Download C15.0021 Money, Banking, and Financial Markets

Money, Banking, and Financial
Markets
Professor A. Sinan Cebenoyan
Stern School of Business - NYU
Set 3
Copyright 1999 A. S. Cebenoyan
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Credit Risk - Chapter 11
• Measurement of credit Risk:
– Pricing of loans
– credit rationing
• Japanese FI’s over-concentration in real estate and
in Asia
– bad loans of 20 trillion yen in 1998
– Japanese Life insurers exposed to these banks
by about 14 trillion Yen in loans
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• C & I Loans
•Different size and maturities
•Secured or unsecured
•Fixed or floating
•Spot Loans or Loan Commitments
•Commercial paper (large corporations, directly or via
investment banker, sidestepping banks, lower rates)
•Real Estate Loans
•various features
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•Individual (Consumer) Loans
•Revolving loans
•High default rates (3-7 %)
•Return on a Loan
•Interest rate
•fees
•credit risk premium
•collateral
•nonprice terms (compensating balances, reserve
requirements)
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•Prime Rate most commonly used for longer-term loans,
fed-funds for shorter term
•LIBOR
The gross return on loan, k, per dollar lent is
f  ( L  m)
1 k  1
1  [b(1  R)]
Numerator is fees plus interest…promised cash flows
Denominator is net outflow from the bank
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•Expected return on the Loan
•Default risk
E (r )  p(1  k )
Retail versus Wholesale Credit decisions
•Retail
•Accept-Reject decisions
•credit rationing…….quantity restrictions rather
than price or interest rate differences
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•Wholesale
•Interest rate and credit quantity used to control credit
risk
•Prime plus a markup for riskier borrowers, BUT
•Higher rates don’t necessarily imply higher return
Measurement of Credit Risk
•Need to measure probability of default
•Information
•Covenants
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Default Risk Models
Three Broad Groups, Qualitative, Credit-Scoring, Newer Models
•Qualitative Models (Expert systems)
•Lack of public information leads to assembly of :
•Borrower Specific information
•Reputation, Long-term relationship, implicit contract
•Leverage, or capital structure (D/E), threshold beyond
which probability of default increases
•Volatility of earnings (stable v.s. high-tech)
•Collateral
•Market Specific Factors (Business cycle, Interest rates)
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•Credit Scoring Models
either calculate default probabilities or sort borrowers into
different risk classes, Thus:
•Numerically establish the factors that explain default risk
•Evaluate the relative importance of these factors
•Improve pricing of default risk
•Better screening of bad loan applicants
•better position to calculate reserves needed to meet expected
future loan losses
•Linear Probability Model
n
Z
i


j
X ij  error
j 1
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Example:
Suppose there were two factors influencing the past default
behavior of borrowers: the leverage or D/E and the sales/assets
ratio (S/A). Based on past default (repayment) experience, the
linear probability model is estimated as:
Z i  .5( D / E ) i  .1( S / A) i
Assume a prospective borrower has a D/E=.3, and a S/A=2.0, its
expected probability of default (Zi ) can then be estimated as:
Z i  .5(.3)  .1(2.0)  .35
Also,
E ( Z i )  (1  pi )
P is repayment probability
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Problem is probabilities can lie outside of 0 to 1. Logit Model
fixes this by:
1
F (Z i ) 
1  e Zi
The left hand side is the logistically transformed value of Zi
The Probit Model is an extension of Logit which considers a
cumulative normal distribution rather than a logistic function.
•Linear Discriminant Models
•Altman’s (of NYU) Z-score, uses various financial ratios in
classifying borrowers into high and low default risk classes:
Z  1.2 X 1  1.4 X 2  3.3 X 3  0.6 X 4  1.0 X 5
Where, X1=WC/TA, X2=RE/TA, X3=EBIT/TA,
X4=MVEq./BVLtd, and X5=Sales/TA, Low Z means high risk
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Altman’s Z has a switching point at 1.81.
Problems:
•Only two extreme cases discussed
•Are the coefficients stable over time?
•Are the ratios relevant over time?
•Qualitative factors ignored
•Lack of data
Newer Models
•Term Structure Derivation
We extract implied default probabilities on loans or bonds using the
spreads between risk-free discount Treasury bonds and discount bonds
issued by corporations of different risks
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Probability of default on one-period Debt Instrument
Assume risk-neutrality, and that the FI would be indifferent between
the corporate and the Treasury of same maturity discount bonds:
p(1+k) = (1+i)
p = (1+i) / (1+k) with i = 10% and k = 15.8%
p = (1.1) / (1.158) = .95 probability of repayment
thus, 5% is the implied probability of default given the market rates, a
5.8% risk premium ( F ) goes along with it.
F = k - i = 5.8%
If all is not lost at default, if g is the proportion of the loan that can
be collected, then
g(1+k)(1-p) + p(1+k) = 1 + i
the first term is the payoff to the FI if default occurs.
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The fact that there will be partial recovery reduces F
(1  i )
k i  F 
 (1  i )
(g  p  pg )
or
1 i
g
p  1 k
1 g
With i= 10%, and p=.95, and g=.9, risk premium F = 0.6
MULTIPERIOD WILL BE COVERED IN CLASS!!!!!!
Mortality rate derivation of credit risk
Focus on historic default risk experience. Substitute mortality rates
for default rates.
MMR1= Ratio of total value of bonds of a certain grade defaulting in
year 1 of issue TO total value of same bonds outstdg. in year1 of issue
MMR2= Ratio of year 2 defaults TO total value of survivors in year2
Problems : backward-looking, period-sensitive, volume+size sensitive.
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RAROC Models
Risk-adjusted return on capital, RAROC, is the ratio of loan income to
loan risk. A loan is approved if RAROC exceeds a FI established
benchmark rate (cost of capital)
Estimating loan risk is possible using a Duration-type approach
L
R
  DL
L
1 R
L   D L  L 
R
(1  R )
Replacing interest-rate shocks with credit quality shocks
R  Max[( Ri  RG )  0]
Do example in book, pages 233-234.
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Credit Risk Continued
• Option Models of Default Risk
• Borrower always holds a valuable default or
repayment option. If things go well repayment takes
place, borrower pays interest and principal keeps the
remaining upside, If things go bad, limited liability
allows the borrower to default and walk away losing
his/her equity.
• KMV corporation (www.kmv.com) has developed a
model called Expected Default risk Frequency EDF
used now by largest US banks.
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Payoff to
stockholders
0
Assets
A1
B
A2
-S
This is the borrower’s payoff function, s is the size of the initial
equity investment, B is the value of Bonds, and A is the market
value of the assets of the firm.
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Payoff to
debt holders
A1
B
A2
Assets
The payoffs to the bond holders are limited to the amount lent B
at best.
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Merton’s model:
F ( )  Be i [(1 / d ) N (h1 )  N (h2 )]
where
  T t
 i
d  borrower' s leverage ratio ( Be / A)
2
h1  [1 / 2   ln( d )] /  
2
h2  [1 / 2   ln( d )] /  
N (h)  probability of deviation exceeding h
2
  asset risk of borrower
We can get the equilibriu m default risk premium
k ( )  i  (1 /  ) ln[ N (h2 )  (1 / d ) N (h1 )]
k ( )  Required yield on risky debt
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On the last equation variance and leverage ratio would affect the risk
premium. But NOTICE that the key variables are A, market value of
assets, and asset risk  2 Neither of which are directly observable.
An Option Model Example is given on page 237.
The KMV model uses the OPM to extract the implied market value of
assets (A), and the asset volatility of a given firm. This is done by
viewing equity as a call-option on the firm’s assets and the volatility
of a firm’s equity value will reflect the leverage adjusted volatility of
its underlying assets. We have in general form:
E  f ( A,  , B , i , )
and
 E  g ( )
Where, the bars (-) denote variables that are directly observable.
Since we have 2 equations with 2 unknowns (A,), we can solve..
Copyright 1999 A. S. Cebenoyan
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The following is a graph that depicts the superior accuracy of
KMV-EDF over agency ratings in capturing expected
default probabilities.
Source KMV Corp.
Copyright 1999 A. S. Cebenoyan
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Loan Portfolio Risk- Chapter 12
• We move beyond default risk measurements to
more aggregate contexts, i.e. portfolios.
• I will focus on two models that are not treated in
detail in the current edition of the Saunders book.
– A simple model : Migration Analysis
– A more sophisticated model: KMV Corporation’s
“Portfolio Manager Model”
Copyright 1999 A. S. Cebenoyan
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Migration Analysis
• A Loan Migration Matrix measures the probability of a
loan being upgraded, downgraded, or defaulting over some
period. Historic data is used, as such it can be used as a
benchmark against which the credit migration patterns of
any new pool of loans can be compared.
• In a Loan migration matrix the cells are made up of
transition probabilities.
• The number of grades are generally around 10 for most
FI’s.
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A Hypothetical Rating Transition Matrix:
Risk Grade
at beginning
of year
Risk Grade at end of year
1
2
3 D=Default
1
0.85
0.1
0.04
0.01
2
0.12
0.83
0.03
0.02
3
0.03
0.13
0.8
0.04
If the FI is evaluating the credit risk of of grade 2 rated borrowers,
and observes that over the last few years a much higher %, say 5%,
have been downgraded to3, and 3.5% have defaulted, the FI may
then seek to restrict its supply of lower quality loans (grades 2 and
3), concentrating more on grade 1. At the very least it should seek
higher credit risk premiums on lower quality loans. Migration analysis is used on commercial, credit card, and consumer loan portfolios.
Copyright 1999 A. S. Cebenoyan
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KMV Portfolio Manager Model
• KMV Portfolio Manager is a model that applies
Modern Portfolio Theory to the loan portfolio.
To estimate an efficient frontier for loans as in the above figure, and
the proportions (Xi), we need to measure :
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•Expected return on a loan to borrower i, (Ri)
•The risk of a loan to borrower i, (i)
•The correlation of default risks between loans to borrowers i and j
KMV measures each of the above as follows:
Return on the Loan:
Ri  AIS i  E ( Li )  AIS i  [ EDFi  LGDi ]
Where,
AIS = annual ‘all-in-spread’ on a loan =
(Annual Fees earned) + (Loan rate - Cost of Funds)
E(L) = expected loss on the loan
EDF = expected default frequency
LGD = loss given default
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Risk of the Loan:
 i  ULi   Di  LGD i  EDFi (1  EDFi )  LGD i
The Unexpected Loss (UL) is a measure of loan risk, i. It reflects the
volatility of the loan’s default rate, Di, times LGD. To measure Di
we assume loans either default or repay (no default), then defaults are
binomially distributed, then the  of the default rate for the ith borrower
Di, is equal to the square root of the probability of default times one
minus the probability of default, as above with EDF, (1-EDF).
Correlation :  ij
Correlation between the systematic return
components of the equity returns of borrower i and j. Generally low.
A number of large banks are using this model or variants to actively
manage their loan portfolios. Some are reluctant especially if involving
long-term customers. Diversification versus Reputation.
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Sovereign Risk- Chapter 16
• Large Exposure
Japan
US
Britain
France
Germany
Other
Foreign banks’ share of total Asian debt at the end of June
1997 (excluding Singapore and Hong Kong. Source BIS)
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•Prior to July 97 Thai crisis, Foreign banks had $389 billion in loans
and other debt outstanding. See slide on page 29.
•This crisis is still unfolding
•Bailouts and loan restructuring packages (South Korea $57 billion
IMF organized loan package)
•Credit Risk
•Sovereign Risk
should dominate
•Repudiation (common before WWII) bonds
•Rescheduling (common since WWII) bank loans
•Relatively small number of banks (1/98 South Korea loans
just over 100 banks involved)
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•Same group of banks involved
•Cross-default provisions
•Governments view social costs of default on international
bonds less worrisome than on loans. Possible incentive
problems?
Country Risk Evaluation
•Outside Evaluation Models
•Euromoney Index
•Institutional Investor Index
•Internal Evaluation Models
•Similar to our Credit-risk scoring models based on explaining
probability of a country rescheduling, like Z-scores
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Common variables in CRA:
•Debt Service ratio=(interest+amortization on debt)/Exports
positive relation with probability of rescheduling
•Import Ratio=(Total imports/Total FX reserves)
positive relation
•Investment Ratio= Real Investment/GNP
+/- relation, arguments on both sides
2
•Variance of Export Revenue=  ER
+ relation
•Domestic Money Supply Growth= M / M
+ relation
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Problems
•Measurement
•Population groups (a finer distinction than rescheduler or not)
•Political risk factors
•Portfolio aspects (systematic risk more important)
•Incentive Aspects (Benefits and Costs) Read section
•Stability (of variables)
Use of Secondary market for LDC Debt to measure risk
•The structure of the market
•Brady Bonds ($ loans exchanged for $ bonds-US Treasury bonds
are used to collateralize the bonds).
•Sovereign Bonds. No US-Tbonds used as collateral
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•Performing Loans
•Non-performing loans
LDC Market Prices and CRA
Regression analysis of price changes to key variables. LHS= periodic
changes in prices of LDC debt in the secondary markets, RHS= set of
key variables.
Once the parameters are estimated, FI can combine these with
forecasts of key variables to estimate price changes.
Has problems but hopefully reduces errors.
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Dealing with Sovereign Risk Exposure
•Debt-Equity Swaps (Industries like motor, tourism, chemicals
have been desirable fo outside investors.)
FI may sell $100 million loan to a company for $93, Company
negotiates with foreign gov. And swaps $100 million for $95
million worth equity in local currency. Company has $2million
buffer, country gets rid of US$ debt, company has to invest in
local markets in local currency.
•MYRA (Multiyear Restructuring Agreements)
•concessionality: The amount the bank gives up in present value
terms as a result of a MYRA.
example:From appandix of chapter.
•Loan sales
•Debt for Debt Swaps (Brady Bonds)
Copyright 1999 A. S. Cebenoyan
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