2.51%
The rate of a synthetic IRS with a term of 1 year is:
(1 + 90/360 x 0.0226) x (1 + 90/360 x 0.0235) x (1 + 90/360 x 0.0248) x (1 + 90/360 x
0.0266) – 1 = 0.0246.
A trader can arbitrage by constructing a synthetic payer’s swap with a term of one
year by selling Mar, Jun and Sep Eurodollar futures against a composed fixed rate
of 2.46% and entering into a receiver’s swap with a term of one year in which he receives 2.49%.
7.6 Applications of interest rate swaps for clients of the bank
Interest rate swaps have many possible applications for clients of the bank. As an
example, banks and pension funds use them to perform their asset and liability
management and companies mostly use them to change the interest rate term of
individual loans.
7.6.1
Fixing the interest on loans with a floating rate
Interest rate swaps are often used by organisations that want to convert a floating
interest rate in a loan into a fixed rate. These swaps are referred to as funding swaps
or liability swaps. The combination of the floating rate loan and the IRS is a synthetic fixed rate loan. By concluding a funding swap, these organisations do not need to
renew their existing loan or make changes to the existing loan agreement. Since an
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interest rate swaps
IRS is, in itself, a standing contract, it does not need to be concluded at the bank that
granted the loan.
example
A company has a loan with a floating interest rate. The interest rate is set at the
3 month EURIBOR with a credit spread of 1.50% (actual/360). The remaining term
for the loan is four years.
The company wants to cover its interest rate risk for the remaining term of the loan
and buys an IRS. The four year IRS rate is 3% (30/360, annual coupon).
Figure 7.2 shows the synthetic fixed rate loan.
Figure 7.2 Combination of a loan with a floating rate and an IRS
As a result, the company pays a total interest rate of 3.00% + 1.50% = 4.50%.
When the swap is concluded based on full synchronisation, the fixed rate is adjusted
as follows.
conversioncalculation
From 30/360 to actual/360
3.00% x 360/365 = 2.961%
From annual to semi-annual
(1+0.02961)1/4 - 1) x 4 = 2.93%
Total interest rate as a result of the
2.93% + 1.50% = 4.43%
combination of the loan and the IRS
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7.6.2 Fixing the floating rate of an investment / asset swap
Investors sometimes use swaps to convert a fixed interest coupon from a bond into
a floating interest coupon. The combination of the fixed rate bond and the IRS is a
synthetic floating rate note and is referred to as an asset swap. Figure 7.3 shows an
example of an asset swap.
Figure 7.3 Synthetic floating rate note (asset swap)
7.6.3 Swap assignment
Sometimes a bank is not able or not willing to accept the total counterparty risk
of an interest rate swap contract with a client. In that case, the bank can choose to
pass part of the contract on to one or more other banks. This is referred to as swap
assignment. The assigning bank, or transferror, is required to inform its client of
the intention to assign the swap before the transaction is concluded. If the client
agrees, then first the interest swap will be concluded for the whole contract amount
between the transferror and the client. At the same time, the transferror will conclude an offsetting swap in the market to close its market risk. In the client confirmation, the transferror should give details of the procedure that will be used if
the swap is indeed transferred. In case of an assignment, part of the client transaction will be novated by a new contract between one of the third banks (referred to as
transferee) and the client. For the transferror, this part of the swap contract will be
replaced by a swap with the transferree for the same part of the contract amount.
The fixed rate that is used in this interbank swap between the tranferror and the
transferree is equal to the fixed rate in the original offsetting swap.
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interest rate swaps
7.7
Basis swaps
A basis swap is an over-the-counter traded derivative in which two floating in­terest
flows are exchanged. If these are denominated in the same currency, only the interest flows are exchanged. An example of this is a basis swap where the one-month
EURIBOR is exchanged for the three-month EURIBOR. Another example is a swap
where the Fed funds rate is exchanged for the T-bill rate.
If the interest flows are in different currencies then, theoretically, at the beginning
and the end of the term, principal sums in these currencies are exchanged, both at
the same exchange rate (the FX spot rate). The term basis swap generally refers to
this variant.
A basis swap where the reference interest rates from different currencies are exchanged can be considered, conceptually, as an FX swap with a long maturity. In
both cases, there is an exchange of the principal sum in the two currencies at the beginning, which is reversed at the end of the period. The main difference is that, with
a basic swap, the interest coupons are paid out explicitly during the contract term
and with an FX swap the interest rate differential is expressed as swap points and
is taken into account with the FX forward rate. With basis swaps, however, the exchange rate used for the exchange of the principal sums at the maturity date is the
same as the exchange rate at the start date. Another difference is that basis swaps
are traded almost exclusively on an interbank basis whilst FX swaps are used by
both clients and banks.
Figure 7.4
Diagram of an FX basis swap
The price of a basis swap is expressed as a spread above or below the benchmark
rate of the quoted currency. If Bank two acts as market maker in the above example,
its quote for the EUR/USD basis swap could be as follows: -3 / -5. In the basis swap,
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Bank one apparently wants to receive USD-LIBOR and gets a spread of minus five
basis points. Based on the quote from the market maker, if Bank one had wanted
to pay USD-LIBOR, the price for the basis swap would have been minus three basis
points.
7.8 Cross-currency swaps
A cross currency swap (CCS) is theoretically the same instrument as a (currency)
­basis swap except that, in this case, at least one of the interest coupons is fixed.
Cross currency swaps are not traded in the professional inter-bank market. This is
because a CCS is, in fact, a structured product. A bank composes a CCS by combining one or two interest rate swaps with one or two basis swaps and offers this combination as one transaction to its clients.
Figure 7.5 Diagram of a cross currency swap
The initial exchange of the principal sum with a CCS can be omitted at the request of
the client. This is possible because this exchange takes place at a the current market
rate, the FX spot rate. In this case, the interest rate derivatives trader supplements
the ‘incomplete’ CCS by means of an internal FX spot deal with the FX spot trader.
A CCS without an initial principal sum exchange is comparable to an FX forward.
An exchange of two currencies does after all take place at a future moment. One difference is that, for a CCS, this exchange takes place against the FX spot rate while,
for an FX forward, it takes place against the FX forward rate. However, in both cases,
account is taken of the interest rate differences between the currencies. For a CCS,
as with a basis swap, both interest flows are explicitly paid out while, for an FX forward, they are incorporated into the FX forward rate.
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interest rate swaps
7.9 Special types of interest rate swaps
Interest rate swaps are available in many variations. A number of these are identified below.
Accreting swap
Swap in which the notional amount increases during the term
Amortizing swap
Swap in which the notional amount decreases during the term
Roller coaster swap
Swap in which the notional amount goes up and down during the term
Swap in arrears
Swap in which the floating rate is fixed at the end of a coupon period
Callable swap
Swap that can be unwound by the buyer without any costs
Putable swap
Swap that can be unwound by the seller without any costs
Deferred start swap
Swap in which the starting date lies in the future
(forward start swap)
Extendable swap
Swap in which the term can be extended
Circus swap
Swap in which two reference interest rates in two different currencies
are exchanged (e.g. US LIBOR vs EURIBOR)
Zero coupon swap
Swap in which all fixed coupons are paid simultaneously at the maturity
date of the swap using compounded interest (as with the fixed coupon of
an OIS swap)
Rate capped swap
Swap in which the floating rate is capped at a pre-agreed level
Constant maturity swap
Swap in which two floating coupons are paid. The reference rate of at
least one of the legs is an interest benchmark rate with a term longer
than one year
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Chapter 8
Options
Options are financial instruments that give one party a unilateral right to enter into
a transaction at a specific future date or to receive a payment if certain conditions
are met at a future date. The other party has the unilateral obligation to perform
this transaction or to transfer the agreed payment. Option contracts with straight
forward conditions are called plain vanilla options. In addition to plain vanilla options, there is also a wide range of so called exotic option.
The right under an option contract can be used as a hedge against adverse price
movements without losing the opportunity to profit from favourable price movements. The right can, however, also be used to speculate on favourable price movements without being exposed to possible adverse price movements. Thus, the
holder of the right can only win. However, to enjoy such a comfortable position, the
buyer of the option must pay a price: the option premium.
8.1 Option terminology
The right in an option contract can involve
–
–
–
the purchase or delivery of a specific financial value
the settlement of a difference between an interest rate or price concluded
in the option contract and the actual interest rate or price at some future
moment
the conclusion of a specific transaction against a predetermined price or
interest rate
The predetermined price or interest rate in an option contract is called the exercise
price or strike price. The party that obtains the right is called the buyer of the option, the party providing the right is the seller. The selling of options is also called
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writing. To acquire the right in an option contract, the buyer must make a payment
to the seller: the option premium.
A right to purchase a financial value or to receive a sum of money if the market price
is higher than the strike price is called a call option. A right to sell a financial value
or to receive a sum of money if the market price is lower than the strike price is
called a put option. The maturity date of an option contract is called the expiry date.
With regard to the moment when the buyer of an option can exercise his right, there
are four possibilities:
–
–
–
–
European style options: the buyer is only entitled to exercise his right on
the expiry date. This applies for most over-the-counter options.
American style options: the buyer can exercise his right at any time during
the option contract period. This applies for all stock exchange options.
Bermudan options: the buyer can exercise his right at specific, predetermined moments during the term of the option contract.
Window options, the buyer can exercise his right during specific predetermined periods during the term of the option contract.
asian option
An Asian option or average rate option (ARO) is an option contract with cash settlement in which, instead of using the price of the underlying value on the expiry date
(maturity value) as the fixing rate, the average price of the underlying value during
the term of the option contract is compared with the strike price. The average price
is calculated based on a number of fixings at predetermined moments. Because the
volatility of an average value is always smaller than the volatility of a single value,
the premium for Asian options is lower than the premium for plain vanilla options.
barrier options
A barrier option is an option that only exists if certain conditions are met. These
conditions generally refer to whether a specific price level has been achieved for
the underlying value during the period of the option. A barrier option is derived
from a plain vanilla option. The plain vanilla option is in fact the underlying value
for the barrier option. The conditions set in a barrier option determine whether the
underlying plain vanilla option exists or not.
The price level that determines whether or not the underlying option exists or not is
called the ‘trigger’ or ‘barrier’. Although the trigger is generally a price for the underlying value of the plain vanilla option, it can also be a price for another financial value.
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options
The premium for a barrier option is lower than that for a plain vanilla option with
the same strike price and maturity. This is because the chance that a barrier option
pays out is, by definition, smaller than the chance that a plain vanilla option pays
out.
There are two variants of barrier options: knock-out options and knock-in options.
A knock-out option is an option in which the underlying plain vanilla option exists only as long as the trigger is not breached. Once this happens, the underlying
option ceases to exist. A knock-in option is an option where the underlying plain
vanilla option only comes into being when the trigger is breached. Triggers can be
in force for the entire period of the contract, only for a particular part of the period
(the window) or only on the expiry date.
The trigger level for a simple knock-in call option is higher than the strike price
while the trigger level for a simple knock-in put option is lower than the strike price.
For a reverse knock-in call option, the trigger is lower than the strike price while, for
a reverse knock-out option, the trigger is higher than the strike price.
digital option
A European style digital or binary option is an option that involves the right to receive a fixed amount on the expiry date.
example
A European style digital call option has a strike price of 50 euro and a fixed settlement amount of 4 euro if the option is in-the-money on the expiry date. If the price
on the expiry date is, for example, 38 euro, the buyer receives nothing. If the price
on the expiry date is for example, 62 euro, the buyer receives the fixed settlement
amount of 4 euro.
For an American style digital option, a fixed amount is paid out if, during the contract period, the price of the underlying value hits a certain level. Another variant
is an option that pays out a fixed amount if during the total contract period of the
option contract, a certain level is not hit. With digital options, how much the price
of the underlying value differs from the strike price on the expiry date is not important.
Variants on an American style digital option are the double one touch and the double no touch options. A double one touch option is an option that pays out a fixed
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amount if, during the contract period of the option, the price of the underlying value hits a lower limit or an upper limit. A double no-touch option does the opposite
– it pays out if neither the lower nor the upper limit is hit during the term of the option contract.
8.2
The option premium
The option premium must be paid at the beginning of the contract period. The premium for otc options is expressed as a percentage of the underlying value or, with
FX options, as a number of points of an FX rate or as an amount to be paid in one of
the currencies involved.
example
A client wants to buy an over the counter GBP call / USD put option. The premium is
expressed in points of the FX rate: 500 points (= USD 0.0500). The size of the option
contract is GBP 2,000,000.
The premium for this option is USD 2,000,000 x 0.0500 = USD 100,000.
8.2.1 Intrinsic value
The option premium is made up of two parts; the intrinsic value and the time or
expectation value. The intrinsic value of an option is the positive difference between the market price of the underlying value and the exercise price viewed from
the standpoint of the buyer. A call option has intrinsic value if the price of the underlying value is higher than the exercise price. If the price of the underlying value
rises further above the exercise price, the intrinsic value increases proportionally;
in other words, for every unit of the price increase, the intrinsic value increases by
one unit. In the table below, the intrinsic value of a EUR call / USD put option with a
strike price of EUR / USD 1.3400 is shown. The intrinsic value can also be found by
answering the following question: ‘What would the value of the option contract be
if the remaining term of the option contract had been zero?’.
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options
fx forward rate
intrinsic value
eur/usd
(usd)
1.32000
1.33000
1.34000
1.35000.0100
1.36000.0200
1.37000.0300
A put option has intrinsic value if the price of the underlying value is lower than the
exercise price. If the exchange rate is the same or higher than the exercise price, the
intrinsic value of a put option is zero. In the table below, the intrinsic value of a GBP
put / USD call option with a strike price of GBP / USD 1.2200 is shown.
fx forward rate intrinsic value
gbp/usd(usd)
1.19000.0300
1.20000.0200
1.21000.0100
1.22000
1.23000
1.23000
An option is said to be in-the-money (itm), if it has an intrinsic value. If an option
has a high intrinsic value, it is called a ‘deep-in-the-money’ option.
If the price of the underlying value is (nearly) the same as the exercise price then
the option is said to be at-the-money (atm). For currency options, the terms at the
money spot and at the money forward are used. With an atm-spot option, the strike
price for the option equals the current spot rate. With an atm-forward option, the
strike price for the option is the same as the FX forward rate corresponding to the
(remaining) term of the option.
If the market price of the underlying value is lower than the exercise price for a call
option or higher than the exercise price for a put option, the option is called out-ofthe-money (otm). Just as with an at-the-money option, the intrinsic value is then zero.
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8.2.2 Expectations value
The option premium is always equal to or greater than the intrinsic value. The difference between the total option premium and the intrinsic value is called the time
or expectation value. The time or expectation value is determined by the difference between the chance that the intrinsic value will increase and the chance that
the intrinsic value will decrease during the remaining term of the option contract.
Both chances depend on how the price of the underlying value will develop during
the remaining term of the option contract. To make an estimation of this development, a stochastic distribution is used. i.e. the normal distribution. The time value
is determined by three parameters: the price of the underlying value, the remaining
term of the option contract and the volatility of the underlying value.
Figure 8.1 shows the range of possible price movements during the remaining term
for an option with a strike price of 30 while the current price of the underlying ­value
is 25. The intrinsic value of the option is zero. The chance that the option will end
up in-the-money and thus will have an intrinsic value is shown as the shaded area
above the strike level. Since the option has no intrinsic value, the downward potential is zero. The expectations value is indicated by the shaded area above the line
that represents the strike price of 30.
30
25
price of the underlying
price of the underlying
price of the underlying
Figure 8.1
30
27
expiry date time
price of the underlying
If the price of the underlying value rises, first, the time value will also increase. Aftime
expirythe
datedownward
ter all, the upward potential for the intrinsic value increases while
potential is still zero. This is shown in figure 8.2. It is clear that the surface of the
shaded area that represents the expectations value increasses for higher prices of
the underlying value, i.e. 27 and 30 respectively.
33
15030
time value
30
options
price of the underlying
price of the underlying
Figure 8.2
30
30
27
piry date time
price of the underlying
price of the underlying
If the price of the underlying value increases above the strike price, the option will
start
30 to have an intrinsic value. This means, that from that moment the intrinsic
value of the option not only has an upward potential, but also has a downward potential. After all, the holder of the option can lose his intrinsic value. Figure 8.3
time value shows the time value for a price of the underlying of 33. The upward potential is
25
30
represented by the light shaded area and the downward potential is represented by
the dark-shaded area. The expectations value
is represented by the non-shaded area
27
below the horizontal line that represents the strike price of 30.
price of the underlying
expiry date time
expiry date time
30
piry date time
expiry date time
price of the underlying
priceprice
of theofunderlying
the underlying
Figure 8.3
30
33
27
expiry date time
30
27
30
time value
expiry date time
derlying
underlying
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derlying
underlying
expiry date time
expiry date time
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expiry date time
expiry date time
If the left sides of both, figure 8.2 and figure 8.3 are compared, it becomes clear that
the time value of the option shows a symmetrical pattern around the strike price.
The diagrams show that the time value of the call option for a price of the underlying of 27 is equal to the time value for a price of 33.
price of the underlying
Figure 8.4
price of the underlying
30
27
30
27
expiry date time
expiry date time
price of the underlying
expiry date time
The second parameter of the option premium is the remaining term of the option.
During the term of the option contract, the time value decreases. This is shown in
figure 8.4 by the shaded areas.
price of the underlying
time value
The third parameter of the option premium is the volatility. If the volatility of the
underlying value increases, the time value will also increase. In figure 8.5 this is
represented by a wider shape of the curve. As a result of an increase in volatility,
the surface of the shaded area above the line that
represents the strike price will in30
30
crease.
27
27
expiry date time
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expiry date time
options
expiry date time
expiry date time
price of the underlying
price of the underlying
Figure 8.5
30
27
30
27
expiry date time
expiry date time
The option premium is the sum of the intrinsic value and the expectation value.
This is shown in the following equation:
Option premium = Intrinsic value + expectation value
8.2.3
Call put parity
If the price of an FX call option is known, the price of an FX put option can be calculated easily and vice versa. Let us, therefore, look at figure 8.4 once again. The current market price of the underlying value was 33 and the expectations value of the
call option with a strike price of 30 was represented by the non-shaded area below
the line that represents the strike price of 30. This would, however, also be the expectations value of a put option with a strike price of 30 and the same term. After
all, the upward potential of the intrinsic value now lies with decreases in the price of
the underlying value. And the put option is in-the-money if the price is lower than
the strike price. This is shown in figure 8.6.
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of 30
price of the underlying
Time value of a put option (left) and a call option (right) with a strike price
price of the underlying
Figure 8.6 33
30
33
30
time value
time value
expiry date time
expiry date time
This leads to the following important conclusion:
The expectations values of an FX call option and an FX put option with the same
term and strike price are the same.
example
The premium for a EUR call / USD put with a strike price of EUR/USD 1.3700 is
0.0500. The current EUR/USD FX forward rate is 1.3800.
The intrinsic value of this call option is 1.3800 - 1.3700 = 0.0100 and the expectation
value of this call option is, therefore, 0.0500 - 0.0100 - 0.0400.
This means that the expectation value of a put option with the same term and a
strike price of 1.3700 is also 0.0400. Because this put option is out-of-the-money it
holds no intrinsic value. The premium for this put option is thus equal to the expectation value and amounts to: 0.0400.
8.2.4
Delta, gamma, theta, rho and vega: the ‘Greeks’
As already has been mentioned, the level of the option premium is determined
by several parameters which may interfere with each other. One of these param154
options
eters, the future price movement of the underlying value, is estimated on the basis of a stochastic probability distribution. As a result, for the calculation of option
premiums, complex pricing models are required such as the model from Black and
­Scholes, which is often used for European style options. For American style options,
the binomial model is frequently used.
The following parameters are included in all option pricing models:
–
–
–
–
the exercise price of the option in relation to the price of the underlying
value
the volatility of the underlying value
the remaining term of the option contract
the interest rate
The extent to which the option premium changes due to a change in one of the price
determining factors is indicated by the Greek letters: delta (and gamma), vega, theta
and rho. These parameters will be discussed in chapter 12.
8.3 Delta position and delta hedging
Option traders trade in volatility. They leave trading in the underlying values of the
options to the share traders, bond traders, FX spot traders et cetera. When an option trader opens an option position, however, the value of this position is not only
influenced by changes in the volatility but also by, amongst other things, the price
movement of the underlying value. In other words: he also has, in fact, a synthetic
position in the underlying value. The amount of this position depends on the delta
of the option.
If the delta is 0155, for instance, a long position in call options with an underlying
volume of 100,000 shares reacts in the same way to a change in the share price as
a long position of 15,500 in the underlying shares. This synthetic shares position
is called the delta position. The position of an option trader who had sold this otc
call option would react, of course, in the opposite way: as a short position of 15,500
shares. The delta position here would have been -/- 15,500 shares.
To neutralise the effect of price changes in the underlying value, option traders usually take a position in the underlying value that is exactly the opposite of the delta position. This is called delta hedging. The options trader’s position is then called delta
neutral. The value of the composite position now only changes as a result of changes in interest rates, the expiry of the term and the volatility. In an ideal world, options traders would also want to make the value of their position also independent of
changes in the time and in the level of interest rates, however this is not possible. For155
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tunately this is not a great problem because these factors are much less volatile than
the price of the underlying value and thus play no major disruptive role.
Because the delta of an option changes if the price of the underlying value changes,
an option trader must constantly adjust his delta position during the term of the option contract in order to keep his position delta neutral. The size of the transactions
under delta hedging depends on the level of the gamma, representing the changes in the delta. For a low gamma, only small transactions are necessary. For a high
gamma, however, the option trader must buy or sell more of the underlying value to
keep his position delta neutral.
example
An option trader sells a GBP call / USD put option to a client with a strike price of
1.4800. The premium for this option is USD 0.0500 per GBP and the size of the option contract is GBP 1,000,000. The delta for this option is 0.25. The current GBP/
USD FX forward rate is 1.4300.
If the GBP/USD FX forward rate rises by 0.0100 to 1.4400, the option premium rises
by 0.25 x 0.0100 to USD 0.0525. Since the option trader has a short position in the
call option, this means that his position now is in a loss situation. Because the size of
the option contract is GBP 1,000,000, the market value of the option position is -/USD 2,500 (0.0025 x 1,000,000).
To neutralize this position, the option trader performs a delta hedge. The delta position required here is GBP 1,000,000 x 0.25 = GBP 250,000. Because the option position reacts the same as a short position in GBP, the dealer must open a long position
in GBP as a delta hedge. Thus, he buys GBP 250,000 against USD.
For the rise of the GBP/USD FX forward rate, the value of the delta position rises by
GBP 250,000 x 0.0100 = USD 2.500. This compensates for the negative impact of the
rate increase on the short option position.
Note that, as a result of an increase in the GBP/USD FX forward rate, the delta also
has increased, for instance to 0.30. The above option trader must now adjust his
delta position by buying extra British pounds. If the delta of an option position increases, an option trader must buy the underlying value and if the delta of the position falls he must sell the underlying value. As a result, he will constantly suffer
small losses. After all, as market user he buys the underlying value at the ask price
and he sells at the bid price.
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options
The option premium is partially a compensation for these trading losses. When
quoting his option premium, an option trader makes an estimate of the volatility
of the underlying value (implied volatility). A high volatility means that the option
trader expects that he will have to adjust his delta position frequently and must accept many trading losses. Thus, he asks a high option premium.
If the option trader had estimated the volatility correctly, he earns the margin on
the premium that he had calculated. If he underestimated the volatility, however,
he would suffer a loss. The premium is then not sufficient to offset the trading losses resulting from the delta hedge.
The delta hedge can be used to explain the importance of the interest rate for the
option premium. After all, an option trader who has a short position in call options,
must buy the underlying value in order to perform his delta hedge. This will involve
interest costs. Similarly, an option trader who has taken a short position in put options must sell the underlying value. This produces interest income.
example
An option trader sells a call option on a share with a term of three months. The delta
for this option is 0.25. The three month interest rate is 4%. The current price of the
share is EUR 40.00.
Due to the delta hedge, the trader must buy 0.25 shares for each option contract unit.
The interest costs of the delta hedge, therefore, are:
0.25 x EUR 40 x 90/365 x 0.04 = EUR 0.10.
The option trader will have to include the interest cost of EUR 0.10 in the option premium.
To calculate the required delta hedge for a composite position, a trader must calculate the delta of the overall position. A simple example is given below.
delta
delta position mio
Long position in
2 mln
1
2
Bought call
4 mln
0,3
1,2
Sold put
- /- 3 mln
-0,6
1,8
underlying value
Total5
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8.4 Synthetic FX forward
A synthetic forward is an option strategy with the same characteristics as an FX forward contract. An FX forward contract in which a market party buys GBP against
USD, can, for instance, be composed synthetically by buying an atm forward GBP
call / USD put option and simultaneously selling an atm forward GBP put / USD call
option. This is called a ‘long’ synthetic FX forward. For a short synthetic FX forward
contract, a market party must sell the atm forward GBP call / USD put option and
simultaneously buy an atm forward GBP put / USD call option. Since the option premiums for these options are the same, (they both have no intrinsic value and have
the same time value) this strategy is cost neutral or zero cost.
If the GBP/USD FX rate on the expiry date is higher than the strike price, the party
that has composed the long synthetic forward exercises his call option and, as a result, buys GBP at the FX forward rate. If the GBP/USD FX rate on the expiry date is
lower than the strike price, the counterparty exercises his put option and, as a result, sells GBP at the original FX forward rate. The party that concluded the long
synthetic forward now also buys GBP at the original FX forward rate. This means
that, whatever happens to the price, the outcome with the long synthetic FX forward contract is that the party who concluded it buys GBP at the FX forward rate
that applied at the start date of the strategy.
8.5 Interest rate options
Most interest rate options are options with a reference interest rate as the underlying value. Interest rate options are generally cash settled, therefore. On the expiry
date, an interest rate differential is calculated which is translated into an interest
amount. However, there are also interest rate options with a financial instrument
as the underlying value. An example of this is a swaption for which an IRS is the
underlying value. On the expiry date of a swaption, the buyer of this option has the
right to conclude an IRS. However, swaptions can also be cash settled.
8.5.1 Interest rate guarantees / caps and floors
An interest rate guarantee is an otc interest rate instrument in which one party has
the right, at a specific moment in the future, to settle the difference between an
agreed interest rate (the strike rate) and the reference rate, generally a 3 or 6 month
EURIBOR or LIBOR rate. An interest rate guarantee is thus a call or a put option with
the EURIBOR or LIBOR as underlying value. An interest rate guarantee is sometimes
also called a fraption. It is really an option on a bought or sold FRA. Since interest
rate guarantees are a part of caps and floors, they are also called caplets or floorlets.
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A cap is an otc interest rate instrument that gives the buyer the right at various moments during the term to settle the difference between an agreed interest rate (the
strike rate) and the reference rate if this reference rate is above the exercise price. A
cap is actually a series of interest rate guarantees; in this case, caplets. Caps can be
used by parties that hold a floating rate loan and want to cover themselves against
rising interest rates and want still to be able to profit from low interest rates.
The characteristics of the caplets that together form a cap are:
–
–
–
–
the same notional amount
the same exercise price
the same reference rate
consecutive underlying periods
The amount paid out on each individual expiry date is calculated by first expressing
the difference between the level of the reference rate and the strike level as a percentage, if the reference rate exceeds the strike price. This percentage is then applied to
the agreed notional amount and settled over the underlying period for the option. If
the reference rate is lower than the strike rate on an expiry date, the option in question will expire worthless The options with a later expiry date still continue to exist.
A floor is an otc interest rate instrument in which one party has the right, at various
moments in the future, to settle the difference between an agreed interest rate (the
strike rate) and the reference rate, generally a 3 or 6 month Euribor, if this reference
rate is lower than the exercise price.
A floor also consists of a number of consecutive interest rate guarantees with the
same exercise price: floorlets. Floors can be used by market parties who have longterm investments with a floating interest rate and who want to protect themselves
against decreasing interest rates.
the premium for a cap or floor
The premium for a cap or floor is made up of the sum of the premiums for the series
of options that together form the cap or floor. This premium is determined by several parameters.
Just as with any option, the volatility of the underlying value plays a major role. As
the volatility of the interest rate increases, the cap or floor becomes more expensive.
If the remaining term of a cap or floor decreases, the number of caplets or floorlets
in the cap/floor decreases and, therefore, the premium for both a cap and floor will
fall. Finally, the premium of a cap rises when interest rates rise and the premium of
a floor rises when interest rates fall.
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The above mentioned parameters interact with each other. To explain this interaction, it is important to investigate what the underlying value of a cap or floor really
is. Initially, it would seem to be an irs but this is not so. This can be explained by recognizing that a cap consists of a series of caplets. These are individual options each
with their own underlying value. For each caplet, this is the implied forward yield of
the underlying forward period.
A cap with a term of four years and with the three month EURIBOR as reference interest rate, for instance, is made up of fifteen caplets. The underlying value for the
first caplet is the 3s v 6s forward yield, for the second caplet it is the 9s vs 12s forward yield, and so on.
For a normal yield curve, the forward yields lie above the current reference rate (e.g.
3 month EURIBOR). This means that the caplets with a long term are much less outof-the-money than caplets with a short term or they may even be in-the-money.
This is shown in Figure 8.7.
Figure 8.7 Underlying forward rates versus cap strike rate
For a normal yield curve, the caplets for periods that lie further in the future are
therefore more expensive than caplets for periods less far in the future. This phenomenon is reinforced by the fact that the volatility of interest rates measured over
a long period is higher than that for a shorter period. This is shown in figure 8.8
where the volatility is represented by the arrows.
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Figure 8.8
Underlying forward rates and volatility of the various caplets in a four year
cap
This is the reason why the cap premium with a normal yield curve rises more than
proportionately as the term increases. Using the same argument for an inverse yield
curve, floorlets with a long term are more expensive than those with a shorter term.
8.5.2 Interest collar
A long interest rate collar or simply collar is an option strategy in which a party purchases an out-of-the-money cap and simultaneously sells an out-of-the-money floor
with the same term and reference interest rate. The premium for the floor is used to
meet the payment requirements for the premium for a cap. This results in a strategy
in which interest costs remains within a certain range. A short collar is a strategy in
which a party purchases a floor and sells a cap.
example
A company has a medium-term loan with a remaining term of four years and a floating interest rate condition based on three-month EURIBOR. The company believes
that the interest rate over the next four years will not go up but also believes that interest rates will not fall much. The company has a policy to limit interest rate risks
and to strive to achieve the lowest possible interest costs. The current three-month
EURIBOR rate is 2.55% and the four-year IRS rate is 3.40%.
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If the company decides on an interest rate swap, it will fix the interest rate at 3.40%
for four years. As a result, compared with the current money market rate, interest
costs will rise immediately by 0.85%.
The company can also opt for a collar: it then buys, for instance, a 4.50% cap and
‘pays’ for this by writing a 2.70% floor. The effect of this strategy is that interest costs
for the company will vary between 2.70% and 4.50%.
If, on a fixing date, EURIBOR rises above the strike rate for the cap, for example to
5.1%, the company pays 5.1% under the loan (excluding risk premiums) but receives
0.60% under the cap. On balance, the company pays 4.50%.
If, on a fixing date, EURIBOR is lower than 2.70%, for example 2.00%, the company
pays 2.00% under the loan and an additional 0.70% to the bank for the floor sold.
On balance, the company pays 2.70%.
For all EURIBOR rates between 2.70% and 4.50%, neither the cap nor the floor is
in-the-money so that neither option needs to pay out. The total interest costs to the
company are then equal to the interest costs under the loan. This is shown in figure
8.9.
Figure 8.9
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8.5.3 Swaption
A swaption is an otc interest rate instrument that gives the buyer the right to conclude an interest rate swap at a predetermined interest rate on a specific future date.
A payer’s swaption gives the buyer of the option the right to pay the long interest
rate in the underlying interest rate swap. If, on the expiry date, the swap rate in the
market is higher than the exercise price, the buyer will exercise the payer’s swap by
concluding the IRS. He then pays a long interest rate that is lower than the current
market rate. A receiver’s swaption gives the buyer of the option the right to receive
the long interest rate in the underlying IRS.
On the exercise date of an in-the-money swaption, the holder can also choose for a
cash settlement. He will then receive the market value of the underlying swap.
example
A company expects that it will need to take up a loan with a term of 10 years after a
period of one year. The company wants to cover itself against rising interest rates,
but at the same time wants to be able to profit from low interest rates. The company
therefore chooses to buy a payer’s swaption with a contract period of one year and a
strike level of 5.5%.
If, after one year, the company really needs to take up a loan, there are two possible
scenarios:
1.
The IRS rate is higher than the strike rate, e.g. 6%.
The company will exercise the swaption and concludes an IRS in which it pays a
fixed rate of 5.5%. To cover its liquidity position, it takes up a floating rate loan
with a term of 10 years.
2.
The IRS rate is lower than the strike rate, e.g. 4%.
The company will not exercise the swaption and let it expire worthless. To cover
its liquidity position, it takes up a fixed rate loan with a term of 10 years and a
fixed rate of 4%.
If, after one year, the company in the previous example does not need to take up a
loan, with the first scenario the company would probably choose to cash settle the
swaption. With the second scenario, nothing will happen. The company will let the
swaption expire worthless. Figure 7.12 shows a Thomson Reuters pricing tool for
swaptions. The swaption that is shown has a contract term of one year. The underlying value is a payer’s swap with a term of five years and a fixed rate of 3.2502%
and a notional amount of EUR 1,000,000.00. The premium for this swaption is EUR
16,304.59. If this premium had been amortized over the term, this would be 35.48
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basis points per year. For this swaption, the Greek parameters are also calculated.
The delta is for instance 0.5558. This means that the swaption is not so far out-ofthe-money.
Figure 8.10 Premium of a payer’s swaption with a term of one year and an IRS with a
term of five years as underlying value
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Chapter 9
Option Trading
Strategies
A wide variety of option combinations are used for taking trading positions. Roughly speaking, these strategies can be divided into two categories – directional strategies and volatility strategies. The aim of directional strategies is to profit from a
specific price movement in the underlying value. Directional strategies are made up
of a purchased and a sold option (purchased and sold volatility) and are thus volatility neutral. A well known example is spreads. In contrast, volatility strategies aim
to profit from a change in the volatility of the price of the underlying value. On balance, these strategies consist of purchased or sold options. Well-known examples
of volatility strategies are straddles and strangles.
9.1 Bull and bear spread
A bull spread is a directional strategy in which a party simultaneously either buys
and sells a call (long bull call spread) or sells and buys a put (short bull put spread)
with the aim of profiting from a price rise. The two variants, the bull call spread and
the bull put spread are shown in the following table.
bull spread
buysell
Bull call spread
call
call with higher strike price
Bull put spread
put with lower strike price
put
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The main characteristics of a bull call spread are:
–
–
–
For any price of the underlying value below the lower strike price the result
is negative and equal to the net premium paid.
The break-even price is at the lower strike price plus the net premium paid.
For prices of the underlying value above the higher strike price the
maximum result is achieved which is the difference between the two strike
prices minus the net premium paid.
example
A trader buys a EUR call / USD put with a strike price of 1.4000 and sells a EUR call
/ USD put with a strike price of 1.4500. The premium for the first mentioned option
is 0.0200 and the premium for the second mentioned option is 0.0075. The net premium payable is, therefore, 0.0125.
The result for the strategy is minus 0.0125 for all FX rates of the underlying value at
expiry under 1.4000. The break-even FX rate for this strategy is 1.4125 and this strategy gives a maximum return of 0.0375 for FX rates of the underlying value of 1.4500
or higher at maturity.
bear spread
A bear spread is a directional strategy in which a party simultaneously either buys
and sells a put (long bear put spread) or sells and buys a call (short bear call spread)
with the aim of profiting from a price fall. The two variants are shown in the following table.
bear spread
buysell
Bear put spread
put
put with lower strike price
Bear call spread
call with higher strike price
call
The main characteristics of a bear put spread are:
–
166
For any price of the underlying value above the higher strike price the
result is negative and equal to the net premium paid.
option trading strategies
–
–
The break-even price is at the higher strike price minus the net premium
paid.
For prices of the underlying below the lower strike price the maximum
result is achieved which is the difference between the two strike prices
minus the net premium paid.
example
A trader buys a EUR put / USD call with a strike price of 1.3800 and sells a EUR put
/ USD call with a strike price of 1.3300. The premium for the first mentioned option
is 0.0200 and the premium for the second mentioned option is 0.0075. The net premium payable is 0.0125.
The result for the strategy is minus 0.0125 for all FX rates at maturity above 1.3800.
The break-even FX rate for this strategy is 1.3675 and this strategy produces a maximum of 0.0375 for FX rates of 1.3300 or lower.
Sometimes, call and put spreads are combined. A combination of a bull call spread
and a bear put spread is called a long box and a combination of a bear call spread
and a bull put spread is called a short box.
9.2 Straddle
A straddle is a combination of a call option and a put option with the same contract volume, exercise price and term in which a market party either buys or sells
both options. In practice, the exercise price for both options is not much different
from the market price of the underlying value; both options are thus at-the-money (atm).
long straddle
A long straddle is a combination of a purchased call and a purchased put with the
same contract volume, exercise price and term. A market party uses this strategy if
he wants to profit from large price movements in the underlying value irrespective
of the direction. This party is called the buyer of the straddle.
To realize a profit on a long straddle, a considerable price change is required. The
buyer of the straddle is, after all, paying the option premium twice. If there is little movement in the price, the expectation value decays and both options expire
worthlessly. At the expiry date, the loss is then equal to the option premium paid for
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both options. Figure 9.1 shows the result of a long straddle for different prices of the
underlying value at maturity.
Figure 9.1 Long straddle
The main characteristics of a long straddle are:
–
–
–
The worst result is achieved if the price of the underlying value on the
expiry date equals the strike price; the trader then loses the total premium
paid.
The break-even prices are at the strike price plus the total premium paid
and at the strike price minus the total premium paid.
Since the strategy is made up only of purchased options, with stable prices
of the underlying and unchanged volatility, the value decreases as time
passes (declining time value because of the negative thèta).
example
An option trader enters into a long straddle position at an FX rate of 1.4500. The premium for the call and the put are both 0.0200.
If, on expiry, EUR/USD is 1.4500, the trader suffers a maximum loss of 0.0400.
The break-even FX rates of this strategy are 1.4100 and 1.4900.
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option trading strategies
short straddle
A short straddle is a combination of a written call and a written put with the same
contract volume, exercise price and term. A market party who enters into a short
straddle position is called the writer of the straddle.
A market party uses this strategy if he wants to profit from small price movements
in the underlying value irrespective of the direction. He profits from the decay in
the expectation value of the option premium. After all, for small price movements,
neither the call nor the put will be exercised. The result for the strategy is then equal
to the premiums received.
However, if the price of the underlying value changes significantly, the writer of a
straddle will suffer a considerable loss. This is because with large price rises, the call
option will be exercised while for large price falls, the put option will be exercised.
Figure 9.2 shows the result of a short straddle for different prices of the underlying
value at maturity.
Figure 9.2 Short straddle
The main characteristics of a short straddle are:
–
–
The best result is achieved if the price of the underlying value on the
expiry date equals the strike price; the trader then earns the total premium
received.
The break-even prices are at the strike price plus the total premium paid
and at the strike price minus the total premium paid.
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guide to treasury in banking
–
Since the strategy is made up only of sold options, with stable prices and
volatility, the strategy becomes more profitable as time passes (the negative
thèta works in favour of the trader).
example
An option trader concludes a short straddle at an FX rate of 1.3800. The premium for
the call and the put are both 0.0250.
If, on expiry, EUR/USD is 1.3800, the trader gains 0.0500.
The break-even FX rates are 1.3300 and 1.4300.
9.3 Strangle
A strangle is a combination of a call option and a put option with the same contract
volume, the same term, but with different exercise prices. The exercise price of the
call option is generally higher than the current market price of the underlying value
and the exercise price of the put option is lower than the current market price of the
underlying value, i.e. both options are out-of-the-money (otm).
With a long strangle, a market party buys both the call option and the put option.
For a short strangle, the market party sells both options. The market party that enters into a strangle has the same objective as with a straddle; he wants to profit from
either large or small price changes, regardless of the direction. The advantage of a
long strangle over a long straddle, however, is that the premium paid by the buyer is
lower. The chance of making profit is also lower, however. Figure 9.3 shows the result of a long strangle for different prices of the underlying value at maturity.
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option trading strategies
Figure 9.3 Long strangle
The main characteristics of a long strangle are:
–
–
–
the worst result is achieved if the price of the underlying value on the
expiry date is between the two strike prices; the trader then loses the total
premium paid.
the break-even prices are at the lower strike price minus the total premium
paid and at the higher strike price plus the total premium paid
since the strategy is made up only of purchased options, with stable prices
and volatility it loses value as time passes (declining time value because of
the negative thèta)
example
An option trader concludes a long strangle at strike rates of 1.4100 and 1.4500. The
premium for the call and the put are both 0.0200.
If, on expiry, EUR/USD is between 1.4100 and 1.4500, the trader loses 0.0400. The
break-even FX rates are 1.3700 and 1.4900 respectively.
The advantage of a short strangle over a short straddle is that the seller has a smaller chance of loss. A strangle, however, earns less premium income. The main characteristics of a short strangle are:
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guide to treasury in banking
–
–
–
the best result is achieved if the price of the underlying value on the expiry
date lies between the two strike prices; the trader then earns the total
premium received.
the break-even prices are at the lower strike price minus the total premium
paid and at the higher strike price plus the total premium paid.
since the strategy is made up only of sold options, with stable prices and
volatility, the strategy gains value as time passes (declining time value
because of the negative thèta works in favour of the trader).
example
A trader concludes a short strangle at strike rates of 1.2800 and 1.3400. The premium for the call and the put are both 0.0300.
If, on expiry, EUR/USD is between 1.2800 and 1.3400 then the trader gains 0.0600.
The break-even FX rates are 1.2200 and 1.4000 respectively.
Figure 9.4 shows the result of a short strangle for different prices of the underlying
value at maturity.
Figure 9.4 172
Short strangle
Chapter 10
Organization and
Execution of Risk
Management with
Banks
During the last twenty years, risk management has become by far the most important topic for banks. Risk management is now considered to be a process that must
be understood and acted on in every part of a bank and must be performed by independent departments and committees throughout the bank. Most banks have set
up dedicated central risk management committees for Credit Risk, for Operational
Risk, for Market Risk as well as a committee for the risks that directly relate to the
bank’s balance sheet structure, i.e. the Asset & Liability Committee.
A bank’s financial markets division carries out financial markets transactions on
behalf of the bank. A number of these financial transactions are concluded with respect to the execution of the bank’s risk management policy. For instance, banks
conclude interest rate derivatives contracts in order tot cover the interest rate risk
in their balance sheet.
All banks draw up a document that contains the types of financial instruments that
they want to trade, for which purpose these financial instruments may be used and
to what extent. This is called limit control sheet. If a bank considers to add a new
type of instrument to the limit control sheet, a committee first investigates the consequences that are involved. This investigation is referred to as the new product approval process.
10.1
Overview of banking risks
Apart from their responsibility of money creation, banks, just like other financial
institutions, also perform a so called transformation function on behalf of their clients. Furthermore, they also act as a market maker. As a result, they are confronted
with several types of risks.
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credit risk
If an investor for example invests his money with a bank he only has the bank as his
debtor. The bank, however, has all its clients as its debtor. This implies that the investor by investing his money in the bank has in fact spread his risk over the whole
loan portfolio of the bank. This type of transformation is called risk transformation.
The related risk for a bank is credit risk in the form of lending risk, i.e. the risk that
a client of a bank will not be able to pay back the principal of the loan or the interest
on the loan. As a result, the bank has to write off part of its assets whilst its liabilities remain equal. As a consequence, the bank’s equity position deteriorates.
interest rate risk
If the contract terms of a bank’s assets and liabilities differ, it is very likely that the
terms for which the interest rates are fixed, i.e. the interest terms, differ as well. As
a result, banks run an interest rate risk. This is the risk that the net interest income
of a bank will be negatively affected by a change in the market interest rates. If, for
instance, the average remaining interest term of the funding is shorter than the average remaining interest term of the granted loans, this means that the interest rate
of the funding will be reset earlier than the interest rate of the loans. And in case of
rising interest rates, this means that the funding of the bank on average will be at a
higher interest rate than the bank’s loans. As a result, the net interest income of the
bank will decrease.
fx risk
FX risk is the risk that a bank loses money as a result of the fact that it has assets or
claims in a foreign currency that are not matched by a liability in that currency or
vice versa. An FX exposure can result, for example, from a foreign investment, from
the fact that an FX trader has deliberately opened a position, or from the fact that
the bank operates as a market maker.
As a market maker, a commercial bank is always prepared to act as counterparty for
its clients in e.g. foreign exchange transactions or transactions in derivatives such
as interest rate swaps. As a result of these transactions, the client’s risk is transferred to the bank. For instance, if an American company has a surplus of euros,
it runs the risk that the euro exchange rate against the US dollar will deteriorate.
To cover this risk, the company can sell the euros to an American bank who acts as
market maker. As a result, the American bank in turn has a surplus in euro, a socalled long position, and therefore runs a foreign exchange risk (FX risk). To offset
this risk, a bank normally immediately concludes the opposite transaction with another market party, commonly a bank.
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organization and execution of risk management with banks
counterparty credit risk and settlement risk
If this same client concludes an FX forward transaction with the bank, apart from
the FX risk, the bank is also faced with another risk. After all, if the client will default during the term of the FX forward transaction, the transaction will not be executed. This means that, at the pre-agreed settlement date, the company will not
transfer the euros to the bank. Of course, in this case, the bank will not transfer the
pre-agreed amount of US dollars to the client either. However, because the bank has
concluded an offsetting transaction at the contract date, it still has the obligation
to sell euros against US dollars at the settlement date. If the bank would not take
any further action, it has a short position in US dollars during the remaining term
of the contract and, at the settlement date, it would still have to buy the euros at the
than prevailing market price in order to be able to fulfil its settlement obligations.
Banks, however, usually take immediate action if a counterparty defaults by concluding a so-called replacement transaction. In this case the bank would buy euros
against US dollars with the same settlement date as the original transaction that it
had concluded with the defaulting company. However, in the meantime the FX rate
may have deteriorated which means that in the replacement transaction the bank
has to pay more US dollars for the same amount of euros than in the original transaction. In this case, the bank will still make a loss. This risk is referred to as replacement risk, pre-settlement risk and, more commonly, counterparty credit risk.
If nothing would happen during the contract term, the bank still runs the risk that it
transfers the US dollars to the company on the settlement date whilst the company
will not transfer the euros. This risk is called settlement risk.
market risk
Banks may allow some of their staff to hold trading positions. This is referred to as
proprietary trading. As a result, banks run market risk. This is the risk that the market value of trading positions will be adversely influenced by changes in prices and/
or interest rates. Since the recent credit crisis, however, banks have become more
prudent in allowing their traders to take positions.
Open positions can either be the result of an intentional action of a trader or be the
consequence of the fact that banks operate as a market maker for a large number
of financial instruments. Generally, a bank that has concluded a transaction with
a customer will directly offset this transaction in the market. Sometimes, however,
this is not possible or prudent. For example if the market is illiquid or if the transaction is for an extremely large amount, the bank is stuck with a (temporary) open
position.
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operational risk
Finally, banks run operational risk. Operational risk is the risk that an organization
loses money or incurs a reputational damage as a result of the fact that something
goes wrong in the business process. In general, four categories of risk can be distinguished: organization, human conduct, computer systems and external factors.
Operational risk also includes the risk that the organization will be legally held responsible if anything goes wrong in the course of its operations, i.e. legal risk.
10.2
The central risk management organization of a bank
It is of crucial importance for a bank that all banking risks are managed adequately.
If this is not the case, then a bank runs the risk that it will collapse or that it must be
saved by the Government. Every bank has a control structure that consists of three
layers: self-control, dedicated control and operational audits.
Self-control is a form of control by which departments keep track of the quality of
their own activities, for instance by checking daily whether all transactions have
been processed. Self-control is often based on the organizational principle of dual
control, also known as the four eye principle, which requires a mini­mum of two employees to be involved in certain specific tasks. A typical exam­ple is the transfer of
large money transfers, whereby one employee prepares the payment and another
sends it.
Dedicated control is a form of control exerted by specially appointed business units.
Dedicated control is normally performed by independent committee and departments throughout the bank. Most banks have formed a risk management structure
that more or less looks like the one that is shown in figure 10.1.
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organization and execution of risk management with banks
Figure 10.1 Risk management structure of a bank
Board of directors
CEO/CFO
Centralized Risk Management Committees
Operational
Risk
Committee
Busines
line 1
Busines
line 2
Financial
Markets
Operational
Risk unit
Operational
Risk unit
Operational
Risk unit
Credit Risk
unit
Credit Risk
unit
Credit Risk
unit
ALM unit
ALM unit
ALM unit
New Product
Approval Comm.
New Product
Approval Comm.
New Product
Approval Comm.
Central
Credit
Committee
ALCO
Market Risk
unit
Figure 10.1 shows three centralized risk committees: the central operational risk
committee, the central credit risk committee and ALCO. In each of these committees, the board of directors is represented by the chief risk officer (CRO) and all committees report directly to the board of directors. Each centralized risk committee
first establishes a charter that contains the purpose of the committee, the composition of the committee, the meeting schedule, the and the committee’s responsibilities. This charter then must be formalized by the board of directors.
Examples of the responsibilities of central risk committees are to develop a central
risk policy and to monitor whether this policy is adhered to, to advice the Board of
Directors about the parameters of the group’s risk/reward strategy and to monitor
the alignment of the risk profile with the defined risk appetite and with current and
future capital requirements. Finally each central risk committee has the responsibility to oversee all risks that are inherent in the group’s operations.
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guide to treasury in banking
Figure 10.1 also shows that for each business unit, a decentralized risk committee is
formed. The responsibility of the decentralized committees is to make sure that the
centralized risk policy is adhered to in the business units that they are related to. All
decentralized risk committees act independent of the business unit that they monitor and report only to the centralized risk committee.
10.2.1 Asset and liability management committee
Banks transform maturities and currencies to meet their customers’ requirements.
These transformations result in liquidity risk, interest rate risk and currency risk
which need to be managed. This is the responsibility of the Asset and Liability Management Committee (ALCO). The members of ALCO are, amongst others, the board
member that is responsible for risk management, the head of the treasury department and the head of the economic bureau.
The asset and liability committee is firstly responsible for the management of all
kinds of mismatches in the bank’s balance sheet and for its performance measurement. ALCO defines and monitors the following objectives: gap management or
mismatch management with respect to interest rate risk, pricing management and
liquidity management.
Interest rate risk is the risk of a bank’s net interest income falling as a result of a
change in interest rates. The fixed-rate periods of a bank’s assets are usually longer than the fixed-rate periods of its liabilities. Examples of assets are, for instance,
mortgage loans and company loans with long interest maturities. Examples of liabilities are deposits with short interest maturities. As a result, the interest conditions of the assets are adjusted more slowly than the interest conditions of the
liabilities. This effect causes the net interest income to fall in the case of an interest
rate increase. The management of the interest rate risk is called interest rate risk
management or gap management. Gap management includes the setting of specific gap management limits, maturity gap targets for each gap period, the desired
maturity for new deposits and loans, the use of alternative investment and funding
instruments and the review of structural interest rate risk positions.
Pricing management includes the definition of specific pricing management limits, targets and guidelines, the setting of profitability and growth targets and the
formulation of specific pricing guidelines to achieve desired profitability, growth,
liquidity or gap targets.
In this respect, ALCO is responsible for funds transfer pricing. Funds transfer pricing is designed to allocate interest margins and interest rate and funding or liquidity risk to the different business units of the bank. Funds transfer pricing is applied
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organization and execution of risk management with banks
to both assets and liabilities and effectively locks in the margin on loans and deposits by assigning a transfer rate that reflects the repricing and cash flow profile of
each balance sheet item. A by-product of funds transfer pricing is that it effectively
allocates responsibilities between the organizational business units and the treasury department. Funds transfer pricing rates must include appropriate premiums
for all elements associated with the banks funding cost such as a liquidity premium.
With respect to liquidity management, ALCO is responsible for setting the framework for the management of liquidity risk. In this respect, it is responsible for setting the liquidity risk policy and the funding plan for the entire bank.
Finally, ALCO is responsible for capital management. ALCO manages the allocation
of the financial resources of the bank, in general, and capital, in particular, and tries
to allocate the available (economic) capital to the business units with the highest
positive impact on the profitability and shareholder value. As a result, ALCO periodically reallocates capital among business portfolios.
10.2.2 Credit risk committee
Credit risk is the risk that a counterparty of a bank fails to meet its obligations as a
result of which a loss originates. In the centralized credit committee the credit policy of the bank is stated and reviewed. The credit risk committee decides on topics
like the composition of the loan portfolio including the allowed concentration in
the loan portfolio, the general levels of the applied credit spreads, the development
in non-performing loans and the market share, all at a portfolio level.
In general, the responsibilities of the centralized credit risk department are to approve and review the framework for the management of credit risk, to review the
performance of the credit portfolio, to approve credit facilities and equity underwriting exposures outside the authority delegated to the decentralized credit committees and to review the bad debt portfolio.
Besides the centralized credit risk committee, every business unit has its own
decentralized credit risk unit. For instance, in a regionally organized bank, each
country may have its own credit committee, next, each region and, next each subregion etcetera. The responsibility of these units is to assess proposals for new
credit lines, for the increase in credit lines and, occasionally, proposals for individual transactions. Each decentralized credit committee is authorized to approve
proposals up to a certain amount. If the requested credit exposure exceeds the authority of a decentralized credit committee, the proposal is send to the next higher
credit committee.
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10.2.3 Market risk committee
Market risk is the risk that the market value of trading positions will be adversely
influenced by changes in prices and/or interest rates. For banks, market risk occurs
because traders in the Financial Markets department trade for account and risk of
the bank. This is called proprietary trading. Many banks execute trading activities
in different dealing rooms. The main responsibility of the central market risk committee is to control the combined market risk for the entire organization. The central market risk committee is normally a sub-committee of ALCO and is responsible
for approving and reviewing the framework for the management of market risk, for
approving the limit and control sheet, for approving new instruments based on the
advice of new product approval committees and, finally, for reviewing the monitoring of the market risk performance and the exposure against limits.
10.2.4 Operational risk committee
The centralized operational risk management (ORM) committee is responsible for
setting up the framework for the management of operational risk and for monitoring the performance of operational risk management.
The centralized operational risk committee is sometimes also responsible for managing compliance risk. In this respects its responsibilities are to review the compliance risk processes that are in place in order to anticipate and effectively manage
the impact of regulatory change on the bank’s operations. ORM also oversees compliance by the bank with applicable laws, regulations and regulatory requirements
that may impact the bank’s risk profile and discusses with management and the external auditor any correspondence with regulators or government agencies and any
published reports that raise issues material to the bank. Finally, ORM reviews the
procedures for the receipt, retention and treatment of complaints received by the
bank including whistleblower concerns received from officers of the bank.
For every single business unit, banks also have formed a decentralized ORM department. These decentralized units are responsible for identifying the operational
risks of the business unit that they are dedicated to and to check whether the line
managers control their operational risks according to the central policy.
The decentralized operational risk units also play a supporting role in relation to
the line managers. They help them to identify the operational risks and advice on
measures that can be taken to control these risks. They also give information to employees in order to increase their awareness for operational risks. Finally, the decentralized departments are responsible for drawing up incident reports.
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organization and execution of risk management with banks
10.3Limit control sheet
One of the most important documents in the Financial Markets department is a
­limit control sheet. A limit control sheet (LCS) is a document in which a bank describes which instruments will be traded and in which currencies, which departments are allowed to trade these instruments and whether proprietary trading is
allowed and, if so, to what extent. The limit control sheet is drawn up by a committee in which staff from market risk management, product control, credit risk and
departments that are responsible for the valuation models are represented. The LCS
is reviewed periodically, e.g. annually, and on an ad-hoc basis, in the case of significant changes in market conditions or when a new instrument is introduced.
A limit control sheet consists of two sections. The first section defines the scope of
the activities of the financial markets department. For all business locations and
for each instrument, the LCS indicates whether only client business is allowed or
whether proprietary trading is also allowed and, if so, in what proportion. For all locations and for all instru­ments, the LCS also defines the systems in which positions
are maintained and the systems in which the market risk is measured. The first
section also contains the product mandate. This product mandate is split into two
parts, the approved product list and the approved tenors and currencies list. The
first list provides an overview of the ways in which all business units are allowed to
trade in the different instruments, e.g. only internally with other business units as
counterparty or also externally, with external counterparties. The second list provides an overview of all approved currencies and tenors.
The second section of the LCS contains the trading limits that restrict the market
risk that the proprietary traders are allowed to take.
10.4New product approval process
Before a new financial instrument is introduced, it is assessed in a so-called new
product approval process. This process is designed to assess the suitability of the
new instrument and includes discussions by representatives from a range of the
bank’s functions, including front-office, back-office, market risk management,
credit risk management, compliance, legal, accounting, IT and finance.
The following topics, among others, should be addressed in a new product approval
process: whether the instrument complies with internal and external regulations,
whether the computer systems are capable of capturing the instrument, whether
staff and customers are able to understand the features of the instrument, the profitability of the instrument, policies to make sure the bank creates and collects sufficient documentation to document the terms of transactions, to enforce the material
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obligations of counterparties and to confirm that customers have received any information they require about the instrument and, finally, policies and procedures to
be followed and controls used by internal audit to monitor compliance with those
policies and procedures.
The process should also include a discussion of whether an instrument should really be considered as a new instrument. When determining whether an instrument is
really new, a bank may consider a number of factors including structural or pricing
variations from existing products, whether the product targets a new group of customers or a new requirement from customers, whether it raises new compliance,
legal or regulatory issues and whether it would be offered in a way that would be
different from standard market practices.
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Chapter 11
Overview of the
Basel Accords
Since 1988, banks must hold capital as a buffer to the possible negative consequences of the risks that they take. This requirement is the most important part of the
Basel Accord, i.e. the recommendations of the Basel Committee. The Basel Committee is a consultation body formed by board members of central banks. The solvency
recommendations of the Basel Committee have been incorporated into the national legislation of all OECD countries, for instance in the Capital Adequacy Directive
(CAD) of the European Union. The capital that banks must hold to comply with legislation is called regulatory capital.
Under the new Basel rules, however, banks will also have to comply with regulations with respect to liquidity. In this new version of the Basel Accords, a leverage
ratio is re-introduced for banks and also the solvency requirements will become
more strict.
11.1 Basel I
The first Basel Accord stems from 1988 and originally only contains solvency requirements for lending risk and replacement risk.
According to the original Basel Accord, Basel I, each bank must at least satisfy the
Cooke Ratio or BIS Ratio. In the first Basel Accord from 1988, this ratio was set at
8%. The first version of the Basel Accord was very straightforward: banks had to
set aside at least 8% capital against the nominal size of their loans. The Basel I accord didn’t take into account the quality of the counterparty; the 8% requirement
applied both, for instance to a new snack bar and to Microsoft. Exceptions were only
made for loans to governments of OECD countries and banks. The first were weighted at 0%; in other words, they were solvency-free. Loans to banks in OECD countries were weighted at 20% and loans to banks in non-OECD countries at 50%. In
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this respect the term risk-weighted asset (RWA) was introduced. The RWA of a 100
million loan to a bank in a non-OECD country was 50% x 100 million i.e. 50 million.
A bank that invested in this loan needed to hold an amount of capital equal to 8% of
50 million i.e.4 million.
In 1997, the Accord was extended by the Market Risk Amendment. From that moment, banks also had to hold capital for their market risk. The required capital was
set at 3 to 4 times the reported VaR, calculated for a holding period of 10 days and a
confidence level of 99%.
11.2 Basel II
In 2007, a complete new version of the Basel Accord was drawn up: Basel II. This
new version was based on three pillars:
1. A bank must set aside sufficient guarantee capital to be able to withstand
any losses resulting from credit risk, market risk and operational risk.
2. A bank must have a risk management process that ensures that it is able
to manage its risks and must have a control system that ensures that this
management is effective, i.e. the internal capital adequacy assessment
process (ICAAP);
a bank must set aside capital for excessive interest rate risk;
supervisors must adhere to the requirements in the SREP, i.e. the super­
visory review and evaluation process.
3. In its external reports (e.g. the annual report), a bank must show the
management framework it has set up, must show how it measures its risks
and must indicate the size of its risk.
The most important point of criticism of the banks regarding Basel I was that the
Accord hardly differentiated between the differences in the creditworthiness of the
banks’ customers. The banks themselves, however, had already made this distinction between the trustworthiness of their customers for a long time. They used internal models to determine the size of the credit risk whereby their customers were
split into different risk classes each with its own probability of default.
The outcomes of these models, however, were significantly lower than those produced by the straightforward approach of Basel I. Banks therefore started a lobby to
change the solvency requirements of Basel I. This lobby was successful and in 2007
the Basel II accord was introduced. With regard to the capital requirements, this new
accord differed in two aspects from the first accord. Firstly, Basel II made a distinction between the creditworthiness of debtors and, secondly, capital requirements for
operational risk were introduced. The BIS ratio, however, remained at 8%.
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overview of the basel accords
Banks must periodically report the size of their risks to the regulator. For credit risk
and market risk they may choose either to use standard reports or to report the outcomes from the internal models that they have created themselves for measuring
their risks. For operational risk banks use standardized reporting methods.
11.2.1 Capital requirement for credit risk
Banks can report the size of credit risk in various ways. The first way, the Standardized Approach, is related to the way in which banks had to report under Basel
I where they reported the nominal value of their loans, in some rare cases adjusted
by a weighting. In Basel II many more weighting factors are distinguished. These
weighting factors are based on the rating from external rating agencies, as is shown
in figure 11.1.
Figure 11.1
Weighting factors with the Standardized Approach
aaa - aa-
a+ - a-
bbb+ - bbb-
bb+ - b- below b-
unrated
Governments 0%
20%50%
100%150% 100%
Banks < 3 months
20%
50%
100%
100%
150%
100%
Banks > 3 months
20%
20%
20%
50%
150%
20%
Corporates
20%
50%100%
100%150% 100%
The second way is to report the outcomes from their own credit risk models. This
method of reporting is called the Internal Rate Based Approach (IRB). Based on the
input for their models, banks determine the value for two variables: the expected
loss and the unexpected loss or credit value at risk. The expected loss is the mathematical expectation of credit loss for the next coming year. Banks may make provisions to form a buffer to withstand the expected loss. The credit value at risk
identifies the maximum amount above the expected loss that a bank can lose with a
specific confidence level. The confidence level in Basel II is set at 99.9%. According
to Basel II, a bank must set aside at least as much guarantee capital as the calculated
credit value at risk.
Since a bank that uses the IRB method reports the size of the loss instead of a nominal value, the reported outcome is multiplied by a factor of 12.5 in order to indicate
the RWA.
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example
A bank that uses an internal credit risk model reports a credit VaR of EUR 2.3 billion.
The RWA is 12.5 x 2,3 billion = 28,75 billion.
If this bank holds an amount of regulatory capital of EUR 3.0 billion, the BIS ratio for
this bank is:
Bis Ratio = 3.0 billion / 28.75 billion x 100% = 10.43%
11.2.2 Capital requirement for market risk
As from the end of 1997 banks are required to measure and apply capital charges in
respect of their market risks in addition to their credit risks. Market risk is defined
as the risk of losses in on and off-balance sheet positions arising from movements
in market prices. The risks subject to this requirement are:
–
–
the risks pertaining to interest rate related instruments and equities in the
trading book;
foreign exchange risk and commodities risk throughout the bank.
fx risk
Banks usually have assets and or liabilities denominated in foreign currency. If the
amount of assets in a foreign currency does not match with the amount of liabilities in that foreign currency, than the bank is exposed to FX risk. In the Basel rules,
this position is considered as a market risk position and banks have to hold capital
to cover this risk. The discrepancies between the assets and liabilities in the balance
sheet are referred to as the net FX spot position fo a bank. Banks, however, may decide to keep a certain net FX spot position in order to protect their capital adequacy
ratio against the effects of fluctuations in exchange rates. This position is called the
structural FX position and if the bank can proof that this position indeed protects
its capital adequacy ratio, then this position is excluded from the capital requirement. Apart from the FX spot position, the FX risk of a bank can also be the result of
other factors such as open forward postions.
According to the Basel Amendment to the Capital Accord to incorporate market
risks, a bank’s net open position in a currency should be calculated by summing:
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overview of the basel accords
–
–
–
–
–
–
the net spot position (i.e. all asset items less all liability items, including
accrued interest, denominated in the currency in question);
the net forward position (i.e. all amounts to be received less all amounts to
be paid under forward foreign exchange transactions, including currency
futures and the principal on currency swaps not included in the spot
position);
guarantees (and similar instruments) that are certain to be called and are
likely to be irrecoverable;
net future income/expenses not yet accrued but already fully hedged (at
the discretion of the reporting bank);
depending on particular accounting conventions in different countries,
any other item representing a profit or loss in foreign currencies;
the net delta-based equivalent of the total book of foreign currency
options.
The responsibility to determine the open FX position lies with the back-office and
is referred to as position keeping. Banks should report their open FX position to the
regulator on a frequent basis. They have a choice between two alternative measures, i.e. the shorthand method which treats all currencies equally and the use of
internal models.
Under the shorthand method, the nominal amount (or net present value) of the
net position in each foreign currency and in gold is converted at spot rates into the
reporting currency. The overall net open position is measured by aggregating the
sum of the net short positions or the sum of the net long positions, whichever is the
greater plus the net position (short or long) in gold, regardless of sign. The capital
charge is calculated as 8% of the overall net open position.
Figure 11.2
currency yen usd chf cad gbpgold
Position
100 bn
5 bn
long
long short short shortlong
-2 bn
-4 bn
-3 bn
Valuation rate
130
1.1000
1.1500
1.5000
0.8000
1.1000
Position in EUR
+0.77 bn
+ 4.55 bn
-1.74 bn
-2.67 bn
- 3.75 bn
+ 273 M
Total long/short
+ 5.32 bn
-8.16 bn
+ 300M
+273 M
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guide to treasury in banking
In this example, the sum of the net short positions (-8.16 bn) is higher than the sum
of the net long positions (5.32 bn). The capital charge in this example would, therefore, be 8% of sum of the net short currency positions (i.e. 8.16 bn) and the net position in gold (0.273 bn) = 8.433 x 8% = 0.6746 bn. The capital requirement would,
however, probably be lower would the bank have used an internal model.
Most banks, therefore, use the outcomes from own models to report the size of their
market risk to the supervisor. Here they must use a confidence interval of 99% and
a holding period of 10 days. In addition, the data used must cover a period of at least
one year, i.e. 250 trading days.
According to Basel II, banks must multiply the outcomes of their market risk models (VaR models) by a correction factor of at least 3 and at the most 4.
example
A bank has calculated its market risk with the use of an internal model. The bank
reports a 10-day VaR of 800,000 US dollars. The model of this bank is rated yellow
and the supervisor has assigned a plus factor of 0.5 which means that the correction
factor is 3.5.
The bank’s market risk is now set by the regulator at 3.5 x 800,000 = USD 2,8 billion.
The RWA for market risk = 12.5 x USD 2,8 billion = USD 35 billion.
To cover this risk, this bank has to hold 8% x USD 35 billion = USD 2,8 billion equity.
basel 2.5
During the 2007-2009 crisis, it became clear that the capital requirements for
market risk for common trading positions were not sufficient. The Basel Comittee
recognized two reasons for this. First, the maximum correction factor of 4 was obviously not sufficient to capture the large losses that banks incurred during this period. Second, the losses in the banks’ trading positions in bonds, CDSs and tradable
loans appeared to be not only the result of a change in interest rates but also the
result of a loss in liquidity and of the deterioration of the creditworthyness of the
counterparties. To overcome these shortcomings, for regular trading positions the
Basel Committee has added two additional capital requirements to the existing Var
requirement: Stressed Stressed VaR and the Incremental Capital Charge (ICR).
The Basel Committee defines Stressed VaR as a measure which ‘is intended to replicate a value-at-risk calculation that would be generated on the bank’s current port188
overview of the basel accords
folio if the relevant market factors were experiencing a period of stress; and should
therefore be based on the 10-day, 99th percentile, one-tailed confidence interval value-at-risk measure of the current portfolio, with model inputs calibrated to historical data from a continuous 12-month period of significant financial stress relevant
to the bank’s portfolio’ (quoted from BCBS). This means that, apart from a regular
VaR banks should measure their Value at Risk by using the market data of a specific time interval of significant financial stress. Banks are free to choose whatever
stressed period they like as long as they are bank-specific and according to the Basel
committee ‘the most challenging given the unique character of the bank’s portfolios’. The stressed VaR should be added to the regular VaR.
The incremental capital charge is a second additional capital requirement that aims
at capturing the effects of default and migration risks in credit instruments such as
bonds and CDSs which are not captured by VaR.
Taken as a whole, the capital requirement for market risk according to Basel 2.5 is:
Capital = max ( VaR, k * ‘average VaR over 60 days’) + max (Stress VaR, k * ‘average Stress
VaR over 60 days’) + IRC.
Where:
–k ≥ 3
–
VaR is measured at 99% confidence level over a ten-day period and combines both general and specific market risk
–
Stress VaR is computed from a stressful period
–
IRC is calculated at 99% confidence level over a 1 year period.
For so-called correlation trading portfolios a specific capital requirement is used,
i.e. the Comprehensive Risk Measure. This measure captures not only incremental
default and migration risks, but all price risks including basis risk. For securitization positions that are not qualified as a correlation trading portfolio, a standard
capital charge is applied. The risk weight of these positions can be as high as high
as 125%.
11.2.3 Capital requirement for operational risk
The capital requirement for operational risk is directly related to the gross income
of a bank. To calculate the required regulatory capital banks can choose between
two methods: the basic indicator approach and the standardised approach. If a
bank uses the basis indicator approach, the capital requirement is set at 15% of the
average gross income of the bank during the last three reporting years. The gross
income is the sum of the net interest income plus other income, e.g. fees.
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guide to treasury in banking
The standardized approach distinguishes between the operational risk of the business lines of a bank. With this approach, for each business line a single percentage
or ‘beta factor’ is applied over its gross income. Figure 11.3 shows the beta factors
that are used with this method.
Figure 11.3
Beta factors for operational risk per activity
business line
beta factor
Corporate Finance
18%
Trading and Sales
18%
Retail Banking
12%
Commercial Banking
15%
Payment and Settlement
18%
Agency Services
15%
Asset Management
12%
Retail Brokerage
12%
11.3 Basel III
In 2010, the Basel Committee has issued a concept version of the Basel III regulatory
capital framework. Apart from an increased overall capital requirement and a narrower definition of qualifying regulatory capital, Basel III contains two completely
new topics. Firstly, Basel III re-introduces the leverage ratio. Secondly, Basel III introduces liquidity requirements.
11.3.1 General changes in solvency requirements
Basel III aims at raising the quality of capital to ensure that banks are better able to
absorb losses on both a going-concern and a gone-concern basis. In Basel III, therefore, three new definitions of capital are introduced:
1. Common Equity Tier 1 (CET1) - Common Equity
2. Additional Tier 1 (AT1) - Additional Going-concern Capital
3. Tier 2 - Gone-concern Capital
In Basel I en II banks were also allowed to include subordinated loans in their capital base (Tier III). In BIS III, however, this is not allowed anymore.
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overview of the basel accords
The following items qualify as Common Equity (CET 1):
–
–
–
–
–
–
Common shares issued by the bank itself
Stock surplus
Retained earnings (including interim profit or loss)
Accumulated other comprehensive income and other disclosed reserves
Common shares issued by consolidated subsidiaries of the bank and held
by third parties (i.e., minority interests) that meet the criteria for CET 1
Dividends removed from CET 1 in accordance with applicable accounting
standards
Items that qualify as Additional Tier 1 capital must meet all of the following requirements:
–
–
–
–
–
–
–
–
–
–
the term must be perpetual
the issuing bank should have no incentive to redeem
repayment should only be possible with prior supervisory approval
they should be callable at the initiative of the issuer only after a minimum
of five years
the issuing bank should not assume or create market expectations that
supervisory approval for repayment will be given
there should be no credit-sensitive dividend feature (i.e. dependent on the
creditworthiness of the bank)
the issuing bank should have full discretion to cancel distributions
a cancellation of distributions must not be regarded as an event of default,
e.g. by the rating agencies
they should be subordinated to depositors, general creditors and to all
other subordinated debt of the bank
they must ensure a principal loss absorption through conversion to
common shares or a write-down mechanism.
Examples of additional Tier 1 instruments are hybrid instruments such as preferred
shares and Cocos. Preferred shares are, for instance, shares for which the institution has to pay a dividend before the other shareholders have to be paid. Cocos
(conditional convertibles) are bonds that are converted to shares if the Tier 1 ratio
follows below a certain trigger. To qualify as Additional Tier 1 capital, a Coco should
have a trigger not lower than 5.125% and have a perpetual term.
Finally, items that qualify as Tier 2 Capital must meet the following requirements:
–
–
–
the minimum term should be five years
the issuing bank should have no incentive to redeem
investors must have no rights to accelerate repayment
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guide to treasury in banking
–
–
–
they should be callable at the initiative of the issuer only after a minimum
of five years
they should not have a credit-sensitive dividend feature
they should be subordinated to depositors and general creditors of bank
Examples of Tier 2 instruments (gone concern capital instruments) are undisclosed
reserves, cumulative preferred shares, subordinated loans with a term longer than 5
years and Cocos with a term longer than 5 years and a trigger of lower than 5.125%.
In contrast to Basel II, in Basel III there is no distinction between lower and upper
tier 2 anymore.
Basel III also introduces higher required levels of capital. The minimum requirement CET1, the highest form of loss-absorbing capital, will be raised. In addition, a
capital-conservation buffer of 2.5% is required. This buffer must be met entirely by
CET 1 capital. The capital-conservation buffer effectively raises the total common
equity requirement to a minimum of 7% in 2019. Systemically important banks can
even be required by their local regulator to have an additional loss absorbency capacity.
Finally, banks may be required by their local regulator to build up a capital buffer
in times of economic growth that can be drawn down in periods of recession. This
‘countercyclical buffer’ must protect the banking sector from periods of excess
credit growth because it raises the cost of credit in period of growth. On the other
hand, because the buffer is decreased in a bear economy, the amount of credit is not
constrained by capital requirements.
Between 2013 and 2019, the common Tier 1 requirement will increase from 3.5% to
7%. The overall capital requirement (Tier 1 and Tier 2) will increase to 10.5% in 2019.
The countercyclical buffer or conservation buffer can build up to 2.5%. Figure 11.4
shows the timetable for the implementation of the new regulatory capital requirements.
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overview of the basel accords
Figure 11.4 Basel III timetable including countercyclical buffer
2012 2014 2015 2016 2017 20182019
Regular
Minimum Common
3.50% 4%
4.5% 5.125%5.700%6.375%
7.00%
6%
6%
6%
6.625%7.125%7.775%
8.50%
8%
8%
8%
8.625%
9.125%
9.875% 10.50%
7.00%
7.625%
8.20%
8.88%
Equity Tier 1
Minimum Total
Tier 1
Minimum Total Capital
Including Countercyclical Capital Requirement
Minimum Common
6%
6.50%
9.50%
Equity Tier 1
Minimum Total
8.50%8.50%8.50%9.125%9.63% 10.28%
11.00%
Tier 1
Minimum Total Capital
10.50%
10.50%
10.50%
11.125%
11.63%
12.38% 13.00%
If a bank is qualified as a systemically important financial institution (SIFI), however, it has to hold 1% to 2% more capital than the above mentioned perentages.
If a bank fails to meet the solvency requirements it must retain a percentage of its
earnings. This percentage is referred to as the minimum capital conservation ratio. Figure 11.5 shows the minimum capital conservation ratio with and without the
2.5% countercyclical capital requirement.
Figure 11.5
Minimum capital conservation ratio
common equity common equity tier 1 ratio
minimum capital
tier 1 ratio
(when subject to 2.5%
conservation ratio
countercyclical capital (as percentage of earnings)
requirement)
4.5% – 5.125%
4.5% – 5.75%
100%
5.125% - 5.75%
5.75% - 7%
80%
5.75% - 6.375%
7% - 8.25%
60%
6.375% - 7%
8.25% - 9.5%
40%
> 7%
> 9.5%
0%
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guide to treasury in banking
example
In 2019, the central bank requires a countercyclical capital buffer of 1%. A commercial bank has the following items in the balance sheet (x billion):
Common shares
Stock surplus
Undisclosed reserves
5.0
16.3
4.0
Retained earnings
1.2
Perpetual bonds meeting all AT1 requirements
5.0
Subordinated bonds meeting all Tier 2 requirements
6.0
The risk-weighted assets of the bank amount to 400 billion.
The CET1 of this bank is 5 + 16.3 + 4 + 1.2 = 26.5 and the total capital is 37.5. This
means that the CET1 ratio is 26.5 / 400 x 100% = 6.625% and the total capital ratio is
37.5/ 400 x 100% = 9.375%.
The bank does not meet the requirements, because the bank does not meet the required CET1 ratio of 8% (7% + 1%). The bank also doesn’t meet the required total
capital ratio of 11.5% (10.5% + 1%).
In Basel III, extra capital requirements will apply for a number of activities. As an
example, securitisation transactions that do not comply with the Basel rules will be
charged with a 350% capital requirement.
11.3.2 Leverage ratio
In Basel III a non-risk-based leverage ratio is re-introduced. The Leverage Ratio refers
to the ratio between the amount of regulatory capital and the nominal amounts of
on- and off-balance sheet exposures and derivatives. The Basel Committee proposes
a minimum Tier 1 leverage ratio of 3%. Off-balance sheet items are, for instance, unconditionally cancellable commitments, direct credit substitutes, acceptances, standby letters of credit, trade letters of credit, failed transactions and unsettled securities.
The leverage ratio will serve as a backstop to the risk-based capital requirement. In
the period before the credit crisis of the first decade of this century, many banks reported strong Tier 1 risk-based ratios while still being able to build high levels of onand off-balance sheet leverage. The use of a supplementary leverage ratio must help
to contain the build-up of excessive leverages.
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overview of the basel accords
For global banks with significant capital market activities, the 3% ratio is likely to
be more conservative than the traditional measures of leverage that have been in
place in some countries. The main reasons for this are the new definition of capital
and the inclusion of off-balance sheet items in the calculation of the leverage ratio.
11.3.3 Liquidity requirements
During the credit crisis, funding suddenly dried up and remained in short supply for
a very long period. This posed a threat to individual banks and the financial system as
a whole. In response, the Basel Committee introduces two global minimum liquidity
standards to make banks more resilient to potential short-term disruptions in access
to funding and to address longer-term structural liquidity mismatches in their balance sheets: the liquidity coverage ratio (LCR) and the net stable funding rate (NSFR).
The liquidity coverage ratio is a ratio that requires banks to maintain unencumbered high-quality liquid assets sufficient to meet 100% (or more) of net cash outflows over a 30-day period under a stress scenario.
The net stable funding ratio is a longer-term structural liquidity ratio. The NSFR ratio distinguishes between available stable funding (ASF) and required stable funding (RSF) whereby the first must always be higher than the second: ASF > RSF. To
calculate ASF and RSF, a percentage is assigned to all balance-sheet items in order to
indicate how stable these items are in terms of liquidity. For instance, for equity the
percentage is set at 100%. This means that equity is considered as a completely stable funding alternative. For current accounts, on the other hand, the percentage is
set at 0%. This means that in terms of stable funding, this item is completely worthless. On the asset side of the bank’s balance sheet, for instance the item ‘cash and
balances with the central bank’ is set at 0%. This means that this item doesn’t need
any stable funding at all. The percentage for loans to clients with a remaining term
longer than 1 year, however, is set at 100%. This means that this item must completely be funded with stable funding.
11.4
Regulatory capital, economic capital and RAROC
Since 1988, banks must hold capital as a buffer against the possible negative consequences of the risks that they take. This requirement is the most important part of
the Basel rules. The capital that bank are required to hold is referred to as ‘regulatory capital’. The risks that the banks have to cover by regulatory capital are credit
risk, market risk and operational risk.
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guide to treasury in banking
Banks also make their own calculations about how much capital they have to hold
to cover the risks arising from their various activities. Allocating funds to the different business activities is called capital allocation and the allocated capital is called
‘economic capital’. In this case, banks calculate the return on each activity and compare this with the economic capital. The result of this calculation is sometimes
called RAROC, risk adjusted return on capital.
On the next reallocation moment, the business units with the highest RAROC will
receive more capital for business purposes. This will be at the expense of those activities with a lower RAROC. In this way, banks try to optimize the return on their
capital.
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Chapter 12
Market Risk for Single
Trading Positions
Market risk is the risk that the market value of trading positions will be adversely
influenced by changes in prices and/or interest rates. For banks, market risk occurs
because traders in the Financial Markets department trade for account and risk of
the bank: proprietary trading. Since the credit crisis, however, banks have become
more prudent in allowing their traders to take positions. Market risk of trading positions can be measured by sensitivity parameters, by the Value at Risk method,
by stress tests, by the extreme value theory and, finally, by the expected shortfall
­method. In order to manage market risk, banks impose trading limits on their traders.
12.1
Market risk sensitivity indicators
The first way to measure market risk is the use of market sensitivity indicators.
Market sensitivity indicators indicate the sensitivity of a position in a financial value to a pre-defined change in the price determining parameter(s) of that financial
value. The following table shows an overview of the most commonly used sensitivity indicators.
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guide to treasury in banking
financial value
sensitivity indicator
price determining variable
Foreign Exchange
Value of one point / pip
FX rate
Interest Rate Derivatives
Basis point Value
Yield
PV01
Delta
Options
Delta
Price of the underlying value
VegaVolatility
Theta
Remaining Term
Rho
Interest Rate
12.1.1 Value of one point / pip
The value of one point gives the sensitivity of an FX position for a change in the FX
rate with one point or pip. For instance, if an FX trader holds a long position in euro
against Sterling for a nominal amount of EUR 10,000,000, the value of one point of
this position is 10,000,000 x 0.0001 = GBP 1,000. This means that the trader gains
1,000 pound Sterling for every rise in the EUR/GBP FX rate and loses 1,000 pound if
the euro depreciates with one basis point against the pound Sterling.
The value of one point is also used as a risk indicator with short-term interest rate
futures (STIR futures). It represents the change of the value of one futures contract,
e.g. a short Sterling contract or Eurodollar contract, if the futures price changes
with one (basis) point.
12.1.2 Basis Point Value
The basis point value (BPV), also called PV01 or (interest) delta, specifies how much
the price of an interest bearing instrument changes if the interest rate changes by 1
basis point (0.01%).
The equation for the BPV is:
Basis point value = dirty price × duration × 0.0001
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market risk for single trading positions
example
If the price of a bond is 98.70 and the bond has a duration of 4.6, the basis point value of this bond is:
BPV = 98.7 x 4.6 x 0.0001 = 0.045.
This means that the price of the bond will decrease from 98.70 to 98.655 if the interest rate rises by 1 basis point.
A disadvantage of the modified duration and the way in which the basis point value
is used above, is that it assumes implicitly that all zero coupon rates move in the
same direction and magnitude; in other words that the yield curve moves in a parallel way. The effect of a parallel shift is shown in figure 12.1.
Figure 12.1
Value of a loan with a face value of EUR 100 million before and after a rise
in interest rates by 1 basispoint
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guide to treasury in banking
Figure 12.1 shows that the value of the above loan as a result of a parallel interest rate
rise of 1 basis point has fallen by EUR 47,417.60. This is also the basis point value for
this bond.
In practice however, instead of assuming a parallel interest rate shift, sensitivityanalyses to interest rate movements are made per time interval or bucket. Thus,
separate analyses are made of the impact of a change in the one year zero coupon
rate, in the two year zero coupon rate, etc. By doing this, it will become clear that the
interest rate sensitivity is almost always different in all time buckets:
bucket (year)
amount
present value
modified
basis point
duration
value
0.5 - 1.5
6,000,000
5,788,712
1 / 1.0365
558
1.5 - 2.5
6,000,000
5,579,480
2 / 1.037
1,076
2.5 - 3.5 6,000,000
5.372,630
3 / 1.0375
1,554
3.5 - 4.5 6,000,000
5,168.468
4 / 1.038
1,992
4.5 - 5.5
106,000,000
87,755,301
5 / 1.0385
42,251
As might be expected, the table shows that the interest rate sensitivity of the bond
principally lies in the five year bucket. After all, this is where the largest cash flow
appears.
The above table is often referred to as a gap report. Financial institutions use these
kinds of gap reports in order to determine how their interest rate exposure is spread
across the various terms. If a bank has a clear idea about the interest rate movement
in a specific part of the yield curve, it can use this detailed information to fine tune
its hedge transactions.
In addition to the basic point value that presents the change in value of an interest bearing instrument or future cash flow as a result of a change of 1 basis point
in the zero coupon rate, there is a comparable indicator. This indicator shows the
change in value of an interest bearing instrument or a single cash flow as a result of
a change of 1 basis point in the credit spread. This indicator is called the credit BPV
or CV01, although some banks still use the term PV01 for this.
12.1.3 The ‘Greeks’
We have seen that the level of the option premium is determined by several parameters, which may interfere with each other. The extent to which the option premium
changes due to a change in one of these price determining factors is indicated by
the Greek letters: delta (and gamma), vega, theta and rho.
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market risk for single trading positions
12.1.3.1 delta
Delta shows the relationship between the absolute change in the option price and
an absolute change in the price of the underlying value. A delta of 0.6, for instance,
means that the option premium increases by 60 euro cents if the price of the underlying value increases by 1 euro. The delta also provides an indication of the chance
that the option will be exercised. A low delta means that this chance is small, whilst
a high delta means that the chance of exercising is high. For instance, a delta of 0.9
indicates that the probability that an option will be exercised is 90%. The table below shows the development of the delta of a GBP call / USD put option with a strike
price of 1.6000 and a remaining term of three months for different GBP/USD FX
forward rates (volatility is 15%).
gbp/usd
intrinsic value
time value
option premium
delta
forward rate
1.5000 0
0.01250.0125
1.5100 0
0.01450.0145
1.5950 0
0.04750.0475
1.6050 0.0050
0.0475*0.0525
1.6900 0.0900
0.01450.1045
1.7000 0.1000
0.01250.1125
0.20
0.50
0.80
* Note that the time value of the in-the-money options is equal to the time value of the equal out-of-themoney options
With a GBP/USD rate of 1.6900, the delta can, for instance, be calculated as follows:
(0.1125 – 0.1045) / (1.7000 – 1.6900) = 0.80.
Call options have a positive delta (between 0 and 1) and put options have a negative
delta (between 0 and -1). The delta for an option that is far otm is close to zero, the
delta for atm options is always around 0.50 (+0.50 for calls or -0.50 for puts) and the
delta for an option that is deep itm is almost equal to 1 (or -1).
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Figure 12.2 The development of the delta of a call option with various prices for the
underlying value (delta as a percentage)
Figure 12.2 shows that the development of the delta depends on the remaining term
of the option contract. As the remaining term decreases, the development of the
delta becomes less gradual. Just before expiry, the delta for atm options changes
dramatically as a result of small price movements.
12.1.3.2 gamma
Figure 12.3 also shows that the delta changes if the price of the underlying value
changes. Each time that an option becomes less otm or more itm, the delta increases. The degree to which this happens is represented by ‘gamma’. Gamma describes
the relationship between the change in the delta and the change in the price of
the underlying value. If an option is very far otm, the change in the delta is always
small. The same applies for an option that is very far itm. In both cases, the gamma
is small. For atm options, however, the gamma is high. This is especially the case if
the option is approaching its expiry date. This is shown in figure 12.3.
Figure 12.3
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The development of the gamma at differing prices for the underlying value
market risk for single trading positions
Figure 12.3 also shows that the gamma increases as the remaining period to maturity of an option contract becomes shorter.
12.1.3.3 vega/volatility
Vega gives the change in the option price due to a change in volatility of 1% point
(for example, from 20% to 21%). Vega decreases if the remaining term of the option
becomes shorter.
When option traders quote prices for volatility, they take into account the so-called
‘smile’ effect. This means that they use lower volatilities for atm options than for far
itm or otm options. The line reflecting the relationship between exercise price and
volatility therefore looks like a ‘smile’. This is shown in figure 12.4.
Figure 12.4 Volatility Smile
12.1.3.4 theta
The option premium decreases as the remaining term for an option becomes shorter. After all, an option that still has only one day left offers much fewer (additional)
profit opportunities than an option that still has a year to run. The relationship between the decrease in the option price and a reduction in the remaining term by
one day is given by theta. Because the option premium decreases as time passes, the
thèta is always a negative number.
As time passes, the theta of an option becomes progressively more negative; in other words, the option premium diminishes to a greater extent day by day. For options
that have nearly expired, the thèta is the most important parameter with regard to
changes in the option premium.
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12.1.3.5 rho
Rho gives the sensitivity of the option premium to a change in interest rates of 1 percentage point (for instance, a change from 5% to 6%). The sensitivity of the option
premium to changes in the interest rate is related to the delta-hedge.
12.2 Value at Risk
The value at risk (VaR) method is a way of estimating the size of market risk under
normal market conditions. A sensitivity parameter shows how much the value of a
position changes as a result of a standard change in the price determining parameter. The value at risk tells you how much the value of that position changes as a
result of a specific scenario of the price determining parameter. Therefore, a sensitivity indicator, in fact, merely gives information about the size of a trader’s position whilst the value at risk gives an approach for the actual loss that a trader can
suffer under the current market conditions.
To calculate the VaR, each day market risk managers determine a number of scenarios for the market parameters that determine the value of a position or a portfolio
for the next day. Which scenario will ultimately be chosen as VaR scenario depends
on the desired confidence interval. This indicates the degree of statistical certainty
with which the chosen scenario really can be considered as a worst-case scenario.
Market risk managers generally use a confidence interval of 99%.
Next, the market risk manager calculates how much the value of a trading position
would fall if the VaR scenario would actually come true. The result is referred to as
the value at risk of the trading position.
The period over which the value at risk is calculated is called the holding period or
time to close position. The duration of the holding period depends on the speed with
which a position can be closed. Trading positions in liquid markets can be closed
quickly. For this reason, the holding period for these positions is set at one day.
For single trading positions, the historical VaR method is used. This is a way of determining the VaR scenario where price changes over a specific historical period are
used in a straightforward way. For trading positions, banks generally use the last
250 to 400 daily price movements.
These historical observations are ranked from the most unfavourable price movement to the most favourable. If a bank wants to use a desired probability percentage
of 99%, for instance, it will choose the observation from the list for which only 1%
of all observations were even less favourable as the VaR scenario.
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example
On 15 June 2009, the market risk system calculated the VaR scenario for the price of
Heineken shares using the last 250 daily price changes.
The system ranked the 250 most recent daily relative price changes for the Heineken
share price. For each observation, a confidence level was calculated. The confidence
level of the worst observation is 100%. After all, based on these 250 scenarios, it
must be 100% certain that the price on the next trading day will not fall by more
than 4%.
scenario
250
249
248
247
246
245
% Price change
–4%
–3.5%
–3%
–2.7%
–2.5%
–1.7%
Probability
100% 99.6%99.2%98.8%98.4%98%
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243
–1.6%
–1.5%
...2
+ 3%
1
+3.5%
97.6%97.2% 0.8%0.4%
This system, however, was programmed with a probability percentage of 99%. As
VaR scenario, therefore, it chooses the scenario with the next higher probability percentage. This is scenario 248, which indicates a price fall of 3%.
If the share trader of this bank has a long position of 100,000 Heineken and the current price of the Heineken share is EUR 20, the market risk system calculates the
trader’s Value at Risk as: 3% x EUR 2,000,000 = EUR 60,000.
12.3 Stress tests
We have seen that banks use a particular confidence interval to determine the VaR
scenario. This means that the largest negative extremes are kept out of the analysis.
Furthermore, banks only use the price movements from the last 250 or 350 days.
This means that banks that use the VaR method not only ignore the most negative
scenarios from the historical period that the observed, but that they also take no account of any ‘disaster scenario’ that took place earlier in the past.
For this reason, banks also use another method in addition to the VaR method to
indicate their market risk. This method provides information about the risks under
extreme market circumstances or ‘market events’. This method is called stress testing. The objective of stress tests is to evaluate if a bank is able to survive exceptional
shocks in the financial markets. The loss on a trading position that appears with a
stress scenario is called event value at risk.
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With a stress test, a bank calculates the effect of one or more possible market events
on the value of its trading positions. The scenarios used for a stress test can be
drawn up in various ways. The first possibility is to use scenarios that have actually happened, such as ‘nine eleven’ (11-9-2001). However, the disadvantage of this
method is that events from the past are highly unlikely to happen again in the same
way in the future.
Banks have therefore also made up their own hypothetical scenarios for extreme
market circumstances. For instance, they assume a change in exchange rates of
10% or an interest rate change of 100 basis points. Many banks use both, historical
and fictitious scenarios.
Apart from stress tests, banks are required to perform reverse stress tests. The purpose of a reverse stress test is to identify scenarios and circumstances that will
cause the banks business model to become unviable.
12.4 Extreme value theory
An alternative for stress testing is studying the behaviour of what can happen during unusual market conditions by using a technique that is referred to as extreme
value theory. The first step of extreme value theory is to identify the observations
during a specific observation period that can be used to characterize the extreme
losses. There are two kinds of model for collecting the extreme observations. The
first one is the block maxima model. This model divides the observation period in
blocks and then takes the maximum loss within each block as a data. For example,
if the observation period is one year and the daily results are registered on a daily basis, we can choose the worst outcome for each month as an ‘extreme’. This is
shown figure 12.5 where the observation period is from March until March the following year. The extreme for each month is indicated by a bold ‘x’.
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Figure 12.5 Block Maxima model
The second, and more commonly used method, is the peak over treshold (POT)
model. In this model all large observations that exceed a certain threshold during
the observation period are identified as extremes. For example during the above
mentioned observation period every outcome over a daily change in prices or rates
of 2% is identified as an extreme. This is shown in figure 12.6. The extremes are
again indicated by a bold ‘x’.
Figure 12.6 Peak over Treshold Model
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Once the extremes are identified, a distribution for extreme ‘tail’ loss is made. This
distribution provides information about the market behaviour during extreme situations. The most important problem of the extreme value theory is obviously the
fact that there are are little data. This can be solved by decreasing the time period of
the blocks in the Block Maxima model or by lowering the threshold in the Peak over
Treshold model. However, in that case it is questionable whether the observations
in the then larger sample can be considered as ‘extremes’.
12.5 Expected shortfall
The expected shortfall, also referred to as conditional VaR, (expected) tail loss or average VaR, is defined as the conditional expectation of loss given that the loss is beyond the VaR level. The expected shortfall is the mean of all the potential losses that
exceed the VaR. Where VaR asks the question ‘how bad can things get?’, expected
shortfall asks ‘if things do get bad, what is our expected loss?’.
example
The expected shortfall in the example in paragraph 6.2 can be calculated by taking
the mean of losses under the extremes -4% -3.5% and -3%. These losses are respectively 80.000, 70.000 and 60.000.
The expected shortfall is (80.000 + 70.000 + 60.000) / 3 = 70.000
12.6 Trading limits
A trading limit indicates the maximum open position that a trader is permitted to
hold. Trading limits may apply either for an entire department within the dealing
room (trading desks) or for individual traders. The trading limit for a trading desk
is determined by the committee that is responsible for drawing up the limit control
sheet (LCS).
The allocation of limits between individual traders at a specific trading desk is the
responsibility of the desk’s departmental head. Junior traders are generally allowed
to hold only small positions. A trader’s limit is raised as his experience and as his
profitability increases. Banks use two types of trading limits to manage market risk,
value at risk (VaR) limits and nominal limits. At any moment in time, a trader must
satisfy all his limits.
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12.6.1 Value at Risk limit
A VaR limit sets a limit to the VaR of a trader, however, it does not set a fixed limit to
the nominal position of a trader.
example
A shares trader has a VaR limit of EUR 500,000. If the VaR scenario for today is a
price decrease of 2%, the maximum allowed market value of the shares position, according to this VaR limit, is EUR 25 million. After all, the VaR is then 2% of EUR 25
million = EUR 500,000.
For a VaR scenario of 1%, however, the maximum allowed market value of the position would be EUR 50 million.
In quiet market conditions, the price changes in the VaR scenarios are relatively
small. If a bank would only use a VaR limit, a trader could hold very large trading
positions. This is dangerous because, even after a very quiet period, the market can
suddenly become extremely volatile and the possible losses could then become very
large.
12.6.2 Nominal limits
With the VaR limit, the allowed size of a position is dependent on the current market circumstances. A nominal limit, in contrast, set an absolute maximum on the
size of a trading position. Since the credit crisis, banks have become much more
careful about using only VaR limits, and they are increasingly using nominal limits
in addition to VaR limits.
Nominal limits impose a limit to the size of a trading position regardless of market
developments. The most simple nominal limit is a positions limit. A positions limit
sets an unconditional limit on the market value of a position. An example is an FX
trading limit where the EUR/USD FX trader is allowed to hold a position of maximum EUR 5 million long or short. For interest rate positions and options, dedicated
limits are used. Finally, sometimes traders are assigned a stress test limit.
12.6.2.1 nominal limits for interest positions
A gap limit sets a limit to the mismatch position in terms of volume and time. A
money market trader is, for instance, only allowed to have a mismatch position in a
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single maturity bucket of not more than 100 million. Another exeample is an interest rate derivative trader who is only allowed to take positions not longer than five
years. If an FX trader or FX swap trader is allowed to trade FX forwards, he is also assigned a gap limit.
A basis point value limit sets a limit to the market value of an interest bearing portfolio measured by its basis point value, assuming a parallel move of the yield curve.
If the BPV limit for a trader is, for example, EUR 50,000 this means that he is allowed to hold the following positions:
market value
modified duration
bpv
500 mio
1
50,000
200 mio
2.5
50,000
50 mio
10
50,000
A variant of the basis point value limit is the credit spread sensitivity limit. This is a
limit to the market value of a bond portfolio measured by its change in price as a result of a change in the credit spread of the issuer of one basis point.
A slope risk limit sets a limit to the market value of an interest bearing portfolio
measured by the change in this value as a result of a pre-defined change in the
slope of the yield curve. For instance, a trader may not loose more than EUR 15,000
if the interest rates for the shorter periods, e.g. up to two and a half years, fall with
1 basis point and at the same time the interest rates for the longer periods rise. A
trader that holds the position that is shown in the table below, complies with this
limit.
bucket (year)
basis point value
result of the pre-defined scenario
0.5 - 1.5
EUR 10,558.43
+ EUR 10,558.43
+ EUR 08,075.93
1.5 - 2.5
EUR 08,075.93
2.5 - 3.5
EUR 06,553.23
– EUR 06,553.23
3.5 - 4.5
EUR 09,991.22
– EUR 09,991.22
4.5 - 5.5
EUR 12,238.79
– EUR 12,238.79
Total change in market value
– EUR 10,148.86
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12.6.2.2 greek limits for option positions
Greek limits set a limit to the value of an option portfolio measured by its Greek parameters, the delta, gamma, rho and vega.
Delta limit and delta hedging
The delta limit sets a limit to the sensitivity of an option position to changes in the
price of the underlying value. The main business for option traders is trading volatility. However, when an option trader opens a position by buying or selling an option, the value of his position is not only influenced by changes in the volatility but
also, amongst other things, by the price movement of the underlying value. In other
words: the option trader also has a ‘virtual position’ in the underlying value. If the
delta, for instance is 0.50, this means that an option position behaves in the same
manner as a position in the underlying value for half the contract amount. This is
called the delta position of the option position.
example
An option trader has a long position in call options with a contract volume of
100,000 shares. The delta of the options is 0.155. The current premium of the options is 4. This means that the market value of the options position is 400,000. If the
price of the underlying rises with 1 unit, the option premium rises with 0.155 and the
market value of the options position rises with 15,000 to 415,500.
The position thus reacts in the same manner to a change in the share price with one
unit as a long position of 15,500 in the underlying shares.
If the option trader would have sold this call option his position would react, of
course, in the opposite way: i.e. as a short position of 15,500 shares. The delta position of this trader is a short position of 15,500 shares.
The common opinion amongst the management of Financial Markets Departments, however, is that options traders must leave trading in shares to share traders, in bonds to bond traders, in FX to FX spot traders et cetera. Options traders with
banks, therefore, normally are not allowed to be exposed to changes in the price of
the underlying value. In other words: their delta limit is set close to zero and they
must make sure that the delta of their position is zero.
Option traders theoretically can realize a zero delta position by always concluding a
call option and a put option with the same delta at the same time. If an option trader, for instance, wants to have a long position in volatility, he can buy either a call
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option or a put option. After all, buying an option means buying volatility. However,
if the trader would only buy a call option , he would enter into a virtual long position in the underlying value. To offset this delta positions, he could buy a put option
with the same (opposite) delta. And if he would only buy a put option, he would enter into a virtual short position in the underlying value. Now he can offset his delta
position by buying a call option with the same delta. However, in reality the delta
position is neutralized in another way: the so-called delta hedge.
To neutralise the effect of price changes of the underlying value, option traders with
banks take a position in the underlying value that is exactly the opposite of their
delta position. This is called delta hedging. The option trader’s position is then said
to be delta neutral. The value of the composite position now only changes as a result of changes in volatility, the remaining term of the option and the interest rate.
In an ideal world, options traders would also want to make the value of their position independent of changes in the remaining term and in the level of interest rates;
however, this is not possible. Fortunately, this is not a great problem because these
factors are much less volatile than the price of the underlying value and thus play
generally no major disruptive role.
Because the delta of an option changes when the price of the underlying value changes, an option trader must constantly adjust his delta position during the
term of the option contract in order to keep his position delta neutral. The size of
the transactions as a result of the delta hedging depends on the level of the gamma,
that represents the changes in delta. For a low gamma, only small transactions are
necessary. For a high gamma, however, an option trader must buy or sell more of
the underlying value to keep his position delta neutral.
example
An option trader has sold a GBP call / USD put option to a client with a strike price of
1.4800. The premium for this option is USD 0.0500 per GBP and the size of the option contract is GBP 1,000,000. At the start date of the option contract term, the delta of this option is 0.25. The current GBP/USD FX forward rate is 1.4300. As an initial
delta hedge, the option trader has bought GBP 250,000 against USD.
On a later moment, the GBP/USD FX forward rate has risen to 1.4400. As a result, the
delta has also increased, for instance to 0.30. The option trader must now adjust his
delta position by buying 0.05 x 1,000,000 = 50,000 British pounds.
If, however, on a still later moment, the GBP/USD FX forward rate falls to 1.4000, and
the delta falls to, for instance, 0.18, the option trader must sell 120,000 British pounds.
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The above example shows that if the delta of an option position increases, an option
trader must buy the underlying value and if the delta of the position falls he must
sell the underlying value. With this, he will constantly suffer small losses. This is
because, in contrast to the ‘golden rule’, he ‘buys high and sells low’.
The option premium is partially a compensation for these trading losses. When
quoting his option premium, an option trader makes an estimate of the volatility
of the underlying value (implied volatility). A high volatility means that the option
trader expects that he will have to adjust his delta position frequently and will have
to accept great trading losses. Thus, he asks a high option premium.
If the option trader estimated the volatility correctly, he earns the margin on the
premium that he had calculated. If he underestimated the volatility, he would suffer
a loss. In this case, the premium is not sufficient to offset the trading losses resulting from the delta hedge.
The delta hedge can also be used to explain the relevance of the interest rate for the
option premium. After all, an option trader who has a short position in call options
must buy the underlying value in order to perform his delta hedge. This will involve
interest costs. Similarly, an option trader who has taken a short position in put options must sell the underlying value. This produces interest income.
example
An option trader sells a call option on a share with a remaining term of three
months. The delta for this option is 0.25. The three month interest rate is 4%. The
current share price is EUR 40.
Due to the delta hedge, the trader must buy 0.25 shares for each option contract unit.
The interest costs of the delta hedge, therefore, are:
0.25 x EUR 40 x 90/365 x 0.04 = EUR 0.10.
The option trader will include the interest cost of EUR 0.10 in the option premium.
Gamma limit and vega limit
Even if an options position has a delta of zero, the position can be very risky. This is
especially the case if the remaining term is short and if, at the same time, the option
is at-the-money. In this case, a small change in the price of the underlying value can
lead to a large delta position that, by definition, only can be hedged at a considerable loss. Therefore all traders are assigned a gamma limit.
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The vega limit sets a limit to the sensitivity of an option position to changes in the
volatility of the underlying value of the options position. Together with the gamma
limit the vega limit is the most relevant limit for an option trader. After all, option
traders trade in volatility.
12.6.2.3 stress test limit and expected shortfall limit
A stress test limit or event risk limit sets a limit to the market value of a position as
a result of a pre-defined market disruption. In order to set an event risk limit, the
market risk management department must design so-called stress tests. With a
stress test, a bank draws up one or more future ‘disaster scenarios’ in order to be
able to assess the risk associated with future extreme mar­ket movements. These
scenarios could be an actual historical scenario such as ‘nine eleven’ (when the twin
towers came down in New York). The disadvan­tage with this method, however, is
that events from the past will most probably not occur again in the same way in the
future.
Market risk management will therefore also usually create its own imaginary disaster scenarios. For example, it will assume a 10% change in the currency exchange
rates or an interest rate change of 100 basis points. Market risk management will
then calculate the possible losses for the traders as a result from these imaginary
disaster scenarios. A stress test limit is a nominal limit because, it is not influenced
by the current market conditions.
Banks can also set a limit on the expected shortfall. The expected shortfall limit prevents traders from taking very risky positions whilst at the same time they satisfy
with their VaR limits.
If, for instance, a trader has a one-day 99% VAR is $10 million, there is a danger that
the trader will construct a portfolio where there is a 99% chance that the daily loss
is less than $10 million and a 1% chance that it is $500 million. The trader is now
satisfying the VaR limits but is clearly taking unacceptable risks. By setting a limit
to the expected shortfall, banks can limit their risk more effectively than by only using VaR.
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Consolidated
Market Risk
Banks have many traders working for them, who all take their own positions independently of each other. A historic VaR is calculated separately for each single position. Banks’ however, have to report their total VaR to the regulators and, therefore,
they must calculate combined VaR figures for all their traders. With this calculation they take into account the effect of correlations. After all, for example, if share
prices go up, normally bond prices go down and vice versa. Banks can chose different manners to calculate their total VaR. They can choose between the full valuation
method, the variance-covariance method and the Monte Carlo method.
All VaR methods leave out a number of observations. And they are all based on the
data of a predefined historical period. This means, by definition, that the outcomes
of a VaR model can not give a one hundred percent certainty about how much the
maximum loss is during the next holding period. That is why banks also use stress
test or extreme value theory to measure their market risk during abnormal market
conditions. The outcomes of stress test must be reported to the regulator too.
To cover their market risk, banks are required to hold capital. The required amount
of capital, the regulatory capital, depends in the outcomes of the banks VaR reports.
However, when they determine the required amount of capital the regulators also
take the quality of the used VaR models into account.
13.1 Full valuation method
A conceptually simple way to calculate the VaR of composite portfolios is the full
valuation method. This method can be compared to the historical VaR method for
single trading positions. In stead of determining a VaR scenario for each single
price determining scenario, with the full valuation method, a combined VaR scenario is determined for all price determining market parameters at the same time.
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With the full valuation method, banks use the data of a predefined historical period. Just as with the historical VaR method for single trading positions, they then
rank all the data and then pick a ‘worst-case’ scenario depending on the chosen confidence interval. The example below shows the relationship between the historical
VaR method and the full valuation method.
example
A bank has three traders: a share trader, a bond trader and an FX trader. On 5 October, the positions are as follows:
traderposition
Shares
Long: 40 million market value
Bonds
Long: basis point value 25,000
FX
EUR/USD 6 million short
On 5 October, after the markets have closed, the risk manager calculates the VaR for
the three individual portfolios using the historical single VaR method with a confidence interval of 99%. This means that for each position he takes the two but worst
scenario to determine the VaR value for day. The results are as follows:
Share portfolio (based on 252 historical changes of share prices)
scenario
date
daily price
change in change market value
Worst
15 October – 0.75%
– 300,000
One but worst
23 October – 0.55%
– 220,000
Two but worst
15 January – 0.445%
– 178,000
99%-confidence VaR
Bond portfolio (based on 252 historical changes of bond prices)
scenario
216
daily price
change in
date
change
market value
Worst
+17 basis points
– 425,000
19 April
One but worst
5 June + 15 basis points
– 375,000
Two but worst
13 February + 13 basis points
– 325,000
99%-confidence VaR
consolidated market risk
FX position (based on 252 historical changes of the FX rate)
daily price
change in
scenario
date
change
market value
+ 3%
Worst
15 October One but worst
15 November + 1.95%
– 117,000
– 180,000
Two but worst
4 August – 78,000
+ 1.3%
99%-confidence VaR
Next, the risk manager calculates the total VaR of the bank using the full valuation
method. In order to do this, he determines the changes in the whole composite position of the bank based on the 252 historical scenarios in which all parameters are
included during the past 252 working days.
scenario
date
daily price change in
Worst
15 October – 0.75%
+ 3%
– 1.4 bp
market value
Shares
– 300,000
FX
– 180,000
Bonds 35,000
Total
One but worst 19 April
Shares + 65,000
– 37,200
+ 0.1625%
– 445,000
+ 0.62%
FX + 17 bp
Bonds – 425,000
Total – 397,200
Two but worst 20 February + 0.06%
Shares + 24,000
+ 1.1%
FX
+ 8.8 bp
Bonds – 220,000
Total
– 66,000
– 262,000
99%-confidence VaR
In this example, the total VaR is based on the scenario of 20 February . This scenario,
however, did not result in a ‘top three’ listing for any of the individual positions.
13.2
Variance-covariance method
With the full valuation method, the composed VaR of a bank is calculated by using one of the scenarios that actually have taken place during the chosen historical period. With other methods, the VaR is calculated by a hypothetical scenario.
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The first example is the variance-covariance method. This is a way of calculating
the combined VaR of multiple trading positions by using a stochastic distribution
for the possible market scenarios, i.e. the standard normal probability distribution.
The variance-covariance method assumes that volatilities and correlations stay the
same.
13.2.1 The standard normal probability distribution
A standard normal probability distribution is probability distribution that has a
mean of zero and that has a shape that is entirely determined by the standard deviation. In the financial world, the standard normal distribution is frequently used,
especially for risk management purposes. A diagram of this type of probability distribution is shown in the left diagram of figure 13.1.
Figure 13.1
Standard Normal Probability Distribution
0,4
0,4
0,3
0,3
0,2
0,2
97.72%
97.72%
0,1
0
0,1
-4
-3
-2
-1
0
1
2
3
4
0
-4
-3
-2
-1
0
1
2
3
4
The vertical axis in both diagrams represents the probability and the horizontal
axis represents the deviation from the average expressed in a number of times the
volatility. A standard normal probability distribution always has an average value
of zero. This is assumed to be the case, for example, for daily price changes. The
average daily change for an exchange rate or a share price is, after all, in reality
also approximately zero. The shape of a standard normal probability distribution
is entirely determined by only one parameter: the volatility. Following a standard
normal distribution, these statements can be made about the possible price movements during the next trading day:
–
–
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there is an 84.13% chance that the price will move in an unfavourable way
by less than 1 times the volatility (or standard deviation);
there is a 95% chance that the price will move in an unfavourable way by
less than 1.645 times the volatility;
consolidated market risk
–
–
–
there is a 97.72% chance that the price will move in an unfavourable way by
less than 2 times the volatility (this is shown in the right diagram of figure
13.1);
there is a 99% chance that the price will move in an unfavourable way by
less than 2.32634 times the volatility;
there is a 99.87% chance that the price will move in an unfavourable way
by less than 3 times the volatility.
With the variance-covariance method, it is assumed that the standard normal distribution not only applies for single price determining parameters, but also for
combinations of price determining parameters. Next, the only thing that has to be
done is to determine the combined volatility of the price determining parameters
of all trading positions by using the correlation factors between these parameters.
13.2.2 The volatility of composed trading positions
The combined volatility of a number of price determining parameters is calculated
by using their own volatilities and the correlation factors between these price determining parameters. The correlation factor represents the degree to which price
movements are related. The level of correlation is indicated by the correlation coefficient. This is always a value between -1 and 1. If, on average during a particular
period, prices move in exactly opposite directions to each other, the correlation coefficient is -1. If, on average, they move in exactly the same direction, the correlation coefficient is 1. If the correlation coefficient and the individual volatilities are
known, the volatility of the composite portfolio can be calculated mathematically.
For a composed position that consists of only two trading position, the combined
volatility can be calculated by using the following equation:
σc = √ (wa2 x σa2 + wb2 x σb2 + 2 x r x wa*σa*wb*σb)
In this equation:
σc = Standard deviation of composite position
σa = Standard deviation of position A
σb = Standard deviation of position B
wa = Weight of position A
wb = Weight of position B
ρ = Correlation coefficient between price movements of position A and position B
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guide to treasury in banking
example
A bank has two proprietary traders working for it, a shares trader and a bond trader.
Both have a position with a market value of EUR 50 million. The current volatility of
the shares is 1.5% and of the bonds 0.6%. The current correlation coefficient is 0.3.
The volatility of the combined position can be calculated as follows:
σ = √ (0.52 x 1.52 + 0,52 x 0.62 + 2 x 0.3 x 0.5 x 1.5 x 0.5 x 0.6) = 0.89%.
In a similar equation, the combined volatility of multiple trading positions can be
derived.
13.2.3 The VaR of composed trading positions with the variance-covariance
method
Once the standard volatility of the composed trading position is known, it is very
easy to determine the Value of Risk of the combined position. After all, under the
assumption of a standard normal probability distribution, there is a fixed relationship between the confidence interval and the possible movements of the combined
parameters. For instance, if a bank chooses a 99% confidence level, this means that
prices, on average, will move in an unfavourable way by less than 2.32634 times the
volatility. As VaR the change in the value of the composed position is taken under
this scenario.
example
The bank in the above example uses a 99% confidence level. The volatility of the
composed position is 0.89%. The total market value of both trading positions is EUR
100 million.
The combined VaR is approached as follows:
Combined VaR = 100 mio x 2.32634 x 0.89% = EUR 2,070,442.60
The sum of the individual VaRs of both composing portfolios can be calculated by
adding the individual VaR figures.
VaR shares trader: 50 mio x 2.32624 x 1.5% = EUR 1,744,672.50
VaR bond trader:
220
50 mio x 2.32624 x 0.6% = EUR 697,869.00.
consolidated market risk
It is clear to see that the combined VaR if calculated by the variance-covariance method is much smaller than the sum of the two individual VaRs, i.e. EUR 2,442,541.50
A result of correlation is that, when one of the positions of the bank is closed, the total VaR does not decrease by the VaR for this individual position If, for instance, the
bond trader in the above example decides to close his position, the VaR of the bank
decreases from EUR 2,070,442.60 to EUR 1,744,672.50. This is a decrease of only EUR
325,770.10 which is smaller than the VaR of the individual bond position. The decrease in the total VaR as a result of the closing of a position is called marginal VaR.
13.3 Monte Carlo analysis
Monte Carlo analysis is a method for calculating the VaR of a composite portfolio by
using a computer system that calculates a very large number, e.g. 10,000, of hypothetical scenarios for the total set of price determining parameters. The model uses
a self-defined probability distribution for each parameter and as data the historical volatilities of all the parameters are entered. Next, the model calculates the outcome of each scenario for the current composed trading portfolio of the bank. The
outcomes are once again ranked and the VaR is determined, based on the desired
confidence interval.
13.4
Back tests
Back testing means testing whether or not a model that has been used has functioned
properly. With the back testing of a VaR model, the ‘predictions’ of the VaR model during a particular period are compared with the hypothetical P&L. This is the P&L for a
trading position on a particular day calculated by leaving out all new deals of that day.
The VaR after all does not take these new deals into account either.
If 99% probability is used for a VaR method then a back test must show that the hypothetical P&L during the observation period must have exceeded the VaR in 1%
of the cases. If this was so in significantly more cases or in significantly fewer cases
then the VaR model is not reliable. The risk manager should then look to improve
the VaR method.
The result of a back test determines the correction factor that is used to adjust the
reported VaR figure when an internal model is used. If the back test proves that the
used VaR model is reliable, then the correction factor is set at 3. If, however, the
back test makes clear that the used VaR model is not reliable, then the correction
factor is set at 4.
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Chapter 14
Interest Rate Risk
One of a bank’s primary business responsibilities is to offer financial products that
meet the needs of its customers. Both, loans and deposits are tailored to the customers’ requirements with regard to tenor, term and rate type. This is the reason
that the maturities of assets and liabilities of most banks do not match. The bank’s
reward for this activity is called net interest revenue (NIR). This is the difference between the interest that the bank earns on its interest yielding assets and the interest paid for the liabilities. Normally, the interest term of the assets and liabilities
do not match. Because of this, banks incur interest rate risk. This is the risk that
the bank’s net interest revenue will change as a result of a change in interest rates.
Banks use different tools to measure and monitor interest risk such as gap analysis, modified duration, scenario analysis and stress testing. The main responsibility
within a bank for the management of interest risk lies with the Asset and Liability
Management Committee. In pillar two of the Basel Accords, the Basel Committee
has set guidelines for interest rate management.
14.1 Definition of interest rate risk
The Basel committee makes a distinction between the following types in interest
risk: repricing risk, yield curve risk, basis risk and option risk.
repricing risk
Repricing risk is the risk that the net interest revenue of a bank is affected by changes in the level of interest rates as a result of the timing mismatch in the interest maturity of assets and liabilities and of interest rate derivatives. If, for instance during
a period with high interest rates, the volume of liabilities that are subject to repricing exceeds the volume of assets that are subject to repricing, the net interest revenue of a bank is negatively affected.
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guide to treasury in banking
yield curve risk
Yield curve risk is the risk related to changes in the slope and the shape of the yield
curve. If, for instance in a specific period, the volume of the assets and the volume
of the liabilities that are subject to repricing are equal but the interest condition of
the assets is based on the general level of the long term interest rate and the interest condition of the liabilities is based on the general level of the short term interest rate, a steepening of the yield curve (decrease in short-term rates or increase in
long-term rates) will affect the bank’s net interest revenue positively whilst an opposite development will affect the bank’s interest revenue negatively.
basis risk
Basis risk is the risk related to hedging an exposure to one interest rate with an exposure to a rate that reprices under slightly different conditions. For instance, if a
bank has hedged a long bond position with payer’s swaps, the bond prices are set as
a result of supply and demand on the exchange whilst the value of the swap is calculated by using a bank’s own pricing curve. This may lead to situations where the
value if the swap portfolio changes differently than the value of the bond portfolio.
option risk
Option risk is the risk related to embedded options. For instance, if a customer has
a redeemable loan or a putable bond with a fixed rate of 6% and the market rate
changes to a level below 6%, the customer may redeem his loan and take up another loan with a lower interest coupon. Option risk is a one-sided risk which means
that the net interest income can only be negatively affected.
14.2 Interest risk in the banking book and in the trading book
The balance sheet of a bank is divided in two parts: the banking book and the trading book. This distinction broadly relates to the main functions of a bank: commercial and retail banking on one hand and investment banking on the other hand.
Commercial and retail banking activities are considered to be a bank’s core business, they include granting loans, taking up funding (savings, deposits, bonds) and
offering customers the possibility to hold current accounts and executing their payments. Investment banking activities are, amongst others, arranging securities issues, supporting mergers and acquisitions and proprietary trading.
The majority of balance sheet items belong to the banking book. This is shown in
figure 14.1.
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interest rate risk
Figure 14.1
Banking book and trading book
AssetsLiabilities
Cash and balances with central banks
2,791
Amounts due to banks
96,291
Short-dated government paper
1,809 Customer deposits and other funds
Amounts due from banks
80,837 on deposit
213,556
Loans and advances to customers
327,253
Debt securities in issue
98,571
Other liabilities
71,338
Debt securities – held-to-maturity
23,769
General provisions
1,029
Subordinated loans
21,413
Investments in group companies
28,252
Investments in associates
561
Total liabilities banking book502,198
Intangible assets
1,375
Equipment597
Equity
Other assets
56,348
Total equity
34,452
Total assets banking book
523,592
Short trading positions in securities
2,345
Derivatives
7,300
Trading Book
Securities – available for sale
18,403
Total liabilities trading book9,645
Derivatives4,300
Total assets trading book22,703
Total assets546,295
Total equity and liabilities546,295
The items in the banking book are valued according to the amortized cost principle
and the items in the trading book are valued at their market price. When measuring their interest rate risk, banks follow this distinction in the balance sheet. They
distinguish between two types of interest rate risk: the interest risk in the banking
book and the interest risk in the trading book.
Interest risk in the banking book refers to the risk that the bank’s net interest revenue falls as a result in a change of interest rates. Due to the long-term nature of
the portfolios in the banking book the net interest revenue will vary from period to
period even if it is assumed that there is no change in the shape or level of the yield
curve. The reason for this is that assets and liabilities periodically reprice.
Whenever the amount of liabilities subject to repricing exceeds the amount of assets subject to repricing, a bank is considered to be ‘liability sensitive’. In this case, a
bank’s net interest revenue will decrease if interest rates rise. Whenever the amount
of assets subject to repricing exceeds the amount of liabilities subject to repricing,
a bank is considered ‘asset sensitive’. In this case, a company’s net interest revenue
will decrease if interest rates fall.
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guide to treasury in banking
If a bank makes a forecast of its future interest income, it uses the implied forward
interest rates to indicate the interest amounts of repricing assets and liabilities.
These implied forward interest rates represent the current overall market’s estimate
of future interest rates. The forward rates normally differ from the spot rates, and
therefore the indicated future net interest income will normally differ from the net
interest income in the current period. This effect is only increased by the possible
deviations of the actual future rates from the forward yields. This last effect is referred to as interest risk in the banking book.
Interest risk in the trading book concerns the risk that the value of the items in the
trading books of a bank changes negatively as a result of a change in interest rates.
For long positions in interest bearing instruments, the risk lies in a rise in interest
rates. And for short trading positions in interest bearing instruments a fall in interest rates is a risk. This risk is normally managed as a part of the bank’s overall market risk by the market risk department.
14.3 Interest rate risk measurement
There are two ways to measure interest rate risk in the banking book. The first
method measures the change in expected net interest revenues in each currency resulting solely from unanticipated changes in forward interest rates. Normally, this
method is used to asses the interest rate sensitivity for the short term, i.e. one year.
This method is sometimes referred to as maturity method.
The second method is the duration method. This method measures the (virtual) change in the bank’s equity position as a result of changing interest rates. This
method is normally used to give an indication of the interest rate sensitivity for the
longer term.
14.3.1 Gap analysis / maturity method
A traditional way to assess the interest at risk in the banking book is to draw up a
gap report, also called an interest rate sensitivity report. This report gives an overview of all interest bearing instruments sorted in maturity buckets by their remaining interest term. Figure 14.2 gives an example of a gap report with 13 maturity
buckets.
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interest rate risk
Figure 14.2 Gap Report
maturity bucket
assets (bn)
liabilities (bn)
1
Sight - 1 month
105
100
5
2
1 - 3 months
15
35
-20
3
3 - 6 monts
25
45
-20
4
6 - 12 months
55
30
25
5
1 - 2 years
25
40
-15
6
2 - 3 years
40
20
20
7
3 - 4 years
30
20
10
8
4 - 5 years
25
17
8
9
5 - 7 years
20
13
7
10
7 - 10 years
10
6
4
11
10 -15 years
5
3
2
12
15 - 20 years
3
1
2
13
> 20 years
2
Equity
30
gap
2
-30
The above gap report shows that 105 billion of the bank’s assets will be repriced
within the next month, 15 billion of the assets will be repriced in the period between
one month and three months et cetera. On the other hand, 100 billion of the bank’s
liabilities will be repriced within the next month, 35 billion of the liabilities will be
repriced in the period between one month and three months et cetera.
Because the volume of the assets that will be repriced in the first bucket exceeds
the volume of the liabilities that will be repriced, the bank that has drawn up the
above gap report is said to have a positive gap in the first maturity bucket, i.e. for
this bucket the bank is asset sensitive. The bank has a negative gap in the second
and third bucket, i.e. for these buckets the bank is liability sensitive etcetera.
Most banks, do not draw up only one gap report, but instead make a separate report for instruments that will be repriced based on a money market rate and instruments that will be repriced based on a capital market rate. Next, banks calculate the
consequences of various interest rate scenarios that are drawn up by the Economics
Department. These scenarios make a distinction between the development in the
money market interest rates and the capital market interest rates.
Banks usually use a number of scenarios to assess the interest rate sensitivity of
their net interest income. For instance, a 100 basis points gradual parallel increase,
a 100 basis points gradual parallel decrease, a 100 basis points gradual curve flattening (increase in short-term rates or decrease in long-term rates) and a 100 basis
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guide to treasury in banking
points gradual curve steepening (decrease in short-term rates or increase in longterm rates) from the forward market curve. Figure 14.3 shows the effect of an instantaneous parallel rise in the interest rates with 50 basis points on the net interest
income of a bank for the next coming year.
Figure 14.3
The effect of an instantaneous rise of interest rates with 50 basis points
maturity average
residual term
bucket
maturity
in years
gap (bn)
income (mio)
Sight
0
1
-100 x 1 x 0.50% = - 500
Sight - 1 month
0.5 months
0.96 ( = 11.5/12)
-10
- 10 x 0.96 x 0.50% = -48
1 - 2 monts
1.5 months
0.88 ( = 10.5/12)
-5
- 5 x 0.88 x 0.50% = -22
2 - 3 months
2.5 months
0.79
20
20 x 0.79 x 0.50% = 79
3 - 4 months
3.5 months
0.71
15
15 x 0.71 x 0.50% = 53.25
4 - 5 months
4.5 months
0.63
-12
-12 x 0.63 x 0.50% =-37.8
5 - 6 months
5.5 months
0.54
10
10 x 0.54 x 0.50% = 27
6 - 7 months
6.5 months
0.46
14
14 x 0.46 x 0.50% = 32.2
7 - 8 months
7.5 months
0.38
-7
- 7 x 0.38 x 0.50% = -13.3
8 - 9 months
8.5 months
0.29
-4
- 4 x 0.29 x 0.50% = -5.8
9 - 10 months
9.5 months
0.21
3
3 x 0.21 x 0.50% = 3.15
10 -11 months
10.5 months
0.12
-2
-2 x 0.12 x 0.50% = -1.2
11 - 12 months
11.5 months
0.04
2
- 100
effect in net interest
2 x 0.04 x 0.50% = 0.4
- 433.1
If the bank that has drawn up the above gap report wants to indicate the consequence of a scenario in which all interest rates immediately rise with 50 basis points
for the next period of one year, it separately calculates the effect for all buckets by
multiplying the gap amount by the residual term and by the assumed change in the
interest rate. For the first bucket the result is, for example, – 100 bn x 1 x 0.50% =
– 500,000,000 (assuming that the position of 100 billion will remain on the balance sheet for the rest of the year). For the second bucket this gives, for example,
– 10 bn x 0.96 x 0.05% = – 48,000,000 etcetera. If this is done for all buckets and if
the results are added, it appears that the total decrease in net interest income as a
result of a 50 basis point rise in the money market interest rate is 460,700,000 for
the next year.
According to the Basel accords, banks must comply with the following guidelines if
they draw up a gap report:
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interest rate risk
–
–
–
–
–
–
–
–
they must include all assets and liabilities and all off balance sheets items
belonging to the banking book;
they must allocate all instruments according to their residual (interest)
term to maturity
they must report all on-balance sheet items at book value;
they may allocate exposures which create practical processing problems
because of their large number and relatively small individual amount on
the basis of statistically supported assessment methods;
they must treat swaps as two notional positions with relevant maturities.
they must consider options according to the delta equivalent amount of
the underlying or of the notional underlying;
and they must use separate maturity ladders for each currency that
accounts for more than 5% of either the bank’s assets or liabilities;
they must treat futures and forward contracts, including FRA as a combination of a long and a short position.
example
A bought 3s v 6s FRA should be reported in a gap report as a given deposit with a
term of three months and a taken deposit with a term of six months.
A sold JUN STIR 3 month EURIBOR future should be reported in the gap report as of
22 May as a given deposit with a term of one month and a taken deposit with a term
of four months.
A payer’s 3-month USD LIBOR swap with a remaining term of five years must be reported as a taken loan with a term of five years and a given deposit with a term of
three months.
A bought 2% floor with a notional underlying of 10 million GBP, a remaining term
of three years and a delta of 0.25 should be reported as a receiver’s swap with a fixed
rate of 2% and a notional of 2.5 million GBP. This swap must, in turn, be reported as a
given loan with a term of three years and a taken three months deposit.
Banks do not only assess the effect of changes in interest rates on their net interest
income, but they also assess the effect of other rate-sensitive factors. One of these
factors is their own pricing strategy on deposits. If a bank, for instance, decides to
lower its deposit rates and increase its credit spread, the bank net interest income
will, of course, be positively affected.
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guide to treasury in banking
Another factor that banks take into account is the change in the forecasted balance
sheet. This change can be related to the bank’s pricing policy. If a bank, for instance
wants to substitute its short term funding partially for long term funding, it can try
to manage this by raising its long term interest rates in relation to its short term
­interest rates. This will have an impact on the future composition of this bank’s balance sheet and, therefore, will also have an impact on the future interest income.
A third factor that banks take into account is the fact that some contracts contain
embedded options, for instance callable or putable bonds or callable or putable
interest rate swaps. With rising interest rates, holders of putable bonds or clients
that have concluded callable receiver’s swaps will, most probably will exercise their
rights and sell the bond, respectively unwind the swap contract. The bank then has
to issue a new bond with a higher coupon or has to conclude new payer’s swaps with
a higher fixed rate. Banks also include the so called pipeline transactions in their
calculations. These are transactions whereby a bank has made a proposal and the
client is given a term during which he can decide to accept this proposal. Banks
make an assumption of the percentage of the proposals that eventually will lead to
a loan contract.
Finally, banks assess the impact of changes in the prepayment rates on loan portfolios into their estimation of the change in their net interest income. For example, in
a scenario with falling interest rates, banks assume that mortgage portfolios are repaid at a faster pace than is agreed upon in the loan agreement.
14.3.2 The duration method
To assess the interest risk for the long term, banks nowadays usually do not use
the maturity method to indicate the possible changes in their net interest income
with different interest rate scenarios. The reason for this is that the uncertainties
in the interest scenarios and the possible changes in the composition of the bank’s
balances sheet are far too large for terms longer than one year. Therefore they use
duration analysis as a rule of thumb to indicate their long-term interest risk. With
this analysis, banks calculate the (virtual) effect of a change in interest rates on
their ­equity.
14.3.2.1 modified duration
The value of interest rate instruments such as fixed-income securities and interest
rate derivatives changes when the interest rate changes. This is because the value
of these instruments is calculated as the sum of the present values of their future
cash flows. If the (coupon) yields change, the zero coupon rates also change and, as
a result, also the present value of the constituent cash flows changes. As a conse230
interest rate risk
quence, the market value of the interest rate instrument changes. Figure 14.4 shows
how the price of a bond with a coupon of 6% and a remaining term of five years increases as a result of a 10 basis points decrease in the yield from 5.9% to 5.8%.
Figure 14.4
1060
60
1
60
2
5,9%
56,65
60
60
3
4
5,9%
5,9%
5
5,9%
5,9%
53,50
50,52
47,71
795,84
‘discounted value’: 1 / (1 + r)n
1004,22
1060
60
1
56,71
60
2
5,8%
5,8%
60
60
3
4
5,8%
5
5,8%
5,8%
53,60
50,66
47,89
799,61
‘discounted value’: 1 / (1 + r)n
1008,47
The modified duration provides an indication of the interest rate sensitivity of a
particular interest rate instrument or a portfolio of interest rate instruments. Modified duration is an elasticity that sets the percentage change in the dirty price of an
instrument due to a change in interest rate against this interest rate change.
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example
The price of a bond is 98.45 and the duration of the bond is 4.72. This means that,
for a rate fall of 1 basis point (= 0.01%), the price of the bond will rise by 0.0472% x
98.45% = 0.0465 to 98.4965.
Using the modified duration, an estimate can be made of the risk associated with
a position in a portfolio of fixed-income securities or interest rate derivatives. If a
portfolio has a high modified duration, this means that the market value of this
portfolio reacts strongly to interest rate changes. Thus, the market risk of this portfolio is high. The modified duration can also be used to provide an indication of the
size of the hedge transactions required to hedge the market risk of interest rate positions.
Calculation of the modified duration
The equation for calculating the modified duration of fixed-income securities is as
follows:
Modified duration =
1 / (1+r) x Σ (PV future cash flow x period /Σ PV future cash flow)
Firstly, the present values of all the individual cash flows of the financial instrument
are calculated, in case of a fixed-income security i.e. the coupons and the principal. The calculated present values are then used as a weighting factor to determine
an average duration for the fixed-income security. The average duration thus determined, the Macaulay duration or simply duration, is represented by the second part
of the right hand side of the above equation.
To determine the modified duration, an ‘adjustment factor’ needs to be applied.
This is the factor ‘1 / 1 + r’ in the first part of the right side of the equation. The modified duration derives its name from this ‘adjustment factor’. The ‘r’ in the equation
represents the effective yield of the financial instrument for which the modified duration is calculated.
example
The modified duration of a bond with a remaining term of 2.5 years (daycount convention 30/360) and an interest coupon of 6% is calculated with all zero coupon
rates being 4%.
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interest rate risk
Firstly, the present values of the three cash flows for this bond are calculated (colterm
cash flow
pv cash flow
pv x term
umn 3) and then each present value is multiplied separately by the corresponding
term of these cash flows (column 4):
1 year
60
60/ (1.04) = 57,69
57.69
2 years
60
60/(1.04)2 = 55,47
110.94
3 years
60 Σ
1060/(1.04)3 = 942,34
2,827.01
1,055.50 2,995.65
The modified duration of this bond is
Mod duration = 1/ 1.04 x 2,995.65 / 1.055,50 = 2.73.
Factors that determine the level of the modified duration
In general, the modified duration of an interest bearing instrument increases as
the remaining term of the instrument increases. The modified duration is, after all,
largely determined by the Macaulay duration that gives the average remaining term
of the cash flows weighted by the size of the present value of these cash flows. An
instrument with a longer remaining term therefore has a higher modified duration
than an instrument with a shorter remaining term.
Because the remaining terms for the cash flows are weighted with their size, if the
remaining term is the same, a bond with a higher coupon has a lower duration than
a bond with a lower coupon. This is because, for a bond with a higher coupon rate,
the shorter periods will weigh more heavily.
Furthermore, the duration of a bond depends on the level of the market interest
rate. For a high market interest rate, the duration is lower than for low interest rates.
After all for higher interest rates, the present value of the cash flows with longer
terms fall more strongly than the present value of the cash flow with shorter terms.
Finally the modified duration is influenced by the fact whether an instrument contains an embedded option or not. A putable bond, for instance, has a lower duration
than a regular bond.
14.3.2.2 additivity of duration
Normally, the duration of the assets of a bank differs from the duration of the liabilities. The difference is referred to as a duration gap. If a duration gap exists, the
bank’s equity is sensitive for changes in interest rate and a the level of this sensitivity can be expressed by the duration of the equity. The equity duration can be calculated by making use of the fact that duration is additive.
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With the help of the modified duration, it is possible to add the risks associated
with different portfolios and to determine the size of hedge transactions required
to achieve a desired reduction in the risk of a specific composite portfolio, e.g. the
assets and liabilities of a bank. For this purpose, use is made of the basis point value
(BPV). The basis point value of a portfolio is calculated as follows:
Basis point value = value of the portfolio x modified duration x 0.01%
The following example shows how the modified duration of a mixed portfolio, can
be calculated by using the BPV.
example
A bond trader has a bond portfolio with a market value of EUR 180 million and a modified duration of 10. The bond trader is considering whether to invest in another bond
portfolio with a market value of EUR 100 million and a modified duration of 7.2.
In order to get an indication of the interest rate sensitivity of the composed portfolio
the bond trader calculates its BPV.
BPV old portfolio +
EUR 180 million x 10 x 0.01% = EUR 180,000
BPV new portfolio = EUR 100 million x 7.2 x 0.01% =EUR 72,000
BPV composite portfolio
EUR 252,000
Using the BPV equation, the modified duration of the composite portfolio can also
easily be calculated:
EUR 252,000 = EUR 280 million x modified duration x 0.01%
From this, it follows that the modified duration of the composed portfolio is:
EUR 252,000 / EUR 280 million x 10,000 = 9.
The ability to add and subtract the risks for two interest bearing portfolios is not
only applicable for portfolios consisting of identical instruments, but for all interest bearing portfolios. Thus, for example, the risks of a bond portfolio, a portfolio of
purchased bond futures and a portfolio of receiver’s interest rate swaps can be added. On the other hand, the risks of a bond portfolio and of a portfolio of sold bond
futures that is used as a hedge can be subtracted from each other.
By using the BPV, for instance, a portfolio manager can easily determine the size of
a hedge transaction that he must conclude if he wants to adjust the modified duration of his portfolio. The conclusion of a contract in other financial instruments
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interest rate risk
with the aim of reducing the duration of an existing portfolio is referred to as duration hedge.
example
A bond trader has a bond portfolio with a market value of EUR 180 million and a
modified duration of 10. He fears a rise in interest rates and he therefore wants to
decrease the modified duration of this portfolio to 5. To achieve this, he plans to sell
bond futures with a modified duration of 9. He now wishes to calculate how much
bond futures he has to sell.
The BPV of the bond portfolio must be reduced from EUR 180 million x 10 x 0.01%
= EUR 180,000 to EUR 180 million x 5 x 0.1% 10,000 = EUR 90,000. This means that
the BPV of the sold bond futures must be EUR 90,000.
The required size of the futures portfolio can be calculated using the BPV equation:
90,000 = market value bond futures x 9 x 0.01%
The trader must therefore sell futures contracts with a total market value of EUR
100 million. If the current price of the bond futures is, for instance, 95 he has to sell
100,000,000 / 100,000 x 100/95 = 1053 bond future contracts each with a nominal
amount of 100,000 (rounded upwards).
14.3.2.3 equity duration
The above method can also be used to calculate the modified duration of the equity
of a bank. In order to do this, first the BPV of the asset side of a bank’s balance sheet
is calculated. Figure 14.5 shows the items on the asset side of the balance with their
average duration. It appears that the modified duration of some of the items is zero.
The reason for this is that these items are not interest-rate sensitive. This is true, for
instance, for equity securities and for investments in group companies. Figure 14.5
also shows that the modified duration of the cash and balances with central banks
items is very small. This is because this item consists largely of balances on current
account with the central bank for which the interest rate can be changed overnight.
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guide to treasury in banking
Figure 14.5
Modified duration of a bank’s assets
Assets
balancemd
Cash and balances with central banks
2,791
0.01
Short-dated government paper and
amounts due from banks
82,646 0.2 Loans and advances to customers
327,253
5.7
Debt securities 38,076
3.7
Equity securities
4,096
0
Investments in group companies
28,252
0
Investments in associates
561
0
Intangible assets
1,375
0
Equipment
5970
Other assets
60,648
0
Total assets546,295
The total BPV of the bank’s assets is calculated by adding the BPV’s of each single
balance sheet item. Note that because the modified duration of the non-interest
rate sensitive items is zero, their BPV is also zero:
Total BPV of assets = 2,791 mio x 0.01 x 0.01% + 82,646 mio x 0.2 x 0.01% + 327,253
mio x 5.7 x 0.01% x 38,076 mio x 3.7 x 0.01% = 202,278,041.
Next, the BPV of the liability side of the bank’s balance sheet is calculated by multiplying the volume of the balance sheet items by their duration and by 0.0001
­respectively. The duration of the item Customer deposits and other funds on deposit
needs some explanation. One would expect the duration of this item to be close to
zero because the balances on many savings accounts and the credit balances on customer accounts are immediately withdrawable whilst the term of most term deposits is also small. However, in practice the majority of these funds stay with the bank
for a number of years without the need for the bank to increase the interest rates in
order to keep these balances. This phenomenon is referred to as stickyness. As a result, the duration of the item Customer deposits and other funds on deposit is much
larger than expected and can be much larger than 1. In our example the duration
is 3. Figure 14.6 shows the items on the liability side with their modified duration.
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interest rate risk
Figure 14.6 Modified duration of a bank’s liabilities
Liabilities
Amounts due to banks
Customer deposits and other funds
on deposit
– Savings account
59,302
– Credit balances on
60,090
customer accounts
– Corporate deposits
34,009
– Other
25,703
Debt securities in issue
Other liabilities
General provisions
Subordinated loans
Balancemd
96,291
0.25
179,104
3
98,571
80,983
1,029
21,413
6
5.3
0
10.35
Total liabilities511,843
Equity
Total equity68,904
Total equity and liabilities546,295
The total BPV of the bank’s liabilities is calculated by adding the BPV’s of each single item:
Total bvp of liabilities = 96,291 mio x 0.25 x 0.01% + 179,104 mio x 3 x 0.01% + 98,571
mio x 6 x 0.01% x 80,983 mio x 5.3 x 0.01% + 21,413 x 10.35 x 0.01%= 180,364,520.
Now that both, the BPV of the assets and the BPV of the liabilities are known, the
BPV of the equity can be calculated by subtracting the BPV of the liabilities from the
BPV of the assets:
BPV of equity = 202,278,041 - 180,364,520 = 21,413,521.
This means that if the interest rate increases by 0.01%, the value of the equity increases by 21,913,521. If the interest rates fall by 0.01% the value of the equity decreases by the same amount.
Finally, by using the BPV equation, the modified duration of the equity can be calculated as follows:
Basis point value = equity value x modified duration x 0.01%
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guide to treasury in banking
21,913,521 = 68,904,000,000 x mod duration x 0.01%
Therefore
Modified duration = 21,913,521 x 10,000 / 68,904,000,000 = 3.18
The modified duration of the equity of this bank is 3.18.
Basel requirements for interest risk and adjustment of the equity duration
The Basel rules for a bank’s maximum interest rate sensitivity can be stated in two
ways:
1. A decrease in the equity as a result of an immediate parallel rise of the
yield curve with 200 basis points may not exceed 20% of a bank’s own
funds.
2. The maximum allowed duration of equity is 10 (20% / 2%).
If the interest rate sensitivity of the equity of a bank is too high, following pillar II
from the Basel rules, the regulator can take several supervisory measures. First,
it can demand that he banks improves its risk management arrangements. Next
it can demand a reduction of the bank’s risk profile. Finally as a penalty, it can increase the amount of required regulatory capital.
A bank with a too high duration can either decrease the duration of its assets or increase the duration of its liabilities. Below are some examples of how a bank can
achieve this:
Decrease of the duration of assets:
–
–
Conclude payer’s swaps with long contract terms
Sell bond futures with underlying bonds with terms from 10 to 30 years
Increase the duration of liabilities:
–
–
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Subsitute repos by customer deposits
Substitute short-term debt securities (CD) by long-term debt securities
(bonds)
interest rate risk
14.4
Hedge accounting
Since 1 January 2005, listed companies in the European Union must ensure that
their external financial reporting is made in accordance with the rules set by the
International Accounting Standards Board (IASB). These international reporting
rules are called the International Financial Reporting Standards, abbreviated to
IFRS. The IASB has chosen for a mixed model variant. This means that there are
two accounting principles: ‘fair price’ and ‘amortised cost’. As a consequence, hedging interest rate risk may have large implications on the profit and loss account of
banks. To prevent the impact of a hedge on their P&L account, banks are allowed to
use a technique that is called hedge accounting.
14.4.1 Fair value and amortized cost
According to ifrs, the fair value of a balance sheet item is the amount, on purchase or sale, for which the item can be settled with a well informed independent
party who is willing to enter into the transaction. According to ias39, an organisation must hold to the ‘fair value hierarchy’ when determining the fair value of
an item. This hierarchy provides guidelines about how the fair value should be
determined:
–
–
If an active exchange price or market price is available then this is considered to be the most reliable fair value. This manner to determine the fair
value is referred to as mark to market.
If no active market price is available then the fair value must be determined using a valuation model. This manner to determine the fair value is
referred to as mark to model. This ‘model’ can consist of:
– The determination of the value with the help of the present value
method or an option model in which current market data (yield curve,
volatility curve, etc.) is used.
– Basing the value on the price of a comparable transaction recently
concluded in the market.
Depending on the classification in which an instrument is included, changes in the
fair value must be reported either in the profit and loss account or in equity.
The amortised cost is determined using the present value method. At each reporting moment, the present value of the future cash flows of a balance sheet item is
calculated adjusted for the interest accrued in the reporting period (clean price).
The interest rate used is always the effective interest rate at the moment when this
item was recognised on the balance sheet. The change compared to the previous reported amortised cost must be reported in the profit and loss account. Costs directly
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guide to treasury in banking
associated with a contract, such as commissions and transaction costs, must be included in the amortised cost.
Whether a financial instrument must be valued at fair value or at amortised cost
depends on the purpose of the instrument. This purpose must be determined and
made known in advance. Generally speaking one can say that items in the banking
book of a bank are value at amortized cost en items in the trading books are valued
at fair value. Derivatives, however, must always be valued at fair value.
14.4.2 The concept of hedge accounting
If an organisation wants to use a derivative to hedge a particular item that is valued at amortised cost then a problem arises. The derivative is after all valued at fair
value and the value changes of the derivative are reported in the profit and loss account. As a result, the profit and loss account displays more volatility than previously even though a risk has been hedged. The bookkeeping treatment of the hedge
does not now reflect the reduced economic risk.
To prevent this, an organisation may use hedge accounting. Hedge accounting ensures that the moment when the results for a hedging instrument must be recognised
in the profit and loss account is the same moment when the results for the hedged
position are reported. As a result, swings in the profit and loss account are avoided.
In order to ensure that hedge accounting is not ‘misused’ to steer the result, three
requirements must be met. The first requirement is that the hedge must fit within
the risk management policy formulated by the organisation. The second requirement is that documentation must be produced in advance about the likelihood of
the risk, about the working of the hedge and about the likely effectiveness of the
hedge. The third requirement is that the effectiveness of the hedge must be measured during the term; the so-called retrospective effectiveness test.
For the retrospective effectiveness test, the change in value of the hedge instrument
during the period to maturity is compared with that of the hedged position. For this
purpose, banks are allowed to use a regression analysis. This comparison must be
performed on a cumulative basis. A cumulative deviation in the change in value of
the hedged item relative to the hedging instrument is called the “ineffective portion”
of the hedge. This part must be accounted for in the profit and loss account. If the
cumulative change in value of the hedge instrument is less than 80% or more than
125% of the change in value of the hedged position then hedge accounting may not
take place at all.
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Three types of hedged are distinguished that are important for banks, the fair value
hedge, the cash flow hedge and the net investment hedge.
14.4.3 Fair value hedge
A fair value hedge is a protection of the fair value of a balance sheet item using a derivative. An example is the conclusion of a receiver’s swap to protect the fair value
of an issued bond. Changes in the fair value of the bond as a result of interest rate
changes are largely offset by changes in the fair value of the receiver’s swap. According to IAS 39, however, the changes in value of the bond is accounted for in equity
while those for the interest rate swap are reported in the profit and loss account.
By applying the fair value hedge, the bank may account for the changes in value of
the bond in the profit and loss account instead of in equity. As a result, the profit
and loss account, on balance, is no longer influenced by changes in the value of the
interest rate swap. After all, now the change in value of the bond and the reverse
change in value of the interest rate swap largely cancel each other out.
In the above mentioned situation, where a single bond is hedged, the hedge accounting technique is referred to as a micro hedge. If a whole portfolio is hedged
and accounting hedge is applied, this is referred to as a macro hedge. Banks use the
macro hedge, for instance, for their mortgage portfolios.
14.4.4 Cash flow hedge
A cash flow hedge is a hedge transaction whereby an enterprise hedges the risk that
the size of future cash flows is lower or higher than expected due to, for example,
changes in interest rates or exchange rates.
An example of a cash flow hedge is the hedging of the uncertain future cash flows for
a purchased floating rate note (FRN) that is not part of a trading portfolio. For an FRN,
the size of the future cash flows is uncertain. A bank can conclude an interest rate
swap as a hedge whereby it is going to receive the fixed interest. As a result, the variable interest rate flow is converted into a fixed interest rate flow.
Because the fair value of a floating rate note is always close to 100%, for the value
determination it does not matter which valuation basis is used, fair value or amortised cost. The problem here is that, according to IAS39, the changes in the fair
value of the interest rate swap must be accounted for in the profit and loss account.
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guide to treasury in banking
With cash flow hedge accounting, the reporting requirements for the hedged item
(the FRN) remain unchanged. The changes in value of the derivative (the interest
rate swap) are now however accounted for in equity instead of in the profit and loss
account. As a consequence, the profit and loss account is no longer influenced by
changes in the value of the interest rate swap.
14.4.5 Net investment hedge
A net investment is an investment in a subsidiary, a participation or a joint venture
that is denominated in a foreign currency, compensated for any intra-group loans
that are eliminated in the consolidated balance sheet. Banks normally hedge the
foreign exchange risk of a net investment with a financial instrument, i.e. a loan in
the same currency or a cross currency swap . In this respect, the bank must take into
account the fact that according to the accounting rules, the net investment is considered to be a so-called non-monetary item whilst the loan or cross currency swap
that is used as a hedge is considered to be a monetary item and that changes in the
value of a monetary item and of a non-monetary item must be reported differently.
Changes in the value in monetary items that result from changes in exchange rates
must be reported in the profit and loss account, whilst changes in the value of nonmonetary items must always be reported in the equity account. As a result, a hedge
for a net investment that can economically be seen as a perfect hedge, increases the
volatility of the profits in stead of mitigating it.
By using the net investment hedge, the bank is allowed to report the changes of the
value in the financial instrument that is used for the hedge in the equity account in
stead of in the profit and loss account, as is the case for the net investment. As a result, the profit and loss account will no longer be influenced by changes in the value
of the net investment as a result of changes in the exchange rate.
14.4.6 Hedge accounting in practice
Many banks use interest rate swaps to swap the interest maturities of all their balance sheet items to a money market benchmark, usually 3-months Euribor of LIBOR. If they would not use hedge accounting, this would mean that their profit and
loss account would be severly affected by the changes in the fair value of all these
interest rate swaps.
To neutralize this effect, banks use several types of hedge accounting. They use the
micro fair value hedge for every bond that they issue. Next, they attribute part of
their interest rate swaps to their mortgage portfolio and use the macro fair value
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hedge. This concerns part of the interest rate swaps in which they are the payer of
the fixed interest (payer’s swaps). To make sure that this hedge is effective, they
draw up the maturity calendar of the mortgage portfolio and match the maturity
calendar of the payer’s swaps as much as possible. This is done on a regular basis,
for instance every month. Another part of the payer’s swaps portfolio is attributed
to the savings accounts portfolio. For the purpose of hedge accounting, banks presume that the interest of part of the savings accounts portfolio, which has an assumed interest rate maturity one to three months, is swapped to a fixed rate. For
this purpose, too, banks use the macro cash flow hedge technique. Finally, for their
net investments banks use the net investment hedge.
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Chapter 15
Liquidity Risk
Liquidity risk is the risk that a bank is not able to fulfil its short term obligations.
Liquidity risk is a far more important risk for a bank than solvency risk. A bank
that has a problem with its liquidity position is deemed to go bankrupt in the short
term, while a bank that is faced with a solvency problem normally has more time to
solve this problem and may even have a good chance to survive. Liquidity risk is in
essence a reputational issue. After all, a bank with an outstanding reputation will
never be confronted with a bank run and will always be able to attract short term
funding. On the other hand, however, a bank that reports rather satisfactory liquidity reports, may be confronted with a bank run if for some reason its reputation deteriorates. In spite of the seemingly satisfactory liquidity position, this bank will most
probably not survive. During the recent global financial crisis, liquidity risk became
an even more important issue than before. This is because during this crisis, banks
stopped trusting each other and, as a result, many banks had to rely on their ‘lender
of last resort’, i.e. their national central bank. The Basel Committee has appreciated
the importance of liquidity risk and has included two liquidity standards in pillar II
of the Basel rules, i.e. the liquidity coverage ratio (LCR) and the net stable funding
ratio (NSFR).
15.1
Availability risk and market liquidity risk
Liquidity risk is the risk that the bank is not able to fulfill its short-term obligations.
The bank then has either not enough money available to repay the loans that it has
taken up or it is not able to accommodate withdrawals on the client current accounts. Obviously the problem is now that the bank has not enough access to funds.
Banks may obtain funds either by taking up loans or by selling their assets. The risk
that the bank may not be able to borrow enough funds at a reasonable interest rate
is referred to as availability risk. Availability risk can have two causes. Firstly other
parties may not trust the bank anymore and secondly there may be general short245
guide to treasury in banking
age of money. The risk that a bank will not be able to sell its assets quickly and at a
fair price is referred to as market liquidity risk. The main responsibility of liquidity management is to make sure that the bank has always acces to funds and/or
that the bank has enough marketable assets to cover the outflows of funds under
stressed conditions.
15.2 Causes of liquidity risk
The main cause of liquidity risk is the fact that the term of assets of commercial
banks normally exceeds the term of a bank’s liabilities. This is, amongst others, the
natural result of the main responsibility of a commercial bank i.e. creating money.
Every commercial bank that has a banking license is allowed to create money. Technically this is very easy: if a bank grants a loan to a customer, it makes two entries
in its ledger. First, the bank debits the item ‘loans’ on the asset side of its balance.
At the same time it credits the item ‘customer deposits and other funds on deposit’,
under the sub-item clients current accounts. Loans can have very different terms,
from one day for an overnight loan to more than thirty years for mortgage loans.
This means that the majority of the loans will not be paid back today or even tomorrow.
On the other hand, clients of the bank are allowed to use the balance that is booked
on their current account immediately as a consequence of the loan agreement.
This means that they are free to transfer the money immediately to another bank
or make a cash withdrawal. This is the essence of liquidity risk with banks. A part
of a bank’s funding consists per definition of immediately demandable items while
its assets normally have a longer term. Banks can try to solve this problem by inducing their clients to place their money on savings accounts and fixed term deposits.
However, it is not possible to decrease the balances on current account to zero just
because of the fact that the customers of the bank, be it private clients or corporates,
need these balances to execute their payments. And, on the other hand, it is also not
possible for a bank to only grant loans with a term of one day to make sure that they
would receive their money back immediately. After all, this would be very inconvenient for their clients.
The balance sheet in figure 15.1 shows the relative importance of the item ‘customer deposits and other funds on deposit’. The volume of this item is over 519 billion
which makes up approximately 55% of the bank’s total liabilities. Although it is true
that this item also contains fixed term savings deposits and other fixed term deposits, approximately twenty to thirty percent of every large bank’s liabilities consists
of balances that can immediately be withdrawn. In case of a bank run, most of these
deposits will be withdrawn which even the most conservative bank will not be able
to survive and go bankrupt.
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liquidity risk
Figure 15.1
Balance sheet of a bank
Assets
Equity
Cash and balances with central banks
9,519
Shareholders’ equity (parent)
34,452
Amounts due from banks
51,828 Minority
interests
617
Financial assets at fair value through P&L
Total equity35,069
– trading assets
125,070
– non-trading derivatives
8,990
Liabilities
– designated as at fair value 3,066
Subordinated loans
21,021
– through P&L
Debt securities in issue 125,066
Amounts due to banks
72,852
Investments
Customer deposits and other funds 519,304
– available for sale
99,200
on deposit
– held-to-maturity
11,693
Financial liabilities at fair value
through profit and loss
Loans and advances to customers
587,448
– trading liabilities
108,049
– non-trading derivatives
15,825
– designated as at fair value 12,707
Investments in associates
1,494
– through profit and loss
Real estate investments
562
Liabilities held for sale
10,415
Property and equipment
5,615
Other liabilities
23,035
Intangible assets
2,265
Assets held for sale
300
Other assets
26,023
Total liabilities898,004
Total assets
933,073Total equity and liabilities933,073
Apart from the above mentioned cause of liquidity risk, there are more factors that
may be the cause that a bank has insufficient funds to fulfil its short-term obligations. First, it is possible that the term of the taken fixed term deposits or savings
accounts is shorter than the term of the granted loans. In this case the bank has to
renew the funding several times during the term of its loans. Next, banks run the
risk that customer’s may use their right to take up their fixed term deposits ear­
lier than the pre-agreed term. And banks also run the risk that some of their assets
prove to be nonperforming which means that the bank will not receive the money
back that it has lent out. Banks may be also be faced with the obligation to pay margin calls if the value of their derivative contracts decreases, whilst at the same time
they will not receive the same margin amount from the counterparty in the offsetting transaction. This is the case, for instance, if the counterparty is a sovereign for
whom banks normally conclude unilateral collateral agreements.
Every day, the back-office department of the financial markets department, draws
up cash management and short-term liquidity reports. These reports include the
following items. First, all maturing loans and deposits. Second, the settlement flows
from securities transactions, FX transactions and derivatives are reported. And fi247
guide to treasury in banking
nally the forecasts of net client money transfers are included. Normally, a liquidity
report shows a negative balance in the short term. This means that bank’s normally
need to find short-term funding.
Under normal market conditions a bank that is perceived to be financially healthy
will have relatively easy access to wholesale funds on the interbank market. And,
also under normal market conditions, customers will also react in a normal rationale manner.
However, if the market is under stress, liquidity may dry up and be less readily available while, on the other hand customers may withdraw their money in order to invest in save assets like Government bond or gold.
Apart from stress conditions in the liquidity market, an individual bank may come
under pressure if there are doubts about its financial position, if for example there
are concerns about its asset quality, earnings, or as a result of the failure of a similar
institution. A bank then may find it more difficult to raise funds in the interbank
market and depositors may withdraw their funds.
It is therefore important for banks to consider liquidity management under stressed
or crisis conditions. For this reason, banks also produce a liquidity forecast under so
called stress conditions. In this report they take into consideration, for instance, the
effects of a flight of volatile deposits or a sudden increase in the margin calls that
they have to pay with respect to their derivative contracts.
15.3 Sources of liquidity
The most important asset of a bank with respect to liquidity is the item ‘cash and
balances with the central bank’ which for most part represents the balance at the
current account that a bank holds with the central bank. Banks use this account for
every inter-bank transfer that they make in their home currency. The central bank
account of most commercial banks was opened hundreds of years ago at the time
that the banks sold their gold reserves to the central bank. Since then, the balance
of these accounts only grow because of the fact that these balances earn interest
and because of the fact that commercial banks from time to time have sold more
gold, foreign exchange or other financial values to their central bank.
However, during the past centuries the balances of the central bank accounts
grew at a much slower pace than the immediately demandable balances of the
customers of the commercial banks as a result of money creation. For instance,
the bank for which the balance sheet was shown in figure 15.1 may only have a
balance of six billion on its central bank account while the total of the immedi248
liquidity risk
ately demandable balances of its clients, for instance, is three hundred billion.
This means that the demandable balances exceed the banks cash liquidity by a
factor fifty! And, in turn, this means that, if the customers would decide to transfer their money to other banks, the balance of this bank’s central bank account
will very soon dry up. If the total amount of the transferred money would exceed (only!) six billion, without taking appropriate measures, this bank would be
bankrupt.
Although the above mentioned ratio of 2% between a commercial bank’s balance
on its central bank account and its demandable liabilities may not seem very realistic at first glance, it is, in fact, the reality in some developed countries. In the euro
area, for instance, banks are only obliged to maintain a so called mandatory cash
reserve of 2%. This means that every bank, for a continuous period of a month (the
retention period), must maintain an average balance on its central bank account for
an amount of only 2% of its short-term obligations, including current account balances, deposits with a fixed term of up to two years, deposits with a notice period of
up to two years and bonds with an original term of up to two years.
If a bank wants to increase the balance on its central bank current account, it can
try to attract deposits from customers. If a fund manager of a bank looks at his cash
management report and finds out that he needs money during the next coming
days, he immediately orders the client advisors of the bank to call their customers
to convince them to deposit their money with the bank. Normally, the fund manager will try to seduce the customers by increasing his bid rate for deposits. This helps
to attract balances of clients that are held with other banks and might also prevent
customers to invest the balance that they hold at the bank with another bank.
Once the source of client money has dried up, the fund manager can try to borrow
money form other banks. Before the global financial crisis, this was very common.
Nowadays, however, it is practically impossible for many banks to fund themselves
in the inter-bank market. If banks are not able to get the needed funding from other
banks, they have to borrow form the central bank as a lender of last resort.
The central bank is not only used as a lender of last resort as a result of the global financial crisis, however. Under normal market conditions, in many developed countries the banks collectively have to rely on the central bank as a lender because of
the fact that in many monetary areas the central bank sets the mandatory cash reserve at a level that exceeds the actual collective balances on the current accounts
of the commercial banks. For instance, the bank in the previous paragraph may
have had a balance of 5.5 billion while the cash reserve requirement was 6 billion.
Since the central bank imposes the cash requirement for all banks, it creates a collective deficit in the money market. This means that banks collectively always have
to borrow money from the central bank. Central banks use many instruments for
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this purpose. The first instrument is open market transactions, i.e. transactions in
financial instruments such as repurchase agreements, deposits, FX swaps and cash
securities transactions.
As an example, the ECB uses four categories of open market transactions:
–
Main refinancing operations (MRO): weekly tenders of repurchase agreements with a term of one week;
– Longer-term refinancing operations (LTRO): monthly tenders of repurchase agreements with a term of three months;
–‘Fine tuning’ transactions: tenders of bilateral repurchase agreements, FX
swaps or time deposits on the last day of a reserve retention period where
the objective is to capture potential imbalances;
– Structural transactions: issue of its own bonds, purchases of securities or
repurchase agreements with the objective of influencing the structural
position of the euro system.
During the global financial crisis, the regular operations were complemented by
euro liquidity-providing operations with a maturity of (around) one, six, twelve and
thirty-six months.
Since the ECB always sets the size of the obligatory cash reserve so that there is always a collective deficit in the money market, the ECB always acts as a repo buyer
with its refinancing operations. Thus, the ECB only expands the money market with
the help of these transactions. The interest rate used by the ECB for the basic refinancing transactions is called the refinancing rate or refi rate. The ECB also uses the
refinancing rate as the interest rate for the balances on the accounts of the commercial that do not exceed the mandatory cash reserve.
Apart from the open market transactions, the ECB has two so-called ‘standing facilities’:
–the marginal loan facility: call money facility against assets acceptable as
collateral. The interest rate on these loans is set 50 basis points to 100 basis
points higher than the refinancing rate and normally acts as a ceiling for
the overnight money market interest rate;
–the deposit facility: an opportunity to hold short-term deposits with the
ECB. The interest rate paid for these deposits is set 50 basis points to 100
basis points lower than the refinancing rate and normally acts as a floor for
the overnight market interest rate.
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liquidity risk
All regular instruments that the ECB uses to provide temporary cash involve collateral. And for every type of collateral, the ECB applies a haircut that depends on the
term of the security given as collateral and on the creditworthiness of the issuing
institution. The surplus percentage for regular securities varies from 0.5% to 20%.
For asset-backed securities, however, it even can be higher than 20%.
In the United States, the Federal Reserve Bank (Fed) sets the cash reserve requirements in such a way that there is sometimes a surplus and sometimes a deficit in
the money market. The Fed concludes so-called System repos to increase the liquidity in the money market and Matched Sales repos to tighten the money market. The
interest rate that the Fed uses is called the fed funds rate. Banks can also borrow
money from the Fed by using the ‘discount window’. The Fed uses the discount rate
for this. This interest rate is at least 1% higher than the fed funds rate. The Fed has
no facility for credit funds. A credit balance at the Fed never earns interest.
As we have seen, if a bank needs to borrow from the central bank, it normally has to
pledge a collateral. This is one of the reasons that banks hold large portfolios of government bonds and other very liquid securities. These are securities that are traded on a liquid market. Features of liquid markets are, for instance, the existence of
market makers. An exchange is normally also considered a liquid market. However,
there is a cost to holding these securities. This is because Government bonds usually have a lower rate of return than long term assets that are less liquid.
15.4
Liquidity risk management
The ultimate responsibility for liquidity management lies with the Asset and Liability Management committee. For the day-to-day execution of the policy and the monitoring of the liquidity risk, however, many banks have installed a dedicated ALM/
Liquidity group within the Financial Markets Department.
The ALM/Liquidity group meets every week and discusses important issues related to liquidity risk. For example the coordination between the credit department
and treasury. A good coordination is essential in order to avoid over extension of
credit. Another topic that is discussed is the central banks actions such as the use
that must be made of the liquidity support of the ECB. Other topics that are regularly monitored are the quality of the assets and the related level of potential non
performing assets, the diversity of depositors and the amount of undrawn commitments.
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guide to treasury in banking
One of the essential responsibilities of the ALM/Liquidity group is to identify
symptoms that may indicate a severe liquidity threat. Examples of such symptoms
on the liability side of the balance sheet are unexpected and significant withdrawals of retail deposits or the non-renewal of wholesale funding facilities on a large
scale. Other signals for possible liquidity problems are a fall of the core retail deposit volumes below projected levels, a shortening of the maturities of the deposits
or a rise in requests to break fixed deposits.
Signals on the asset side of the balance sheet include a faster than projected growth
in retail advances, a lengthening of the term of loans, a larger than expected drawdown of committed facilities, a significant rise in undrawn committed facilities, a
rise in defaults and the fact that prepayments of loan facilities fall below historic
behavioural norms.
To identify liquidity risk, bank use gap reports as the most important tool. A liquidity gap report gives an overview of the remaining contract terms of all assets and liabilities. The report shows the net asset position for every time bucket. Besides the
gap report, banks calculate the liquidity/asset ratio, i.e. the ratio of liquid assets to
total liabilities. Finally banks calculate concentration ratios to measure the relative
importance of funding from a particular source.
If one or more of these reports indicate a liquidity problem, the ALM/Liquidity
group may suggest a number of measures to the Asset and Liability Committee:
–
–
–
–
–
–
–
–
–
A cap on interbank borrowing or call borrowing
A decrease in the concentration of wholesale funding
An increase in the average duration of the liabilities
Demanding a matched funding for large loans
Decrease the amount of committed credit lines
Raise retail deposit interest rates
Raise loan interest rates to discourage new borrowings
Reduce liquid assets to the regulatory minimum
Place a cap on the balance sheet growth
In order to be able to avoid that temporary liquidity problems may turn into a severe liquidity crisis, the ALM/Liquidity group sets up a contingency plan for liquidity management. This plan must contain a blue print for asset sales, a blue print for
access to alternative markets, a blue print for the restructuring of the maturity and
composition of assets and liabilities, a description of alternative options of funding
and a description of the possibility of back-up liquidity support in the form of committed lines of credit.
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liquidity risk
15.5
Basel II minimum global liquidity standards
As a response to the fact that during the global financial crisis, funding suddenly
dried up, the Basel Committee has decided to introduce two global minimum liquidity standards to make banks more resilient to potential short-term disruptions
in access to funding and to address longer-term structural liquidity mismatches in
their balance sheets: the liquidity coverage ratio (LCR) and the net stable funding
rate (NSFR). These ratios are added to pillar II of the Basel rules.
15.5.1 Liquidity Coverage Ratio
The liquidity coverage ratio (LCR) is a ratio that requires banks to maintain unencumbered high-quality liquid assets sufficient to meet at least 100% of net cash
outflows over a 30-day period under a stress scenario. Unencumbered means not
pledged as collateral. There are two important elements in respect to the LCR. Firstly the estimated (net) cash outflows during the next coming thirty days and secondly the amount of so called High Quality Liquid Assets (HQLA). The official BCBS
document on the LCR states: ‘The objective of the LCR is to promote the short-term
resilience of the liquidity risk profile of banks. It does this by ensuring that banks
have an adequate stock of unencumbered high-quality liquid assets that can be converted easily and immediately in private markets into cash to meet their liquidity
needs for a 30 calendar day liquidity stress scenario.’
To find out whether a bank complies with the LCR requirement, firstly all scheduled
cash inflows for the next 30 days are detemined. However, a cash inflow ratio is applied to all the contractual inflows or facilities. This ratio is either 0, 50% or 100%.
If the ratio is 50%, then the scheduled cash inflow is only reported for 50% of the
scheduled amount. If a bank has, for instance, 400 million maturing loans during
the next 30 days, then only 200 million is reported in the LCR report. If the ratio is
100%, then the scheduled cash inflow can be taken in the LCR report for the whole
amount. If there is a scheduled inflow on behalf of an interest rate swap of 10 million after three weeks, for instance, this can be reported as a LCR cash inflow of 10
million. And if the ratio is 0%, then this means that in the LCR report this item is
not reported as a cash inflow at all. Reverse repos backed by level 1 assets, for instance are not reported in the LCR report.
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guide to treasury in banking
type of loan / facility
% cash inflow
Retail loans
50%
Loans to financial institutions
100%
Reverse repo backed by level 1 assets
0%
Reverse repo backed by non-HQLA assets
100%
Operational deposits (clearing, custody, cash management, collateral)
0%
Committed facilities
0%
(Scheduled cash inflows stemming from derivatives contracts)
(100%)
(Scheduled cash flows stemming from derivatives contracts)
(100%)
Secondly the cash outflows are determined. This is the sum of all scheduled cash
outflows (adjusted with a ratio) and a number of unscheduled cash outflows. Examples of scheduled cash outflows are maturing deposits, maturing money market papers issued by the bank or maturing bonds. Examples of non-scheduled cash
outflows are withdrawals on non-maturing liabilities such as balances on current
accounts or balances on savings account without a contractual term. Another example of non-scheduled outgoing cash flows are early repayments for loans that
the bank has taken up itself or extra collateral requirement in case of a downgrade
of the bank. Still another example is the potential extra drawing on credit lines by
­clients of the bank. And finally an example of an additional stressed cash outflow
are margin calls as a result of a decrease in the market value of already pledged collateral.
type of funding
prescribed run-off %
Stable deposits (covered by a deposit insurance scheme)
3%
Less stable deposits
10%
Small business customers
10%
Operational deposits (clearing, custody, cash management)
25%
Non-financial corporates
40%
Issued securities
100%
Derivatives
100%
Repo / covered bond backed by level 1 HQLA
0%
Repo / covered by non-HQLA assets
100%
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liquidity risk
additional stressed cash outflows
Result of downgrading, early repayment / pledge of extra collateral
Draws on credit facilities
Margin calls as a result of a decrease in market value of collateral
Next the net (stressed) cash outflows are calculated as the difference between the
(stressed) cash outflows and the cash inflows. The (net) cash outflow is then compared to the amount of HQLA.
High quality liquid assets (HQLA) are assets that have low credit and market risk,
be easy and certain to value, have a low correlation with risky assets and, if marketable, must be listed on a developed and recognized exchange market. They also
should be traded on an active and sizeable market, where committed market makers operate, where there is a low market concentration and where there are investors that show a tendency to move into these assets during a systemic crisis (move
to quality).
The LCR requirement is two-fold. Firstly the amount of HQLA should be higher
than the net stressed cash outflows. And secondly the amount of HQLA should be
higher than 25% of the total reported stressed cash outflows.
example
A banks reports the following figures in its LCR report:
Cash inflows:
110
Cash outflows:
130
HQLA:
30
To determine whether this bank complies with the LCR rules, the amount of HQLA
should be compared to the net stressed cash outflows and to the total net cash outflows respectively.
HQLA (30) > net stressed cash outflows (20) p the bank complies
HQLA (30) < 25% total stressed cash outflows (32.5) p the bank does not comply
Since the bank must fulfill both requirements at the same time, the bank does not
comply with the LCR rule.
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guide to treasury in banking
15.5.2 Net stable funding ratio (NSFR) – 2018
The net stable funding ratio is a longer-term structural liquidity ratio. The NSFR ratio distinguishes between available stable funding (ASF) and required stable funding (RSF) whereby the first must always be higher than the second: ASF > RSF. To
calculate ASF and RSF, a percentage is assigned to all balance sheet items in order
to indicate how stable this item is in terms of liquidity. For instance, for equity the
percentage is set at 100%. This means that equity is considered as a completely stable funding alternative. For amounts due to banks, on the other hand, the percentage is set at 0%. This means that in terms of stable funding, this item is completely
worthless. Balances on current accounts held by clients are considered to be fairly
stable. This is why they are assigned a weighting of 80% to 90%. On the asset side
of the banks’ balance sheet, for instance the item cash and balances with the central
bank’ is set at 0%. This means that this item doesn’t need any stable funding at all.
The percentage for loans to clients with a remaining term longer than 1 year, however, is set at 100%. This means that this item must completely be funded with stable funding.
As available stable funding the following items qualify:
–
–
–
–
Weighting 90%
Stable non-maturity deposits and/or term deposits with maturities of less
than one year provided by retail and small business customers.
–
Weighting 80%
Less stable non-maturity deposits and/or term deposits with maturities of
less than one year provided by retail and small business customers.
–
256
Weighting 100%
Capital (both Tier 1 and Tier 2) after deductions
Preferred stock not included in Tier 2 with effective remaining maturities
of one year or greater
Liabilities with effective remaining maturities of one year or greater.
Weighting 50%
Unsecured wholesale funding, no-maturity deposits and/or term deposits with residual maturity of less than one year provided by non-financial
corporates, sovereigns, central banks, PSEs and multilateral development
banks.
liquidity risk
The Required Stable Funding is the sum of the following items:
–
Weighting 0%
Cash and money market instruments; securities with effective remaining maturities of less than one year; securities where the bank has an
offsetting reverse repo with the same CUSIP or ISIN; loans to financial
institutions that are not renewable or for which the lender has an irrevocable call right.
–
Weighting 5%
Marketable securities with residual maturities of one year or greater representing claims on sovereigns, central banks, BIS, IMF, EC, non-central
government PSEs or multilateral development banks rated AA or higher
and assigned 0% risk weight under Basel II standardised approach,
provided that active repo-markets exists.
–
Weighting 20%
Corporate bonds or covered bonds (but not loans) rated at least AA-with
an effective maturity of one year or greater satisfying all Level 2 criteria for
corporate and covered bonds under LCR; marketable securities with residual maturities of one year or greater representing claims on sovereigns,
central banks, non-central government PSEs satisfying all Level 2 criteria
under LCR.
–
Weighting 50%
Gold; equity securities not issued by financial institutions or an affiliate listed on a major exchange and included in a large capital market
index; corporate bonds and covered bonds (a) eligible for central bank
intraday and overnight liquidity needs, (b) not issued by financial institutions or affiliates, (c) not issued by a bank or affiliate, (d) rated A+ to A-(or
equivalent PD), and (e) traded in large, deep and active markets; loans to
non-financial corporate clients having a residual maturity of less than one
year.
–
Weighting 65%
Residential mortgages qualifying for 35% risk weight under the Basel II
standardised approach; loans (excluding loans to financial institutions)
with a maturity of one year or greater qualifying for 35% risk weight under
the Basel II standardised approach.
–
Weighting 85%
Loans to retail and small business customers with a residual maturity of
less than one year.
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guide to treasury in banking
–
Weighting 100%
All assets subject to a claim of another party (encumbered assets) and all
other on-balance sheet assets.
example
In its NSFR report, a bank reports the following data to its central bank (x billion):
–
Capital, preferred stock, liabilities with remaining term > 1yr
–
Stable non-maturity retail and small business deposits > 1 yr
100
–
Less stable non-maturity retail and small business deposits , 1 yr
250
–
Unsecured wholesale funding etc
120
–
Cash and money market instruments
35
–
Marketable securities on AA rated Sovereigns > 1 year
20
–
AA-rated Corporate bonds > 1 yr
10
–
Equity securities not issued by financial institutions
–
Mortgages qualifying for 35% risk weight under Basel II SA
–
Loans to small businesses < 1 yr
–
Other assets
20
20
150
20
235
The available stable funding of this bank can be calculated as follows:
–
Capital, preferred stock, liabilities with remaining term > 1 yr
–
Stable non-maturity retail and small business deposits > 1 yr
100 x 100%
20 x 90%
–
100
18
Less stable non-maturity retail and small business deposits , 1 yr
250 x 80%
–
Unsecured wholesale funding etc
120 x 50%
200
60
Total AFS378
The required stable funding of this bank can be calculated as follows:
258
–
Cash and money market instruments
35 x 0%
–
Marketable securities on AA rated Sovereigns > 1 year
20 x 5%
–
AA-rated Corporate bonds > 1 yr
10 x 20%
0
1
2
liquidity risk
–
Equity securities not issued by financial institutions
20 x 50%
–
150 x 65%
–
10
Mortgages qualifying for 35% risk weight under Basel II SA
97.5
Loans to small businesses < 1 yr
20 x 85%
–
Other assets
235 x 100%
Total RSF
17
235
362.5
Because AFS exceeds RSF, this bank meets the RSF ratio.
259
Chapter 16
Credit Risk
Credit risk is the risk associated with the event that a counterparty will fail to meet
its obligations in a financial contract. To calculate credit risk a bank must estimate
the probability that a counterparty will fail to meet its obligations, the value of the
obligations at the time of failure and the part of the exposure that will eventually be
lost.
16.1 Types of credit risk
Banks make a distinction between three types of credit risk: debtor risk, settlement
risk and pre-settlement risk.
16.1.1 Debtor risk
Debtor risk is the risk that a borrower cannot pay the interest and/or repay the principal sum of a loan. Debtor risk starts with the conclusion of the credit agreement or
with the purchase of an interest bearing security and ends at the moment of repayment. With debtor risk, some banks make a sub-division into three types of credit
risk: the risk associated with loans, investment risk and money market risk. Risk associated with loans is the risk that borrowers are unable to meet their obligations.
Investment risk is the risk that the institutions issuing the bonds in an investment
portfolio are unable to meet their obligations. Money market risk is the risk that
counterparties with whom banks have placed their short-term liquid assets are unable to meet their obligations.
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guide to treasury in banking
16.1.2 Settlement risk or delivery risk
The risk that a counterparty defaults with the settlement of a transaction is called
settlement risk or delivery risk. Settlement risk only occurs when both parties have
a simultaneous delivery to settle money amounts or other financial values. The risk
entails one party meeting its delivery obligations while the other does not.
Banks run this risk, for example, with FX transactions and with cash securities
transactions. The two opposing transfers arising from these transactions often take
place independently of each other. For example, for a shares transaction, the transfer of the shares takes place at the central securities depository while the transfer of
the money may take place at the central bank. For cur­rency transactions, the transfer in both currencies takes place at the two different central banks of the traded
currencies.
The amount of the settlement risk arising from FX transactions is calculated by calculating the sum of the values of the incoming transfers resulting from the transactions that must be settled on a particular date with one and the same counterparty.
To calculate the counter value of these incoming transfers in the bank’s own currency, the current spot rates are used.
example
A German bank has concluded the following FX transactions with another bank
each of which will be settled on 16 October.
Buy USD 1 million against CHF, contractual exchange rate is 1.3200
Sell EUR 10 million against USD, contractual exchange rate is 1.2700
Buy GBP 5 million against USD, contractual exchange rate is 1.8000
The current FX rates are:
EUR/USD
1.2300
USD/CHF 1.3000
EUR/GBP
0.9000
The size of the delivery risk in euro is
1st transaction: 1,000,000 / 1.2300 = EUR 813,008.13
2nd transaction: 10,000,000.00 x 1.2700 / 1.2300 = EUR 10,325,203.25
3rd transaction: 5,000,000 / 0.9000 = EUR 5,555,555.55
Total: EUR 16,693,766.94.
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credit risk
16.1.3 Replacement risk or pre-settlement risk
Pre-settlement risk or replacement risk is the risk that a counterparty is unable
to meet its obligations under a derivatives contract and, as a consequence, this
contract needs to be replaced in the market at unfavourable conditions. Contract
parties run pre-settlement risk from the moment that a derivative contract is concluded until the maturity date of that contract.
If a contract has a positive market value for the bank, the bank therefore incurs a
credit risk as they stand to lose this positive market value if their counterparty defaults. The value of this risk involves all the future cash flows, thus including any
net periodic payments that the counterparty has not yet paid (dirty market value).
The concept of replacement risk can easily be illustrated by the diagrams below. Figure 16.1 shows an original client transaction (left), an IRS with a term of five year
and a fixed rate of 5%, and the offsetting transaction that the bank had concluded
on the same moment (right).
Figure 16.1 Client transaction and offsetting transaction in the market
5%
Customer
5%
Bank
EURIBOR
Market
EURIBOR
Pre-settlement risk or replacement risk is the risk that, during the term of the contract, the client will prove not to be able to fulfil its obligations. If the client defaults,
the original client transaction may be ended without repercussions for the client.
As a result, the bank now has an open interest rate position, that it should close by
concluding a so-called replacement transaction on the market. If the conditions of
this new contract are worse than the conditions of the origi­nal client transaction,
the bank will suffer a loss.
Figure 16.2 shows what happens if the client defaults after six months and the IRS
market rate has then decreased to 4%.
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guide to treasury in banking
Figure 16.2 Replacement of the original client transaction
5y
5y
5%
5%
Customer
Bank
EURIBOR
Market
EURIBOR
4,5y
4%
Market
In order to close its, now open, position, the bank concludes a receiver’s swap with
a remaining term of 4.5 years and a fixed rate of 4%. As a result, the bank will lose
1% per year over the notional amount of the IRS for the remaining term of the IRS,
i.e. 4.5 years. If the fixed coupon of the original IRS was paid annually, the bank also
will lose half a year interest, i.e. 0.5 x 1% over the notional.
Credit risk is a one-sided risk. This means that the bank can only lose as a result of
credit risk and is, under any circumstance, not able to take profit from a default of
one of its customers. If, at the moment of default, a contract has a positive market
value for the defaulting party, the administrator of this party will allow the contract
to continue its normal course and the bank must continue to meet its obligations,
alternatively the administrator may ask the bank to unwind the swap contract and
receive from the bank the positive market value of the IRS.
16.2 Factors that determine the amount of credit risk
Bank make a distinction between expected losses and unexpected losses. Expected
loss is the most probable loss that a bank will suffer during a pre-defined time interval (according to the Basel rules: one year). Expected loss is approached by a stochastic calculation based on certain assumptions. To cover its expected loss, banks
keep provisions for which they use the credit spread that they charge in their financial contracts. Unexpected losses are the possible deviations from the expected loss.
To cover unexpected loss, banks have to hold capital.
There are three factors that determine the expected loss as a result of credit risk: the
probability of default (PD), the exposure at default (EAD) and the loss given default
(LGD). The amount of expected loss can be calculated by the following equation:
Expected loss = PD x EAD x LGD
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credit risk
probability of default
The probability of default (PD) is the average probability that a counterparty in a
specific credit category will not meet its obligations on a specific moment or during
a specific term. According to Basel II, a default takes place if a counterparty is more
than three months overdue in fulfilling its obligations.
exposure at default
Exposure at default (EAD) is the value of a claim or a financial contract at the time
that a counterparty defaults. If a bank has entered into a loan or if it has purchased a
bond, the exposure at default is easy to determine. In that case the EAD is the nominal value of the loan or bond, including accrued interest, less any repay­ments or
write-downs (impairments).
With derivatives contracts, the EAD during the term is measured by calculating the
present value of all mathematical expected future cash flows. With interest rate instruments, therefore, accrued interest is taken into account too. This is because if a
counterparty defaults, a bank will fail to receive all future cash flows, including the
part of the first next interest coupon for which the bank already has accounted the
accrued interest.
Subsequently, banks construct scenarios, based on the historic volatility, for the
price determining variables (and other factors) during the remaining term of the
contract to determine the average expected exposure. For this, they normally use
Monte Carlo simulation models. The idea is to generate many scenarios, i.e. 3000
- 10.000.
For each scenario the market value of a single contract or is calculated. Next, all the
calculated market values are ranked from high to low. Banks will select the market
value of a high percentile, such as 95% or 97.5%, to approach their potential future
exposure (PFE) and the 75% percentile to approach their expected eposure (that is
used for CVA calculations).
If a bank calculates the EAD of a contract, it takes into account the collateral it
has received for that contract. If there is a contractual netting agreement in place,
only the netted market value of the contracts is considered as an exposure. Contractual netting or close-out netting is an agreement between two parties to offset
the positive and negative values of all the contracts they have concluded should
one of the parties go bankrupt. In this way, only one net risk remains. A close-out
netting agreement is often included in master agreements such as an ISDA or an
IFXCO agreement. IFXCO stands for International Foreign Exchange and Currency
Option Master Agreement. Contractual netting, however, is only possible for con265
guide to treasury in banking
tracts that are part of a netting set, which means that they are concluded under one
and the same master agreement. Master agreements are typically signed on a legal
entity level. The agreement may or may not include different branches from both
sides.
Sometimes, the exposure at default and the probability of default are correlated.
This phenomenon is referred to as wrong-way risk. The terms ‘wrong-way risk’ and
‘wrong-way exposure’ are often used interchangeably. Ordinarily in trading book
credit risk measurement, the creditworthiness of the counterparty and the exposure of a transaction are measured and modelled independently. In a transaction
where wrong-way risk may occur, however, this approach is simply not sufficient
and ignores a significant source of potential loss.
example
A bank concludes a repo transaction with a bank in a very small country as a repo
buyer. As a collateral it accepts bonds of another bank that has its domicile in the
same country as the counterparty in the repo transaction.
If there is a dramatic change in the economic or political situation in the home country of the counterparty in the repo transaction, the creditworthiness of this party is
very likely to decrease, i.e. its PD will go up. The same will be true, however, for the
issuer of the bonds that are accepted as collateral. As a result, the market value of
these bond will decrease and, therefore, the exposure of the repo will increase.
The conclusion is that the chance that the repo buyer will lose money and the
amount of money that he will lose are positively correlated.
loss given default
Loss given default (LGD) is the part of the exposure that a bank will lose if a counterparty defaults. The LGD depends on the effort and skills of the admin­istrator who
takes care of the unwinding of the defaulted company and of the value of the assets
of the company that are not used as collateral.
the expected loss on a portfolio level
To calculate the expected losses for their total credit portfolio, banks simply multiply the EAD, the LGD and the PD for each risk category and then add all the outcomes. The following table shows an example of the calculation of the expected loss
for a total credit portfolio.
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credit risk
category
12 34567 8 910
PD (%)
0,51 23468121520
EAD (bn)
62,550
87,5
10050
37,525
12,5
6,252,5
433,75
LGD (%)
EL (bn)
8080 8080808080 80 80 80
0,250,4 1,42,41,61,81,6 1,20,75 0,411,8
The first row of the table shows that this bank has divided its credit portfolio
into ten categories. The second row shows the PD of each category; the PD of the
catego¬ry with the most creditworthy clients is 0.50% and the PD of the category
with the less creditworthy clients is 20%. The third row shows the total exposure
in each category. The total exposure of this bank to credit risk is the sum of all the
exposures in each risk category: 434 billion. The fourth row shows the loss given default in that category. For each category the expected loss is calculated by multiplying the figure in the second, third and fourth row (PD x EAD x LGD). The expected
loss for catego¬ry 1 is 0.5% x 62,5 billion x 80% = 250 million. And the expected loss
for category 10 this is 20% x 2,5 billion x 80% = 400 million. The total expected loss
is calculated as the sum of the expected loss for each category and amounts to 11.8
billion.
Banks are allowed to take provisions to form a buffer to cover their expected loss.
However, there is no certainty that the expected loss will be the loss that is realised
the future. It may turn out that the loss will be much larger. A bank that would only
hold a provision against the expected loss, runs a 50% risk that it would not have
sufficient coverage against its credit risk.
16.3 Regulatory capital for debtor risk
Under the Basel rules banks are required to hold capital to cover unexpected losses.
Banks can report the size of the unexpected debtor risk under Basel II and Basel III
in various ways. Small banks normally chose for the Standardized Approach. With
this approach the nominal value of each exposure is weighted according to the external rating of the counterparty.
The Standardized approach is related to the way in which banks had to report under
Basel I: i.e. the nominal value of the loans adjusted by a weighting factor. Under the
current Basel rules, the weighting factors per customer group are linked to the ratings of rating agencies. This is shown in the following table:
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guide to treasury in banking
aaa - aa- a+ - a-
bbb+ - bbb-bb+ - bb- bb- - b-
below b- unrated
Governments
0% 20%50%100%
100%
150%
100%
Banks 20%20%20%50%50%150%
20%
< 3 months
Banks 20%50%50%100%
100%
150%
50%
> 3 months
Corporates
20% 50% 100%100%150%150%100%
example
A bank that uses the standardized approach to report its credit risk reports the following outstandings on its counterparties, i.e. the sum of the not yet amortized
amounts of its loans including accrued interest and the potential future exposure of
all derivatives contracts.
aaa - aa-
a+ - a-
bbb+ - bbb-
bb+ - bb- bb- - b-
below b-
unrated
Governments
20 bn
6 bn
3 bn
1 bn
1bn
0
0
Banks 00
0
000 0
< 3 months
Banks 10 bn
5 bn
2 bn
0
0
0
0
50 bn
40 bn
20 bn
10 bn
0
5 bn
100 bn
> 3 months
Corporates
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credit risk
The weighted nominal amount are calculated as follows:
aaa - aa-
a+ - a-
bbb+ - bbb-
bb+ - bb- bb- - b-
below b- unrated
Governments 20 bn x 0%
6 bn x 20%
3 bn x 50%
1 bn x 100%
1bn x 100% 0
= 0
= 1.2 bn
= 1.5 bn
= 1 bn
= 1 bn
Banks 0
0
0
0
0
0
0
0
0
0
0
5 bn
100 bn
0
< 3 months
Banks 10 bn x 20% 5 bn x 50%
2 bn x 100%
> 3 months
= 2 bn
= 2bn
Corporates
50 bn x 20% 40 bn x 50% 20 bn x 100%
10 bn x 100% 0
= 10 bn
= 10 bn
= 2.5 bn
= 20 bn
= 20 bn
The total weighted nominal amount of all the contracts is 178.70 billion. This bank,
therefore has to hold 8% x 178.7 billion = 14.29 billion of capital as a buffer against
its credit risk.
internal rate based (irb) approach
Banks that use internal models to calculate their credit risk are allowed to use the
internal rating based method (IRB) to report their unexpected credit risk. With this
method, the capital requirement for a credit exposure is expressed as a percentage
of the EAD by the following equation:
Capital requirement (K) = [LGD * N [(1-R)-0.5 * G(PD) + (R/(1-R))-0.5 * G(0.999)] – PD*LGD] *
(1-1.5 x b(PD))-1 * - (1+(M-2.5) * b(PD)
Legenda:
N
= standard normal distribution
G
= inverse of the standard normal distribution
R
= level of asset correlation; R is set according to PD within a range of 12% (for PDs of
100%) to 24% (for PDs of 0%) and is adjusted to firm size (0% adjustment for borrowers with 50 mln annuals sales and higher, 4% adjustment for borrowers with 5 mln or
less annual sales). For retail portfolios, R is set in the lower range of 3% to 16%.
M
= average maturity of the portfolio. M reflects the decrease in the value of loans as a result of rating downgrades.
b(PD) = smoothed (regression) maturity adjustment (smoothed over PDs). M is adjusted for
PD since M is higher for exposures with a low PD than for exposures with a high PD.
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From the equation it becomes clear that the required capital is equal to the differende between the total credit risk and the expected loss times the maturity adjustment. Afer all, the equation can be divided into the following three parts:
1. The total credit loss with a probability interval of 99.9%:
[LGD * N [(1-R)-0.5 * G(PD) + (R/(1-R))-0.5 * G(0.999)]
2. The expected loss:
PD*LGD
3. A maturity adjustment as a function of PD and M
(1-1.5 x b(PD))-1 - (1+(M-2.5) * b(PD)
The regulatory capital that a bank should hold can be calculated by the following
equation:
Regulatory capital = K x EAD
For the Foundation IRB method banks may only use self-determined PDs as input for the equation. For all other parameters they must use values which are prescribed by the Basel Committee. With the Advanced IRB method, banks may also
use self-determined values for LGD. But in order to be allowed to do so, they have to
convince the supervisor of the quality of their internal model. The spuervisor stays
responsible for setting R and M.
The equation for K represents point D in the probability distribution which is shown
in figure 16.3.
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credit risk
Figure 16.3
Probability distribution of credit losses
Probability
Confidence interval
95 97,5 99 99,9
Unexpected
Loss
(Credit VaR )
0
provisions
Expected Loss
95%
97,5%
99%
99,9%
A
Loss
B
C
D
Regulatory capital
In figure 16.3 the expected loss is at a point on the x-axis where the probability density for both smaller and greater losses is equal: 50% (e.g. at the 50% percentile).
This is shown by the vertical line. The credit value at risk depends on the chosen
confidence interval and is given by the distance between the total loss with a given
probability interval and the expected loss. For a confidence level of 95% the credit
value at risk, is for instance, represented by the line ‘A’ and for a confidence level of
99.9% the credit value at risk is represented by the line ‘D’. This is exactly the confidence level that is prescribed by the Basel Committee.
16.4
Regulatory capital for counterparty credit risk
To report the credit risk of their derivative contracts, banks are also offered two alternatives. These alternatives mainly differ in the way how the EAD of the contracts
is determined.
The first way that banks can use to approach the EAD is the current exposure method. With this method they have to calculate the current exposures of all contracts
and then use an add-on table to adjust this figure. With the current exposure method, netting is not taken into consideration. The add-on table that is prescribed in
Basel II is shown below.
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guide to treasury in banking
remaining term
interest rates
fx
commodities
< 1 year
0
1
10
1 - 5 years
0,5
5
12
> 5 years
1,5
7,5
15
Next, the outcome of this calculation is adjusted by a weighting. According to the
standardised approach in the Basel rules, the weighting factors per customer group
are linked to the ratings of rating agencies.
aaa- / aa-
a+ / a-
bbb+ / bbb-
bb+ / b- below b-
unrated
Governments0%
20%
50%
100%
150%
100%
Banks > 3m
20%
50%
100%
100%
150%
100%
Banks < 3 m
20%
20%
20%
50%
150%
100%
50%
100%
100%
150%
100%
Corporates20%
If a derivative transaction is cleared by a central counterparty (CCP), the weighting
factor is set at two percent provided that the CCP, amongst others, complies with
CPSS/IOSCO recommendations for CCPs.
Below, several examples are given of the calculations for the capital required by
banks that use the Standardised Approach.
position calculationcapital
requirement
3 month EUR/USD forward contract
1% x EUR 5,000,000 x 100% x 8%
EUR 4,000
4 years IRS
CHF ( 1,200,000 + 0.5% x 100,000,000) CHF 68,000
notional amount: CHF 100,000,000
x 20% x 8%
Notional amount EUR 5,000,000
client: BB-rated corporate client
moment: start date
client: A-rated Bank
remaining term: 3 years
current market value: CHF 1,200,000
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credit risk
The second alternative how banks can approach the EAD of derivative contracts is
to simulate the price determining variables over the future contract term. The EAD
is then set at a level that is referred to as Effective Expected Positive Exposure (Effective EPE).
During the financial crisis, when banks suffered significant counterparty credit risk
(CCR) losses on their OTC derivatives portfolios, it became clear that the majority
of these losses did not come from counterparty defaults but from fair value adjustments on derivatives. The value of outstanding derivative contracts with a positive
value was written down as it became apparent that counterparties were less likely than expected to meet their obligations, i.e. a decrease in their creditworthiness
but not yet a default. Under the Basel II market risk framework banks were only required to hold capital against default and migration risk, but there was no requirement to capitalise against variability in CVA. In Basel III, therefore, also a capital
charge to cover future changes in CVA was implemented, i.e. the CVA variability
charge also only referred to as CVA. CVA, therefore, has two meanings. Firstly the
price of counterparty credit risk internally used to determine the credit spread for a
derivative contract and secondly a capital charge for the variability of the CVA.
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Chapter 17
Credit Risk – Risk
Mitigating Measures
Introduction
In order to restrict the exposure to a counterparty banks may take a number of
measures. First, they set a counterparty limit for each counterparty. Second, they
can use netting contracts. Third, they can ask collateral. Next, they can use a central
counterparty and finally, to restrict settlement risk, they can make use of the CLS
bank. Finally, they can use credit default swaps or set up securitisation transactions.
17.1 Counterparty limits
A counterparty limit is a limit on the size of the obligations of a particular counterparty. Counterparty limits are usually entered in a separate limits system by an
employee of the Credit Risk Management department. This limits system often has
a direct interface with the front-office systems of the traders in the dealing room.
If a trader wants to conclude a transaction, he must first enter it in his front-office
system to check that the counterparty limit will not be exceeded. This is part of the
pre-trade compliance.
Counterparty limits are applied for by account managers and determined by separate independent credit committees. The level of the counterparty limit depends
on the creditworthiness of the counterparty in question. When deter­mining creditworthiness, credit committees evaluate factors such as the eco­nomic data of the
counterparty, the quality of the management, the prospects within the business sector in question and the competitive position of the coun­terparty. In addition, credit
committees take the concentration within the credit portfolio into consideration.
After all, an individual debtor may not form too great a part of the entire portfolio and the same applies to a specific business sector or region. A counterparty limit normally applies to all of the organiza­tions that together form a legal entity and
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guide to treasury in banking
for transactions concluded by every part of the bank, including foreign offices. The
counterparty limit is then referred to as a global limit.
A counterparty limit is sometimes divided into sub-limits for particular instru­
ments or groups of instruments. Sometimes, there is a sub-limit for FX for­wards
and FX options. This sub-limit is called a forex limit. When other instruments, such
as interest rate swaps, are also administered under this sub-limit, the limit is sometimes referred to as a derivatives limit.
Each time a dealer or salesman concludes a transaction with a specific counter­party,
it is administered under the counterparty limit. For derivatives, this is done based
on the potential future exposure. If the total size of the exposure equals the amount
of the limit, no further transactions may be concluded with this counterparty. The
dealer or salesman must then wait until a current transac­tion has been settled or he
must get approval from his manager.
In addition to counterparty limits, banks have settlement limits or delivery risk limits. These limits set a maximum for the delivery risk that a bank runs with a specific
counterparty.
17.2 Covenants
In loan agreements, bank normally take up covenants as a measure to mitigate
credit risk. Covenants are conditions that a borrower must comply in order to adhere to the terms in the loan agreement. If the borrower does not act in accordance
with the covenants, the loan can be considered in default and the bank has the right
to demand payment (usually in full).
Banks use two types of covenants, financial covenants an non-financial covenants.
Financial covenants relate to business-economic ratios. Examples of financial covenants are a maximum debt to equity ratio or a minimum interest coverage ratio.
Non-financial ratios, amongst others, refer to the bank’s position as a lender. Examples of non-financial covenants are the pari-passu clause and the cross-default
clause. In a pari passu clause the borrower states that he will not use his assets as a
collateral for another obligation without written consent of the bank. In the crossdefault clause the borrower states that if the borrower defaults in an obligation towards a third party, the bank is allowed to end the loan agreement and may ask its
money back.
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credit risk – risk mitigating measures
17.3 Contractual netting / close-out netting
The second way to reduce the exposure at default is contractual netting or close-out
netting. Contractual netting is an agreement between two parties to net-off the positive and negative values of all the contracts they have concluded if one of the parties
should go bankrupt. In this way, only one net risk remains. A close-out netting is often included in master agreements such as an ISDA or an IFXCO agreement. IFXCO
stands for International Foreign Exchange and Currency Option Master Agreement.
example
A bank has concluded an interest rate swap and an FX forward contract with a single
counterparty.
The interest rate swap has a positive market value of EUR 500,000.
The FX forward contract has a negative market value of EUR 300,000
Without contractual netting, if the counterparty becomes insolvent then the bank
must comply with its obligations under the FX forward contract while the counterparty allows the interest rate swap contract to be dissolved. In this case, the bank will
lose an amount of EUR 500,000. With contractual netting, the market values of the
two contracts are netted off against each other and the bank only loses the balance
of EUR 200,000
Sometimes, two parties agree to nullify all existing contracts and to replace them by
a new contract. This is called netting by novation.
17.4 Collateral
One way to restrict the loss given default is to demand collateral. Collateral is a
pledge that acts as security in the event that a counterparty is in default. Some parties such as the Dutch State never have to provide collateral. On the other hand, there
are parties who always request collateral irrespective of the creditworthiness of the
counterparty. Examples of such parties include clearing houses and, Treasury agencies of OECD Governments. Since the outbreak of the credit crisis, it has become
more usual for banks to demand 100% collateral on all derivative transactions.
The main types of collateral are cash collateral – a sum of money – and securities.
The collateral is entered in a separate collateral system that is linked to the counterparty limits system. With the entry of new collateral in the collateral system, the use
of the counterparty limit will decrease accordingly.
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guide to treasury in banking
cash collateral
Collateral in form of money is used for derivatives transactions and for some securities lending transactions where the money can be seen as the collateral for the borrowed securities. The settlement of cash collateral generally takes place on a daily
basis as a result of changes in the value of the contract during the previous trading day. Cash collateral for derivatives is called margin. Asking cash collateral in
respect to derivatives transaction is a normal routine between banks. When banks
conclude derivative transactions with non-financial companies, they often do not
demand cash collateral but block a part of the counterparty limit.
Banks sometimes employ a threshold. This means that the counterparty only needs
to deposit collateral if the market value of a contract has exceeded a specific predetermined value. From this moment, the margin is settled on a daily basis. Since the
credit crisis, the threshold has, in many cases, reduced to zero
Even if banks demand 100% cash collateral in the form of margins for derivatives,
they impose a specific amount on the counterparty limit of the counterparty. This
amount is called add-on for potential future exposure. There are two reasons for
this. The first reason is the risk that the counterparty, in the event of bankruptcy,
will probably stop with depositing the margins whereby an exposure can originate
in case of further negative price movements. The second reason lies with the replacement risk. If it is clear that a counterparty is no longer able to fulfil its obligations then a bank must conclude a replacement transaction. In such a case, it is
possible that the contract cannot be concluded against the prevailing market conditions. It is possible, then, that the value of the collateral is not sufficient to make
good for the entire loss.
collateral in the form of securities
For repurchase agreements and sell and buy back transactions, securities are used
as collateral. Banks generally only accept securities issued by a party with good
creditworthiness. To determine this, they often make use of credit ratings. In addition, in order to prevent under-coverage, they generally prefer securities whose
prices do not fluctuate much - thus those with a low volatility. Furthermore, they
take into consideration whether the securities can easily be sold if the counterparty
defaults. The securities must therefore be traded on a liquid market. Finally, banks
only accept securities that they can easily value themselves and that they can deposit with one of their custodians.
For collateral in the form of securities, there is the risk of under-coverage. If securities prices fall, the value of the collateral can fall below the level of exposure on
the counterparty. To reduce this risk of under-coverage, banks often apply a haircut.
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credit risk – risk mitigating measures
This means that the bank demands that the value of the collateral is higher than the
claim against the counterparty. A haircut means that only a specific percentage of
the value of the collateral is considered as a cover. If this percentage is 90%, for instance, then the haircut is 10%. The percentage used for the haircut is based on the
volatility of the collateral.
example
A pension fund concludes a securities lending transaction with a hedge fund. The
pension fund delivers 1,000,000 shares in Royal Dutch Shell to a hedge fund under
the agreement that after 1 month the hedge fund will return 1,000,000 shares in
Royal Dutch Shell to the pension fund.
The market price of Royal Dutch Shell is EUR 30. The value of the shares is then:
1,000,000 x EUR 30 = EUR 30,000,000.00. The pension fund, however, only excepts
Dutch State bonds as collateral and uses a haircut of 2%.
The value of the collateral must then be 100/98 * EUR 30,000,000.00 =
EUR 30,612,245.
If the price of the government bonds is 100.37 then the hedge fund must deliver EUR
30,612,245 / EUR 1,003.70 = 30,500 state bonds as collateral.
remargin period
If a bank asks collateral, its credit exposure may seem to be reduced to zero. There
is, however, an important point that must be considered in order to properly assess
the extent of risk reduction. This point refers to the remargin period. This is the period it takes for a bank in a worst case scenario to receive the collateral after a margin call. This period is influenced by the following factors:
–
–
–
Valuation/margin call: the time needed to calculate the current exposure
and the current market value of collateral, working out whether a valid call
can be made and finally making a call. This includes the time delay due to
the agreed margin call frequency;
Receiving collateral: The delay caused due to a counterparty processing a
collateral request from the point they receive the request (fax/mail) to the
point at which they release the collateral;
Settlement: Cash collateral may settle on an intra-day basis whereas securities will take longer;
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guide to treasury in banking
–
Grace period: If a counterparty will not transfer the collateral, there may be
a relevant grace period before the counterparty would be deemed to be in
default.
The remargin period will be significantly longer than the actual agreed margin call
frequency, which is normally 1 day. During the remargin period, a bank still runs
credit risk. Collateral, therefore, will not reduce credit risk to zero, but it reduces the
term of the credit risk exposure from the entire contract term to the term of the remargin period. Although this normally will lead to a tremendous drecrease in credit risk, it is true that there still is a credit risk. Banks normally assume a period of 10
days for the remargin period. In Basel III, the remargin is extended from 10 to 20
days for OTC derivatives netting sets that have illiquid collateral.
17.5 Central counterparties
A central counterparty (CCP) or clearing institution is a financial institution that
acts as an intermediary between market participants. CCPs provide various services to their members, clearing members, with respect to the processing of securities and derivatives transactions. By using a central counterparty, a bank can switch
from many different counterparties to only one. Because this counterparty has a robust framework of risk measures, the chance that this single counterparty will default is approximately zero. Therefore, the credit risk is reduced to a minimum.
Until the credit crisis, broadly speaking, only transactions that were concluded via
an exchange were processed through a CCP, e.g. securities, options and futures.
After the implementation of the G20 requirements concerning the use of central
counterparties and the reporting of derivatives contracts, central clearing is also
required for over-the-counter traded instruments, i.e. plain vanilla interest rates
swaps and credit default swaps. The G20 directive also requires that all derivatives
contracts are reported to a special entity, a trade repository, in order to make the derivatives market more transparent.
The obligation to use a central counterparty is documented, for instance, in the
Dodd-Frank Wall Street Reform and Consumer Protection Act (Dodd-Frank) in the
United States, and in the European Market Infrastructure Regulation (EMIR).
A central clearing provides three services. The first service of a CCP is that the CCP
acts as a legal intermediary between the clearing members who act as an agent for
the market parties (principals) that conclude a contract in a financial instrument.
This is shown in figure 17.1.
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credit risk – risk mitigating measures
Figure 17.1
Market Party
1
Role of a central counterparty
Clearing
Member 1
CCP
Clearing
Member 2
Market Party
2
The second service of a CCP is that it cancels out opposite transactions with one and
the same counterparty. This is called ‘netting’. Each day and for every single clearing member, CCPs calculate the net and the net amount of each individual security
to be delivered or received and a net sum of money to be paid or received. The cash
flows that a CCP includes in this process have to do with the option premiums, deposits or repayments resulting from collateral obligations (margins) and with the
cash settlement of options and futures. Once interest rate swaps and credit default
swaps will be processed by a CCP, also the coupon payments of interest rate swaps
and the premium and the contingent payments related to credit default swaps will
be taken into this calculation.
The third service of a CCP is that it sends settlement instructions to the central securities depository and the central bank. CCPs are normally authorised to have the
clearing members’ accounts debited for this purpose.
risk management with a ccp
The CCP runs the risk that a clearing member will not fulfil its obligations. In that
case, the CCP has to conclude a replacement transaction with the chance that the
terms are less favourable than those of the original contract.
To cover this risk, a CCP asks a deposit at the start date of each contract that is concludes. This deposit is called the initial margin. Upon contract maturity, the CCP
returns the initial margin to the clearing member. This also applies if the clearing
member closes its position prior to maturity. The CCP amount of the initial margin
is related to the volatility of the underlying asset and the market liquidity in the underlying asset.
With derivatives contracts, the CCP also demands a ‘variation margin’ or ‘margin
call’. This is the daily offsetting of the profits and losses of a derivatives contract
during the contract term. The margin call is always equal to the change in the market value of a contract during the past business day.
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guide to treasury in banking
example
A dealer has 10 Eurodollar contracts purchased against a price of 98.45. At the closing of the exchange, the price has risen to 98.75. The contract value of a Eurodollar
contract is 1 million US dollars.
Because the price has changed with 30 points, the trader’s result for the first day that
he holds the position is a gain of 10 x 1,000,000 x 0.0030 = USD 7,500. The clearing
house will transfer this amount to the trader’s bank account.
If, a day later, the price falls to 98.64 (a decrease of 11 points) the trader’s result is
negative:
10 x 1,000,000 x – 0.0011 = – USD 2,750. The clearing institution now debits the
trader’s account for this amount.
If a counterparty defaults, it will fist stop paying the margin calls. After a certain
period the clearing house then will conclude a replacement transaction. The clearing house recovers any losses resulting from this replacement transaction as much
as possible from the clearing member in default. For this purpose, it uses the initial
margin.
As an extra security precaution, all clearing members are required to deposit money in a so called guarantee depot: the clearing fund. If the central counterparty is
not able to recover the loss resulting form the replacement transaction from the defaulting member, the clearing house will withdraw money from this depot. The other clearing members then each take responsibility for part of the loss.
17.6 CLS
Many banks make agreements about offsetting opposing payments with a single
counterparty in a single currency. This is called payment netting. Payment netting
reduces the size of the settlement risk. Payment netting sometimes takes place at
third parties. Payment netting, however, is only possible if the two payments take
place in the same currency.
When two different financial values such as two currencies are exchanged or a currency is exchanged against a security then payment netting is not possible. In this
case, the two parties can agree to use a third party who will ensure that they both
meet their obligations simultaneously. However, this is only possible if both par282
credit risk – risk mitigating measures
ties maintain accounts for both financial values that are to be exchanged at the
same institution. This institution is then able to verify whether the required balances are in the accounts that must be debited. If so, the institution simultaneously performs the transfers in its own system. This happens, for example, at a central
securities depository such as Euroclear when securities transactions are concluded
under the condition delivery versus payment (DVP). Another example is the settlement of FX transactions at the CLS Bank which are made on a payment versus payment (PVP) basis.
cls bank
The CLS Bank is a settlement institution that settles the FX transactions in the major currencies for about 70 of the world’s largest banks. In order for a FX transaction
to be settled via the CLS Bank, both of the transaction parties must be settlement
members of the CLS Bank. A bank that is not a settlement bank can arrange for its
FX transactions to be settled via a settlement member. Such a bank is called a user
member.
The CLS Bank settles FX transactions in the following currencies: Euro, US dollar,
British pound, Japanese yen, Canadian dollar, Australian dollar, New Zealand dollar, Hong Kong dollar, Singapore dollar, Korean won, Danish Krone, Norwegian
Krone, Swedish Krone, Swiss Franc, South African rand, Mexican peso, Israeli
shekel.
In order to make the settlement of the FX transactions possible, all of the participating banks have an account in each of these currencies with the CLS bank. The CLS
bank, in turn, has accounts in these currencies with the central banks. For example,
the CLS bank has a US dollar account with the Federal Reserve Bank (FED), a JPY account with the Bank of Japan and a Euro account with the ECB. Banks can use these
accounts to transfer amounts to the accounts they have with the CLS bank. These
transfers are called pay-ins.
example
Rabobank International must deposit an amount in its USD account at the CLS Bank.
To this end, it must give its correspondent bank, JP Morgan Chase, an instruction to
transfer the US dollar amount to the US dollar account of the CLS Bank at the FED in
favour of the US dollar account of Rabobank International at the CLS Bank.
The CLS Bank processes transfers in three phases. Firstly, the delivery of instruc­
tions and pay-ins via the central banks, secondly, the internal settlement within the
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CLS Bank and finally the external settlement via the central banks. The RTGS systems of all currencies involved are operational throughout these three phases.
phase 1: the delivery of instructions and pay-ins
All member banks send SWIFT messages of the FX transactions they have con­
cluded to the CLS Bank (MT304). Based on all the transactions delivered, CLS Bank
creates a pay-in schedule for each member bank every day. This is an overview of
the payment obligations in all currencies of the banks involved as a result of the FX
transactions they have concluded and that need to be settled on that day. The cutoff time for the notification of transactions that have to be processed on that same
value date is 06:30 CET (Central European Time).
phase 2: internal settlement within the cls bank
The settlement of transactions subsequently takes place between 07:00 CET and
09:00 CET. For the Far East, this at the end of the afternoon and for the United States
it is in the middle of the night. The CLS system processes the FX trans­actions on an
order-to-order basis. This means that the CLS Bank processes each transaction separately, on a first in first out basis. The payment-versus-payment principle (PVP) applies to each individual transaction. This means that the two cash flows resulting
from an FX transaction take place simultaneously and that the CLS bank only debits a member’s account if it is certain that another account belonging to the same
member is simultaneously credited in another currency.
The CLS Bank also processes an FX transaction under certain circumstances if a
bank does not have sufficient funds in a currency to be delivered. In such cases, the
bank must have sufficient collateral in the form of balances in other currencies.
However, the CLS Bank does not take the entire balance in other currencies into account, but subtracts a safety margin: the haircut. This is how the CLS Bank allows
for possible changes in exchange rates during the day.
example
Société Générale carries out an FX spot transaction with Deutsche Bank. It sells 100
million British pounds for 130 million US dollars.
Settlement takes place at the CLS Bank.
However, the balance on Société Générale’s British pound account at the CLS Bank
is only GBP 75 million. The CLS Bank would therefore not carry out the transaction
based on the GBP balance alone.
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credit risk – risk mitigating measures
However, Société Générale also has a credit balance of 100 million euros on its euro
account. At a EUR/GBP exchange rate of 0.75, that is equiva­lent to GBP 75 million.
The CLS Bank applies a 10% haircut. This means that the collateral value of the euro
credit balance is equal to 90% x GBP 75 million = GBP 67.5 million.
Because Société Générale has sufficient collateral, the CLS Bank will execute the
GBP/USD FX transaction.
If a bank has sufficient collateral, the CLS Bank therefore also executes transac­tions
that result in a debit position on an account in a certain currency. The advantage of
this is that a member bank does not need to transfer money immediately to the CLS
Bank to make up the debit balance. That would not be efficient, because it is very
possible that a debit balance on this account would be supple­mented through the
settlement of another transaction that is processed later in the day.
This is why banks do not need to carry out pay-ins for each separate currency equal
to the net amount to be transferred based on all the FX transactions they have deposited. Instead, they ensure that the account in their own currency has a surplus,
in order to be able to provide the necessary collateral for possible interim debit positions in other currencies. Settlements through the CLS bank therefore have considerably less impact on the liquidity position of the members’ banks than the
traditional method of settlement.
The CLS Bank does however impose a limit on the size of the debit balance of an account. If this limit is reached, the member bank must cover the deficit of the currency account concerned before the CLS Bank continues to process the transactions
chargeable to this account. This applies regardless whether the bank concerned has
sufficient collateral.
A deficit can be covered in three ways: through an interim payment in to the CLS
Bank, through an in/out swap (I/O swap) or through a today/tomorrow swap.
An I/O swap is an intraday FX swap whereby one leg is completed within and the
other leg is completed outside the CLS system. In order to remove a debit balance
in euros, for instance, a member can conclude an I/O swap with another member
in which the member buys euros within the CLS system for US dollars and sells the
euros outside the CLS system for US dollars at the same rate. The second leg of the
swap is settled outside the CLS bank, through the central banks’ RTGS systems. A
disadvantage of an I/O swap is that part of the settlement risk is being reintroduced
to the parties. After all, the second leg of the swap takes place outside the CLS bank.
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A today/tomorrow swap is an FX swap that is settled entirely within the CLS bank.
The settlement of the first leg takes place on the day the today/tomorrow swap is
concluded. The settlement of the second leg takes place a day later. The advantage
of a today/tomorrow swap over an I/O swap is that no settlement risk returns. The
drawback of the today/tomorrow swap is that the liquidity position of both members in the two currencies is influenced for an entire day.
phase 3: external settlement through the central banks
During the final phase of the settlement process, the CLS Bank pays out the balances that are on the member banks’ accounts after the internal settlement of all transactions has been completed. In order to do this, the CLS Bank instructs the central
banks to debit its account there and credit the account of the mem­ber banks. These
transfers are called pay-outs.
The CLS bank only transfers amounts to a member after the member has covered
any debit balances on its accounts. This is why the member banks still have the opportunity to make interim pay-ins during phase 3, too.
At the end of phase 3, all the accounts within the CLS bank will have a zero balance.
This also applies to all accounts that the CLS bank holds at the central banks. Phase
3 ends at 10:00 CET for the Asia and Pacific region and at 12:00 CET for the Europe
region.
17.7 Credit default swap
A credit default swap is a financial instrument that gives one party, the protection
buyer, the possibility to cancel out the losses as a result of a credit event of a specific counterparty, the reference identity, or of a credit portfolio. In return for this
protection, the protection buyer has to pay a periodical premium to the protection
seller during the term of the contract: the CDS spread. These payments continue
until either the CDS contract expires or the reference identity defaults. The payments are usually made on a quarterly basis, in arrears. The CDS spread, is based on
the creditworthiness of the reference identity at the start date of the CDS contract.
The premium stays the same during the term, regardless of the development of the
creditworthiness of the reference identity.
In the case of a credit event, the protection seller compensates the protection buyer
for the losses in a pre-agreed manner. The compensation can have the form of the
payment of a sum of money to the protection buyer, i.e. cash settlement, or the purchase of the future cash flows of the underlying contract at a pre-agreed price, for
instance 100%, i.e. physical settlement. A credit event can also have many forms.
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It can be, for instance, the declaration of the bankruptcy of the reference identity, a
payment delay for a pre-agreed term or a downgrading by a rating agency.
Figure 17.2 shows a simple diagram of a credit default swap.
Figure 17.2 Protection
buyer
Concept of a Credit Default Swap
premium 25 bp
contingent obligation
Protection
seller
Interest (4%)
and repayment
Reference
entity
The protection buyer in figure 17.2 has granted a loan to the reference entity for a
nominal amount of ten million US dollars and a term of four years. The interest rate
for this loan was set at 4%. At the start date of the loan, the risk-free rate was, for
instance 3.9%. This means, that the credit spread on the loan was 10 basis points.
This correspondents with the rating of the reference entity at that time, i.e. AAA.
After one year, however, the creditworthiness of the reference entity has deteriorated to AA and the protection buyer decides to conclude a CDS with Deutsche Bank
as counterparty. The contract amount of the CDS is also ten million US dollars. The
CDS spread at the start date of the CDS reflects the current creditworthiness of the
reference identity and is now, for instance, 25 basis points for a term of three years.
For the remaining term of the loan, the protection buyer is now protected against
the risk that the reference identity defaults. The effective price for this protection
is 25 basis points - 10 basis points = 15 basis points. During the remaining term of
the loan the protection buyer also receives the risk-free interest rate of 3.90% that
was set at the start date of the loan. The effective rate for the protection buyer is now
3.90% - 15 basis points = 3.75%.
Suppose, for instance, that the contract parties have defined a change in the credit
rating as a credit event and that, for every downgrade, the protection seller will pay
10% of the nominal amount to the protection seller. If, for instance, the rating of the
reference identity is lowered from AA to A, then Deutsche Banks as the protection
seller must pay an amount of 10% of ten million is one million to the protection
buyer. This amount must be seen as a compensation for the fact that the market value of the loan decreases as a result of the downgrading.
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Credit default swaps can also be used to hedge against concentration risk. A bank’s
risk management committee may, for instance, advise that the bank is overly concentrated with a particular borrower or industry. The bank can then lay off some of
this risk by buying a CDS. Because the borrower, as the reference entity, is not a party to a credit default swap, entering into a CDS allows the bank to achieve its diversity objectives without impacting its loan portfolio or customer relations. Similarly,
a bank selling a CDS can diversify its portfolio by gaining exposure to an industry in
which the selling bank has no customer base.
17.8Securitisation
Banks can use their loan portfolios in order to obtain funds. The first way in which
a bank can do this is by pledging a loan portfolio as a collateral when issuing bonds.
The issued bonds are now referred to as covered bonds. The remuneration of a
­covered bond is usually fixed and is not related to the performance of the loan portfolio.
The second way how a bank can use as loan portfolio for attracting funding is to
transfer the claims of the loan portfolio. This is referred to as securitization. There
are two types of securitization. The first type is pass through securitization. In this
case the bank issues bonds itself and agrees with the investors that as a remuneration it will forward the proceeds of the loan portfolio to them. The second type is
pay through securitization. In this case the bank sets an organization between itself
and the investors. This organization is referred to as special purpose vehicle or SPV.
This organization should be legally independent from the bank. Usually, the loan
contracts are not changed and the banks stays responsible for servicing the loans.
As a result, the clients of the bank usually do not know that their loans are securitized. Securitization does not only give the bank access to new funding, but it can
also help to reduce credit risk.
The special purpose vehicle raises its funds by issuing fixed-income securities, e.g.
bonds, medium terms notes or commercial paper. These securities are generally referred to as asset backed securities (ABS) or collateralized debt securities (CD),
or more specific, if a mortgage portfolio is securitized mortgage backed securities
(MBS). The issue proceeds are transferred to the bank. Figure 17.3 shows the balance
sheet of a special purpose vehicle.
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Figure 17.3
Balance sheet of a special purpose vehicle
Purchased assets
– regular credit loans
– mortgages
– other assets
Securities
(MBS, ABS, CDO)
– commercial paper
– bonds, notes
The securities that are issued by a special purpose vehicle are usually issued in
tranches, for instance a junior tranche, a mezzanine tranche and a senior tranche.
The securities in the junior tranche have the highest yield but bear the highest risk.
If some of the borrowers fail to pay their installments, the holders of the junior securities will not receive part of their return. As a result, the price of these bonds will
fall. If more of the borrowers fail to pay, first the interest income of the junior securities will fall to zero and next the holders of the mezzanine securities will receive
only part of their interest income. During this process the price of all securities will
fall. The price of the junior bonds will, of course, react the most dramatically. However, also the prices of the mezzanine and senior securities will be negatively affected. Often, the bank and the SPV agree that the bank buys part of the junior tranche.
Obviously this decreases the mitigating effect on the credit risk of the bank. Figure
17.4 shows the composition of the CDOs issued by a special purpose vehicle.
Figure 17.4
Composition of the CDOs of a special purpose vehicle.
Purchased assets
– regular credit loans
– mortgages
– other assets
Securities
1. senior tranche / AAA-rating
2. subordinated tranche
(mezzanine) / AA-rating
3. junior tranche
equity / unrated
(first losses)
Sometimes, additional security instruments are used to mitigate the credit risk for
the buyers of the securities. This is referred to as credit enhancement. Examples of
credit enhancement are:
– overcollaterialisation, in which the underlying loan portfolio is larger than
the volume of the issued securities;
– the purchase of an external insurance policy or a guarantee;
– a reserve account.
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The above described form of securitisation is referred to as true sale securitisation.
An alternative form is synthetic securitisation, in which the credit risk is mitigated
by buying credit default swaps. With synthetic securitisation, the bank, of course,
will not obtain additional funding. Neither will it have its funding costs.
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Chapter 18
Funds transfer pricing
The largest contribution to the result of a bank is the net interest income (NII),
i.e. the difference between the interest received on assets and the interest paid
for ­liabilities. The NII, however, is the result of a great number of factors, i.e. the
spread taken by an account manager when granting a loan, the credit spread that
the ­account manager has to apply to cover the credit risk of this loan, the margin on
savings accounts and also the deliberately taken mismatches on the bank’s balance
sheet. Funds transfer pricing is a method to allocate the NII to all relevant business
units and rewarding them properly for their contribution.
18.1
Matched maturity funds transfer pricing
Broadly speaking in respect to funds transfer pricing, the bank is divided in three
parts: a client funding department, a commercial loan department and the central
treasury (ALM). The funding department is assumed to transfer the client funding
to the treasury and is assigned an internal interest rate. And, in turn, the loan department is assumed to borrow internally from the treasury and is also assigned an
internal rate. These internal rates are called funds transfer prices.
In setting the funds transfer prices, several elements are taken into account, e.g. the
term of the funding or loan, the possiblity of early redemptions, the fact that banks
may not be able to fund themselves for the same term as a loan, the fact that banks
have to hold HQLA to cover liquidity risks and, finally, certain optionalities like an
option to extend a loan. A method that takes all these elements into account is the
matched maturity funds transfer pricing method. With this method each single
type of funding and each single loan type is assigned its own transfer price whereby
all the mentioned elements are taken into account. Another important element of
the matched maturity transfer pricing method is that the funds transfer price for
a loan is set independently from the decision of how this loan is funded and that
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the transfer price for a liability is set indepently of the decision what the funding is
used for.
18.2 Application of the matched maturity funds transfer pricing
method
To understand the concept of the matched maturity funds transfer pricing method,
first we have to look at the yield curves in figure 18.1
Figure 18.1 Swap curve and funding curve
The swap curve shows the fixed rates for interest rate swaps for several terms. The
fixed IRS rate for an IRS with a term of one year, for instance, is 0.70% and the fixed
rate for an IRS with a term of ten years is 2.50%. The rates for interest rate swaps
are regarded risk free rates (at least if the reference rate for the floating coupon is
an overnight benchmark). During the credit crisis banks started to take into consideration the fact that liquidity was not always freely available, especially for the
longer terms. A bank that wants to take up a loan with a term of one year has to pay,
for instance, an interest rate of 0.90% in staed of the risk free rate of 0.70% and a
bank that wants to take up a loan with a term of ten years has to pay, for instance,
an interest rate of 3.20% in staed of 2.50%. This is 0.20% and 0.70% higher than
the fixed rates for IRSs respectively. The difference between the IRS rates and the
funding rates are referred to as the liquidity premium. Banks that use the matched
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maturity funds transfer pricing method take the liquidity premium into account,
amongst others. We will show this by a number of examples.
1. A bullet loan with a term of 10 years and a fixed rate that is funded by a 10
year certificate of deposit. The funds transfer prices for both, the loan and
the CD are set at 3.20%.
2. A bullet loan with a term of 10 years and a fixed rate that is funded by a 1
year CD. The funds transfer price for the loan is set independently of the
funding and is therefore still 3.20%. The funds transfer price of the CD is
set at 0.90%.
3. A floating rate loan with a term of 10 years that is funded by a 10 years
floating rate loan. The funds transfer price of both the loan and the bond is
set at EURIBOR + 0.70%. After all, the bank has to pay the liquidity spread
of 0.70% if it issues a 10 year bond.
4. A floating rate loan with a term of 10 years that is funded by a 1 year floating rate loan. The funds transfer price for the loan is still set at EURIBOR
+ 0.70% (independently of the way that is is funded). The funding price of
the CD is set at EURIBOR + 0.20%. This is because the liquidity premium
for one year is 0.20%.
5. Non-maturing savings accounts. For these accounts, an estimation is made
for their stickyness. If this estimation would, for instance, be that the funds
are staying with the bank for one year on average,then a funds transfer
price of 0.90% is assigned. Usually the transfer price is set lower because
the effect of the LCR is taken into account, i.e. banks have to hold HQLA to
cover the risk of early withdrawal of savings accounts. And since the return
on HQLA is lower than the return for other assets, the bank is faced with
an opportunity loss. This loss is attributed to the item that the HQLA was
held for.
6. A mortgage loan with a fixed interest term of 15 years for which a model
states that the effective term is 10 years (taken contractually allowed early
redemptions into account). This loan will be assigned the 10 years IRS rate
plus the 30 year liquidity premium. Since the 30-year liquidity premium
is the same as the liquidity premium for 10 years, i.e. 50 basis points, the
assigned funds transfer price is 3.20%.
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Chapter 19
Operational Risk
Introduction
Operational risk is the risk of an organisation losing money or suffering damage
to its reputation because something goes wrong during the performance of its activities. In general, four areas are identified in which an organisation can run operational risk: organisation, human behaviour, computer systems and external events.
Operational risk also covers the risk of a business being held legally responsible as
the result of an error in these areas: legal risk. Following the Basel rules, however,
reputational risk is not categorized as operational risk.
In the Financial Markets department of a bank, the operational risks are greater than for many other business units. This is due to the complexity of the instruments and the elaborate nature of the processing procedure. Another reason is the
more stringent duty of care, which means that it is easier than before to hold banks
liable if they fail to act in their clients’ interests.
Within banks, separate operational risk management (ORM) departments have
been set up to formulate and implement policy regarding the control of operational
risk and to estimate the size of the risks. Banks are obliged to do this according to
the Basel rules. According to these guidelines, they must also retain a capital base
to protect against the operational risks they run.
19.1
The cause-event-effect concept
When managing operational risk, banks make use of the cause-event-effect concept. According to this concept, causes in the four risk areas ‘organisation’, ‘human error’, ‘computer systems’ and ‘external events’ can lead to negative events
which, in turn, result in a loss or damage. The cause-event-effect concept was
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adopted in the most important regulations for banks in the field of operational
risk, Basel II. Figure 19.1 presents an overview of the cause-event-effect concept in
diagram form.
Figure 19.1 Cause-event-effect according to Basel II
Cause
Event
Effect
Failed internal
processes
Internal fraud
Legal responsibility
External fraud
Intervention by legal
authorities
People
Working conditions &
safety at the workplace
Loss of or damage
to assets
Clients, products &
entrepreneurship
Systems
Damage to
tangible assets
Operational breakdown
& System failure
External events
Implementation, transfer
& process management
Refund/indemnification/
compensation
Loss of right
of recourse
Depreciation
An example of a cause-event-effect process is indicated in bold in figure 19.1. A
­client adviser gives his client an investment advice that is not in line with his client
profile. As a result of this advice, the client suffers a heavy loss on his investment
portfolio. The client subsequently holds the bank responsible for this loss and takes
legal action. The client wins this case and the bank is ordered to indemnify the loss.
As the fault was the result of human error, the cause in this case comes under the
category ‘people’. The event clearly comes under the category ‘clients, products and
entrepreneurship’. The consequences, the financial loss and probable damage to
the bank’s reputation are not easy to classify into an effect category. Possible choices are ‘legal responsibility’ or ‘refund, indemnification or compensation’. The latter
option was chosen here.
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19.2 Internal processes
The organisational structure is the way in which tasks are allocated within an organisation and the way in which sub-tasks are subsequently coordinated. A good
organisational structure is characterised by a well-implemented separation of duties and a reliable system of internal controls.
19.2.1 Separation of duties
The separation of duties refers to the fact that essential tasks which are associated
with a certain production process or procedure related to providing a service are
carried out by different staff and/or different departments. The separation of duties
involved with effecting transactions in financial instruments is achieved by setting
up a number of departments each with its own responsibility:
– Front Office concluding transactions;
– Back Office verification, confirmation, sending
settlement instructions, reconciliation;
– Payment department making payment instructions in
connection with transactions;
– Product Control checking market data that is used for
the valuation;
– Middle Office / Investment measuring results/checking result
Control calculations;
– Risk Management setting limits and checking use of limit;
validating valuation models;
– Finance including the transaction data in the
ledger.
Not all of the above functions necessarily have to be implemented in different departments or even by different members of staff. The duties of Product Control,
Middle Office and Risk Management departments can easily be carried out within one department. That is also what actually happens with many banks. However,
there are some responsibilities which must remain separate under all circumstances. The front-office function, for example, must always be separated from the payment function, from the risk management function and from the measurement of
results.
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example
In the case of Barings, Nick Leeson had the opportunity to pass on completely wrong
positions to head office. That was because he not only entered his deals himself, but
was also able to authorise them. In addition to this, as head of the back office, he was
able to authorise payments. There was thus no evidence of a separation of duties.
An exaggerated separation of duties can also have its disadvantages. With many organisations, one sees that certain specific tasks are performed by just one or two
employees or that certain information is only known to one or two employees. If
this person or these persons leave the organisation, are ill or on holiday, this can
cause a problem. This is sometimes also referred to as key staff exposure.
19.2.2 Internal controls
Internal controls refer to all measures which an organisation takes with the aim of
ensuring that the organisation operates effectively and efficiently, that the financial data compiled are reliable and that the organisation and its employees comply
with the relevant rules. To achieve these objectives, every organisation draws up a
structure of control measures, and tests whether or not these control measures are
effective. Despite the fact that banks have paid a lot of attention to their internal
controls, many losses can still be attributed to a poor control structure or to the fact
that the controls are not carried out correctly.
A control structure consists of three layers.
–
–
–
self control
dedicated control
operational audits
self control
Self control is the control whereby departments themselves check the quality of
their activities, for example a daily check to see if all transactions have been processed. With self control, use is often made of the organisational principle of dual
control, which is also referred to as the four-eye principle. This means that at least
two members of staff are involved with a specific task. An example is the transfer of
large sums of money whereby one employee prepares the payment instruction and
another one dispatches it. Another control measure is the handshake concept. This
concept is used with the transfer of work. The department that takes care of the
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next step in a process checks if the quality of the work supplied by the department
that performed the previous step meets the agreed quality requirements. These requirements are sometimes set down in a service level agreement (SLA).
dedicated control
Dedicated control is the control performed by specially appointed business units.
These include the Operations Control, Product Control, Market Risk Management,
Credit Risk Management and Compliance departments.
operational audits
The Internal Accountants Department (IAD) is the final element of the control
framework and, after self control and dedicated control, is referred to as the ‘third
line of defence’. In addition to financial audits, in which it checks the internal financial responsibilities, the IAD conducts operational audits. These are risk analyses
in which it forms an opinion on the quality of how the organisation is controlled.
It does this by reviewing the design and operation of control measures. Sometimes
operational audits are conducted by a separate internal auditing department.
19.3
Human error
Staff are often considered to be a company’s most valuable asset. However, the performance of employees can sometimes suffer if the pressure of work is too great in
connection with low staffing levels or the need to work with unrealistic budgets and
deadlines. Employees can also make mistakes due to a lack of knowledge and experience, as a result of which clients may receive the wrong advice or transactions are
entered incorrectly, for example. The latter is often related to high staff turnover in
back-office departments.
Many mistakes are due to carelessness. The attention of a trader or a salesperson
with a Financial Markets department, for example, is geared more towards closing
a deal and less on entering this deal. Sometimes, after a successful transaction, his
head is still so much in the clouds that he makes one mistake after another when
entering the data in the front-office system.
Finally, traders with banks are focused more on the chance of making a profit than
on possible losses. That is related to the fact that they get a big bonus if a profit is
made, whereas they experience no direct negative financial consequences in the
event of a loss. On balance, risk-taking behaviour on the part of traders is therefore
rewarded. The phenomenon of employees taking undue risks because they do not
themselves experience the consequences of negative results is called moral hazard.
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19.4
Computer systems
Nowadays, banks are completely dependent on computer systems to operate their
business. A financial organisation must be able to rely on the fact that the information provided by these systems meets a number of criteria. First of all, the computer
systems must be secure. Secondly, they must know for certain that the systems provide all relevant data and, thirdly, that all the data is processed correctly. Finally, the
data provided by the computer systems must always be available (on time).
19.4.1 Confidentiality
For a bank it is of crucial importance that it only is possible for authorised persons
to perform certain actions in a computer system or to have access to certain information in that system. In order to achieve this, employees are usually given a login
code and a unique password, which only allows them to access that part of the system which they need to perform their specific task. This is called authorisation. Organisations must ensure that staff do not know their colleagues’ passwords, which
would give them access to other than their own authorisations. After all, this could
undo the effect of a necessary separation of duties. It would also make it more difficult to demonstrate who was responsible for possible wrongful acts.
It is important that an inventory is made frequently of the user rights of all employees. The confidentiality of data was violated in 2008, for example, at the Société
Generale where trader Jérome Kerviel was still able to make use of an authorisation
that had been granted to a previous position. As a result, he was able to close large
future transactions at the expense and risk of the bank. A periodic check on the
user rights could have prevented this.
Another measure which banks take to guarantee the integrity of data is that they
make almost exclusive use of the SWIFT network when communicating with other
banks. This reduces the chance of messages being changed by unauthorised persons.
19.4.2 Integrity
Integrity means that it is certain that the computer systems process all relevant
data. As large banks usually comprise different business units, which often operate
from all over the world, the computer systems of these organisations are vulnerable
and their integrity could be compromised.
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Banks often have several dealing rooms. The position information of the traders in
these dealing rooms must be brought together to a central system via interfaces. If
the interfaces have not been programmed well, or are even non-existent, the information from the local systems will not be transferred completely or correctly into
this central system. The bank then has no clear idea of the total position, and the
risk this bank runs is estimated wrongly.
19.4.3 Correctness
Computer systems often retrieve information from other systems and frequently
translate this information. An organisation must be able to rely on the fact that the
data every system produces is correct.
A well-known example of data that is often retrieved by other computer systems is
static data. Examples of static data are client information and product features of
financial instruments. If the static data is not entered properly, that has a knock-on
effect in all of the systems which make use of the static data. As a result of errors
in permanent client data, an incorrect confirmation could be sent, for example, or
a transaction could be settled wrongly. This can lead to claims or even to an end of
the relationship. This is because clients really dislike administrative errors and may
want to choose a different bank as a result of the scale (in terms of both numbers
and size) of administrative mistakes.
An example of a system that translates data is a valuation system. It is sometimes
extremely difficult to value financial instruments. One reason for this is because
the most complicated financial instruments are continually being developed. For
instance, the variety of structured notes is immense. With the introduction of new
product variants, there is sometimes a great temptation to process these in full or
partially in a separate spreadsheet program. Banks even take measures to cover
themselves against the incorrect valuation of some instruments.
19.4.4 Availability
Systems must be operational at all times. They must therefore be secure against, for
example, viruses and power failures. Often, banks have back-up systems which ensure, in the event of a failure in their own systems, that the business can continue to
operate. Most banks even have a back-up dealing room.
Computer systems must also have reserve capacity to cope with increasing volumes
and new product variants. When purchasing a new system, users must therefore
have an important say in this. After all, they are in the best position to estimate fu301
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ture needs. On the other hand, the systems managers must have a big say when it
comes to the development of a new product variant. After all, they are the ones who
can guarantee that the systems will be able to process the new instrument. Banks
have often devised a procedure that guarantees the participation of all relevant specialisms in the development of a new instrument. Such a procedure is referred to,
for example, as a new product approval process. The Front Office, Market Risk Management, Product Control and IT departments are involved in this process.
19.5 External factors
The most important external factor that can cause operational losses is criminality.
In addition to committing a bank robbery or money transport robbery, criminal organisations can, for instance, try to hack into a bank’s computer systems. However,
banks also run the risk of criminals involving them in money laundering or in funding terrorism. If a bank accepts money from a client whilst knowing, or being able
to reasonably suspect, that this money was obtained through crime, this bank can
be prosecuted for receiving stolen goods or for money laundering. A bank is also liable to punishment if it becomes involved with funding terrorism. Other possible
causes of operational losses, besides criminality, are disasters such as a fire or an
earthquake.
business continuity plan and disaster recovery plan
A business continuity plan (BCP) is a logistical plan containing measures to enable
an organisation to start functioning again quickly following a criminal activity or
disaster. Among other things, a business continuity plan (BCP) states which members of staff play an important role in getting things rolling again and indicates
what these employees must do in the event of a disaster. In a BCP, a communications plan is also drawn up in order to channel contact with the media, with the aim
of protecting the organisation’s reputation. Part of a BCP is a disaster recovery plan
(DRP), which contains all IT related measures. This plan describes what the most
important computer applications are and how these can be started up again quickly. Another part of a DRP covers measures to protect the static data and the stored
transaction information against destruction and/or misuse.
19.6
Operational risk under the Basel rules
The following requirements apply with respect to operational risk:
–
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Pillar 1: Every bank must retain a capital base to cushion possible losses
resulting from operational risk;
operational risk
–
–
Pillar 2: Every bank must have an Operational Risk Framework to ensure
that it can control its operational risks and also set up a control system to
guarantee that this control is effective;
Pillar 3: Every bank must be transparant, in its official reports, about the
Operational Risk Framework it has set up and about the effectiveness of
the risk control process. It must also indicate how it reports the size of the
operational risks to the supervisor.
capital requirements for operational risk and reporting
As is the case with credit risk and market risk, a bank must retain a capital base for
operational risk that is at least as large as the risk it has reported. A bank can choose
between three methods for estimating the size of the operational risk.
The first method is the basic indicator approach, whereby the size of the operational
risk is estimated by taking a percentage of the net profits of the bank. This percentage is 15%.
The second method is the standardised approach, whereby a distinction is made
between the operational risks of different business activities. The Basel rules differentiate between eight lines of business: corporate finance, trading & sales, retail
banking, commercial banking, payment & settlement, agency services, asset management, and retail brokerage. For each of these lines of business, a different capital requirement applies, expressed as a percentage of the net profits of the different
lines of business. As banks can choose between the basic indicator approach and
the standardised approach. They only choose the latter if, as a result, the risks and
the capital they need to retain are estimated lower. For this reason, the Basel rules
set an extra requirement on institutions which choose the standardised approach,
i.e. they must keep a loss database.
The third method is the advanced measurement approach (AMA). According to this
method, a bank estimates its operational risks with the use of internal models. In
order to be able to do this, it must draw up a loss database with a history of at least
three years. As banks do not usually have enough data themselves to fill a database,
the supervisor provides collective data to every company that wishes to draw up reports in accordance with the AMA. In addition to this, a bank that wishes to draw
up reports in accordance with the AMA must develop a model for estimating the
future operational risks. Such a model need not be a statistical model, but may also
take the form of a scorecard. An advantage of the AMA is that, normally, the reported operational risk is lower than that according to the other methods and that the
required capital base is therefore also lower.
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Index
A
accreting swap 143
accumulation factor 42
actual/360 37
actual/actual 38
Additional Tier 1 190
adjusted 35
advanced measurement approach 303
ALCO 178
ALM/Liquidity group 251
AMA 303
amortizing swap 143
amount of discount 47
amounts due from Banks 19
amounts due to Banks 20
Asian option 146
Asset and Liability Management
­Committee 178
AT1 190
at-the-money (atm) 149
attracting funding 23
availability 301
availability risk 245
average rate option (ARO) 146
B
back testing 221
balance sheet 18
bank bill 62
banker’s acceptance 62
barrier 146
barrier option 146
base currency 73
basis point value 198
basis risk 121, 224
basis swaps 141
BCP 302
big figure 76
binary option 147
BIS Ratio 183
BPV 198
broken period 39
broker 29
bull spread 165
business continuity plan 302
C
callable repo 65
callable swap 143
call deposit 58
call option 146
cap 159
capital adequacy assessment process
184
caplets 159
Cash and Balances with Central Banks
19
cash flow hedge 241
cash management 22
cause-event-effect concept 295
CCP 280
central counterparty (CCP) 28, 117, 280
certificate of deposit (CD) 62
CET1 190
circus swap 143
clean deposit 58
clearing 27
clearing custodian 32
clearing members 117
close-out netting 277
CLS Bank 283
cock date 86
305
guide to treasury in banking
collar 161
collateral 277
commercial banking 17
Common Equity Tier 1 190
confidentiality 300
constant maturity swap 143
contractual netting 277
correctness 301
correspondent bank 22, 32
counterparty limit 275
coupon date 34
covered bonds 288
covered interest arbitrage 105
credit default swap 286
credit enhancement 289
Credit Risk Committee 179
Crestco 62
cross-currency repo 64
cross currency swap (CCS) 142
cross rate 77
current exposure method 271
customer deposits and other funds on
deposit 20
cut-off time 32
D
daycount conventions 36
daycount fraction 33
debtor risk 261
Debt Securities and Equity Securities
20
debt securities in issue 21
dedicated control 176, 299
deep-in-the-money 149
deferred start swap 143
deliver-out repo 67
delivery option contract 93
delivery risk 262
delta 198, 201
delta hedge 212
delta hedging 155
delta limit 211
delta position 155
306
deposit 58
deposit facility 250
depth of the book 28
derivatives limit 276
directional strategies 165
direct quoted FX rate 74
discount factor 42
discount window 251
DMO (Debt Management Office) 62
double dipping 67
double indemnity 64
double one touch option 147
E
EAD 265
economic capital 196
electronic broking services (EBS) 29
EMMI 71
end-of-month convention (EOM) 35
EONIA 71
EONIA SWAP INDEX 71
EUREPO 71
EURIBOR 71
European Money Markets Institute 71
event risk limit 214
ex ante dates 90
exchange 27
Exchange Delivery Settlement Price
(EDSP) 120
executing bank 30
exercise price 145
expectation value 150
expected shortfall 208
expected shortfall limit 214
expiry date 146
exposure at default 265
extendable swap 143
extreme value theory 206
F
fair value hedge 241
fair value hierarchy 239
fill or kill order 117
index
financial future 115
financial markets 21
fine tuning transactions 250
floor 159
following 34
forward leg 96
forward rate agreement (FRA) 123
FRABBA terms 123
full valuation method 215
fully synchronised 133
funding swaps 138
funds transfer pricing 291
fungibility 117
future value 42
FX forward contract 80
FX quotation 73
FX spot rate 73
FX swap 96
interest rate parity theorem 105
interest rate risk 223
interest rate sensitivity report 226
interest risk in the banking book 225
interest risk in the trading book 226
International Accounting Standards
Board 239
in-the-money (itm) 149
intrinsic value 148
investment banking 17
ISO-codes 74
G
gamma 202
gamma limit 213
gap report 226
general collateral (GC) 66
Gone-concern Capital 190
good settlement value 32
good until cancelled order 117
L
LCS 181
leverage ratio 194
LGD 266
liability swaps 138
LIBOR 72
limit control sheet 181
limit order 116
liquidity premium 292
liquidity provider 30
liquidity risk 245
Loans and Advances to Customers 20
long box 167
long cash position 68
longer-term refinancing operations
250
long leg 96
loro account 31
loss given default 266
LTRO 250
H
hedge accounting 240
I
IASB 239
ICAAP 184
icing 67
IMM FRAs 121
IMM swaps 97
indirect quoted FX rate 74
initial consideration 65
integrity 300
interest delta 198
interest rate collar 161
interest rate guarantee 158
J
junior loans 21
K
knock-in option 147
knock-out option 147
M
main refinancing operations 250
mandatory cash reserve 249
307
guide to treasury in banking
marginal loan facility 250
market liquidity risk 246
market maker 29
market order 116
market risk 197
Market Risk Committee 180
market segmentation hypothesis 50
mark to market 239
mark to model 239
matched maturity funds transfer
­pricing 291
matched principal swaps 99
matched sales 65
Matched Sales repos 251
maturity buckets 226
maturity consideration 65
maturity method 226
merchant banking 17
modified duration 231
modified following 34
money creation 14
money market paper 59
Monte Carlo analysis 221
month ultimo date 35
MRO 250
multilateral trading facility (MTF) 28
N
net investment hedge 242
net stable funding ratio 256
netting 117
new product approval process 181
nominal limit 209
non-deliverable forward 108
normal yield curve 49
nostro account 22, 32
notice deposit 58
O
open interest 116
operational audits 299
operational risk 295
Operational Risk Committee 180
308
option risk 224
Other Assets 20
Other Liabilities 21
out-of-the-money (otm) 149
overnight index swap (OIS) 134
overnight swap 102
over the 15th 124
over-the-counter market (OTC ­market)
28
P
pass through securitization 288
payer’s swap 132
pay through securitization 288
PD 265
pips 76
points 76
post-trade transparency 28
present value 42
pre-settlement risk 263
prime-broker 29
probability of default 265
proprietary trading 24
pure discount rate 47
pure expectations theory 50
putable swap 143
put option 146
putting stock on hold 67
PV01 198
Q
quoted currency 73
R
RAROC 196
rate capped swap 143
receiver’s swap 132
regulatory capital 195
remargin period 279
replacement risk 263
repo buyer 64
repo seller 64
repricing 68
index
repricing arrangement 68
repricing of a sell-buy-back 68
repricing risk 223
repurchase agreement (REPO) 64
reverse stress test 206
roller coaster swap 143
round trip commission 116
S
sales 25
scale order 117
self control 298
sell/buy back 67
sensitivity indicators 197
separation of duties 297
sequence 119
settlement date 32
settlement instruction 32
settlement risk 262
short box 167
short cash position 68
short collar 161
short-dated Government paper 19
short leg 96
SIFI 193
spot coupon curve 49
spot leg 96
spot/next deposits 58
spread 75
SREP 184
standardized approach 267
STIR future 118
stop limit order 117
stop loss order 117
straddle 167
straight deposit 58
strangle 170
Stressed VaR 188
stress test 206
stress testing 205
stress test limit 214
strike price 145
structural transactions 250
Subordinated Loans 21
supervisory review and evaluation
process 184
swap assignment 140
swap in arrears 143
swap points 80
swaption 163
synthetic securitisation 290
systematic internalization 30
systemically important financial
­institution 193
system repo 65, 251
system reverse repo 65
T
T-Bill 61
tenor 36
term repo 65
theta 203
Tier 2 190
time option forward contract 93
tom/next deposits 58
tom/next swap 102
to the figure 76
trade currency 73
trade repository 28
trading limit 208
trading system 27
transferror 140
transparency before the trade 28
trigger 146
tri-party repo 67
true sale securitisation 289
two-way price 75
U
unadjusted 35
underlying period 51
unmatched principal swaps 99
V
value at risk 204
value date 32
309
guide to treasury in banking
value of one point 76, 198
value today 90
value tomorrow 90
VaR 204
variance-covariance method 218
VaR limit 209
vega 203
vega limit 213
volatility strategies 165
W
WI (When Issued) 62
wrong-way risk 266
Y
yield 46
yield curve 49
yield curve risk 224
Z
zero-coupon curve 49
zero coupon swap 143
310