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Futures, Options, and Swaps
Fin 288
Drake Fin 288
DRAKE UNIVERSITY
Derivatives
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Basic Definition
Any Asset whose value is based upon (or derived
from) an underlying asset.
The performance of the derivative is dependent upon
the performance of the underlying asset.
The Derivative Debate
Positives
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Derivative securities have the potential to allow
both financial firms and non-financial firms to
greatly decrease risk and increase the efficiency
of markets. Example of possible benefits include
the ability to: decrease interest rate risk,
decrease price risk, decrease transaction costs,
increase the efficiency of markets, provide
investors with new non replicatable products,
and increase information availability.
The Derivative Debate
Negatives
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Use of derivatives has resulted in some dramatic
financial losses
Financial Firms (loss) – Allied Irish Bank ($700 Million),
Barings Bank ($1 Billion), Daiwa Bank (> $1 Billion),
Kidder Peabody ($350 Million), LTCM ($4 Billion),
Midland Bank ($50 Million), National Westminister
Bank ( $130 Million)
Non Financial Firms (Loss) – Allied Lyons ($150
Million), Hammersmith and Fulham ($600 million), MG
($1.8 Billion), Orange County ($2 Billion), Shell ($1
Billion), Sumitomo ($2 Billion)
The Derivative Debate*
Overview
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Warren Buffett –
“We view them as time bombs, both for the parties
that deal in them and the economic system.”
“Derivatives are financial weapons of mass
destruction, carrying dangers that while now latent,
are potentially lethal.”
Alan Greenspan“Although the benefits and costs of derivatives remain
the subject of great spirited debate, the performance
of the economy and the financial system in recent
years suggests that those benefits have materially
exceeded the costs.”
Quotes on slides labled The Deivative Debate were found in "The Great Derivtives Smackdown" www.forbes.com
The Derivative Debate
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To fully understand the benefits and risks of
using derivative requires an understanding of the
products available and the markets in which they
trade.
In class we will focus on the most popular and
common forms of derivative products: Futures,
Options, and Swaps. We will also focus on the
use of derivatives to manage risk and look at
what caused the large individual losses outlined
above.
Two Myths Concerning Derivatives
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1) Derivative Securities are a recent development
2) The large losses associated with derivative
securities indicate that derivative securities are
the equivalent of gambling.
Myth 1
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Derivative Securities are a recent development
Truth:
Derivative contracts can be traced back as far as 2000
B.C. in India and also appeared in Ancient Greece
where contracts similar to options were traded on
olives during the winter prior to the spring harvest.
Brief History of Derivatives
Markets*
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1100’s Forward contracts were used by Flemish traders
who gathered -- a letter de faire- forward contract
specifying delivery at a later date
1600’s
Japan -- Cho-ai-mai (Rice Trade on Book) Essentially futures
contracts on rice designed to manage the volatility in rice prices
caused by weather, warfare and other risks.
Netherlands -- formal futures markets developed to trade tulip
bulbs in 1636
Options also appeared in Amsterdam during the 1600’s
*History taken from Darrel Duffie, Futures Markets 1989
Brief History Continued
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1700’s – trading in options began in the US and
in England, but the exchanges were perceived as
being dishonest
1863 -- Confederacy issued 20 year bonds
denominated in French francs and convertible to
cotton (a dual currency cotton indexed bond)
Brief History Continued.
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Organized Exchanges in US
Chicago Board of Trade
Established in 1848 to bring farmers and merchants
together. Futures Contracts were first traded on the
CBOT in 1865. Developed the first standard contract
Chicago Mercantile Exchange
Started as the Chicago Produce Exchange in 1874 for
trade in perishable agricultural products. In 1919 it
became the Chicago Mercantile Exchange (CME).
Introduced a contract for S&P 500 futures in 1982.
NYMEX 1872 KCBOT 1876
Brief History Continued
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Early 1900’s Put and Call Dealers Association
formed to bring together buyers and sellers of
options, however the organization did not
establish a secondary market and there were no
contract guarantees.
1970’s The uncertainty associate with the
economic environment created an increase in the
design of new derivative products designed to
manage risk, and interest in options increased.
Brief History continued
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1973 The Chicago Board of Trade forms the
Chicago Board of Options Exchange (CBOE).
Early 1980’s The daily volume of trading on
options exchanges is greater than the daily
trading volume of the underlying assets. Options
on major indexes and options on futures are
developed.
Myth 2
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The large losses associated with derivative
securities indicate that Derivative Securities are
the equivalent of gambling.
Truth:
Many of the losses were the result of poor
operational oversight, excessive speculation, a lack of
risk limits, and poor understanding of markets
(especially liquidity risk).
The Derivative Debate
Large Losses and Market Efficiency
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Alan Greenspan“Even the largest corporate defaults in history (WorldCom
and Enron) and the largest sovereign default in history
(Argentina) have not significantly impaired the capital of
any major financial intermediary”
Warren Buffett“In the energy and utility sectors, companies used
derivatives and trading activities to report great ‘earnings’ –
until the roof fell in when the actually tried to convert the
derivatives related receivables on the balance sheets into
cash. ‘Mark to Market’ then turned out to truly be ‘mark to
myth’
Legitimate Questions about
Derivatives
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What are the intended economic benefits and
risks?
Has the rapid growth in use of derivatives
increased the possibility of systematic risk?
Has there been a concentration of risk due to a
limited number of dealers?
Does Regulation do a good job of monitoring and
limiting derivative related risk?
What happened in the cases of the large losses?
Economic Benefits of Derivatives*
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Risk Management – given the link to the
underlying asset a derivative can be used to
decrease or increase the risk of owning the
underlying asset
Price and Informational Discovery – since many
claims are contingent on future events derivative
markets can provide information about the
markets perception of the future.
An Introduction to Derivatives adn Risk Managmetn by Don Chance
Economic Benefits Continued
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Operational Advantages – generally derivative
markets have lower transaction costs and greater
liquidity compared to the spot market.
Additionally they allow easier short sales helping
to “complete” the market.
Market Efficiency - Spot market prices are
sometimes not consistent with assets true
economic value and arbitrage opportunities exist.
Derivatives help eliminate arbitrage and increase
price efficiency.
Some Financial Risks
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Legal Risk
Default Risk
Liquidity Risk
Market Risk
However all financial assets bear most of these
risks.
Other Risks
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Ability to increase leverage via use of derivatives
can cause increased risk when the derivative
security is used incorrectly. Sources of this
possible problem include:
Excess optimism about forecasting ability
Excessive speculation instead of risk management
Poor understanding of security being traded
Lack of liquidity in the market
Growth of Derivative Use
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Has the rapid growth in use of derivatives
increased the possibility of systematic risk?
This question is especially relevant for the
banking sector which of course spills over to the
entire financial sector.
Notional value
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Approximate Market Capitalization of the Wilshire
5000 (represents 98% of equities traded in US)
= $13.6 Trillion
Approximate size of outstanding debt in all fixed
income markets = $23.5 Trillion
The notional value of derivative securities held by
commercial banks in the US as of Sept 30, 2004
= $84 Trillion
Increase in Derivative use by
Commercial banks
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Year
Notional Value of Derivatives
1996
$20 Trillion
1998
$32.5 Trillion
2000
$40.1 Trillion
2002
$55.4 Trillion
2004
$84 Trillion
Concentration Risk
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5 banks account for 95% of the total notional
amount of derivatives with more than 99% of the
total held by the largest 25 banks.
Over-the-Counter contracts comprise 92% of the
total notional holding and only 8% are exchange
traded – increasing credit risk and liquidity risk.
During the third quarter of 2004 banks charged
off $91 million from derivatives and total past
due contracts were at $41 million
Size of the Market and
Concentration Risk
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Notional value is a very misleading measure of
risk since the represent the value of the
underlying security, not necessarily the value that
may be lost in the event of a bad outcome.
However, this also makes it very difficult if not
impossible to estimate the actual amount of risk
that is present especially since such a large
percentage are over the counter instruments.
The Derivative Debate
Concentration Risk
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Alan Greenspan –
“One development that gives me and others some
pause is the decline in the number of major derivative
dealers and its potential implications for market
liquidity and for concentration of counterparty risk”
Warren Buffett“Large mounts of risk, particularly credit risk have
become concentrated in the hands of relatively few
dealers, who in addition trade excessively with each
other.”
Regulation
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Does Regulation do a good job of monitoring and
limiting derivative related risk?
There has been increased reporting requirements
relating to derivative securities for both financial
and non-financial firms, increasing transparency.
The amount of off balance sheet securities has
come under increased scrutiny in the banking
sector.
The Derivative Debate Regulation
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Warren Buffett –
There is no central bank assigned to the job of
preventing the dominoes from toppling in insurance or
derivatives. (total return swaps ) and other kinds of
derivatives severely curtail the ability of regulators to
curb leverage and get their arms around the risk
profiles of banks, insurers and other financial
institutions.
The Derivative Debate Regulation
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Alan Greenspan –
Except where market discipline is undermined by
moral hazard owing for example to federal guarantees
of private debt, private regulation generally is far
better at constraining excessive risk taking than is
government regulation.
This Class.
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Our goal is to explain the functioning of
derivative markets in detail and then introduce
how they can be used by business to manage
both financial and non-financial risk.
Basic Types of Derivative
Contracts
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Forward Contracts
Agreement between two parties to purchase and sell
something at a later date at a price agreed upon today
Futures Contract
Same idea as a forward, but the contract trades on an
exchange and the counter party is not set.
Basic Types of Derivative Contracts
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Options Contract - Agreement that gives the
holder the right, but not the obligation, to buy or
sell a security in the future as a designated price.
the
Swaps Contract – An agreement between two
entities to exchange cash flow streams based
upon a prearranged formula.
Other Derivatives
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Options on futures: The right to buy or sell a futures
contract at a later date
Swaption: The option to enter into a swap at a future
date
Collateralized Mortgage Obligation (CMO) A mortgage
backed security where investors are divided into classes
and there are rules outlining the repayment of principal
to each class.
Indexed currency option notes: Bonds where the amount
received but the holder at maturity varies with an
exchange (usually a foreign exchange rate)
Credit, Weather, Electricity and other derivative classes
Forward Contracts
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Agreement between two parties to purchase
(and sell) something at a later date at a price
agreed upon today.
Legal contract where both parties have the
obligation to either buy or sell a specific product
in the future at the designated price. Largest risk
is the risk of default.
Payoff on Forward Contracts
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Long Position
Agreeing to buy a specified amount (The Contract
Size) of a given commodity or asset at a set point in
time in the future (The Delivery Date) at a set price
(The Delivery Price)
Payoff
The payoff will depend upon the spot (Cash) price at
the delivery date.
Payoff = Spot Price – Delivery Price
Example
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Assume you have agreed to buy €1,000,000 in 3
months at a rate of €1 = $1.6196
Spot Rate
$1.65
$1.6169
$1.55
Spot – Delivery Price
Payoff
$1.65-$1.6196=$0.0304 $30,400
$1.6196-$1.6196=0
0
$1.55-$1.6196=$0.0696 -$69,600
Example Graphically
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Payoff
.0304
1.55
-.0696
1.6196 1.650
Spot Price
Payoff: Short Position
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Agreeing to sell a specified amount (The Contract
Size) of a given commodity or asset at a point of
time in the future (The Delivery Date) at a set
price (The Delivery Price).
Payoff on Short position
Since the position is profitable when the price declines
the payoff becomes:
Payoff = The Delivery Price – The Spot Price
Long vs. Short
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For a long position to exist (someone agreeing to
buy) there must be an offsetting short position
(someone agreeing to sell).
Assume that you held the short position for the
previous example:
sell L 1,000,000 in 3 mos at a rate of L1 = $1.6196
Spot Rate Spot – Delivery Price
Payoff
$1.65
$1.6196-$1.65=-$0.0304 -$30,400
$1.6169
$1.6196-$1.6196=0
0
$1.55
$1.6196-$1.55= $0.0696 $69,600
Example Graphically
Payoff
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.0304
1.55
-.0696
1.6196 1.650
Spot Price
Zero Sum Game
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The contract and many other derivative securities
are often referred to as a “zero sum game”
In the contract above the combined profit of the
long and short position is zero. One party gains
and the other looses by an equal amount.
Contract Goals
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The goal of the contract is to decrease risk, assume that
you had to pay L1,000,000 in 3 months for the shipment of
an input. You are afraid that the $ price will increase and
you will pay a higher price.
Similarly the other party may be afraid that the $ price will
decrease (maybe they are receiving a payment in 3
months).
Both parties can hedge by entering into the forward
agreement – however after the 3 months, one party will
actually be “worse off” compared to not hedging
Determining the delivery price
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The delivery price will be determined by the
participants expectations about the future price
and their willingness to enter into the contract.
(Today’s spot price most likely does not equal the
delivery price).
What else should be considered?
They should both also consider the time value of
money
Storage costs especailly if the asset is a commodity
Future and Forward contracts
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Both Futures and Forward contracts are contracts
entered into by two parties who agree to buy
and sell a given commodity or asset (for example
a T- Bill) at a specified point of time in the future
at a set price.
Futures vs. Forwards
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Future contracts are traded on an exchange,
Forward contracts are privately negotiated overthe-counter arrangements between two parties.
Both set a price to be paid in the future for a
specified contract.
Forward Contracts are subject to counter party
default risk, The futures exchange attempts to
limit or eliminate the amount of counter party
default risk.
Other Forward
Contract Risks
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One goal of the negotiation is to specify exactly
the type, quantity, and means of delivery of the
underlying asset.
The chance that an asset different than
anticipated might be delivered should be
eliminated by the contract.
Futures contracts attempt to account for this
problem via standardization of the contract.
Futures Contracts
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Long Position: Agreeing to purchase a
specified amount of a given commodity or
asset at a point in time in the future at a set
price (the futures price)
Short Position: Agreeing to sell a specified
amount of a given commodity or asset at a
point of time in the future for a set price (the
futures price).
Option Contracts
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The first difference between an option and a
future (or forward) contract is that the holder of
the option has the right to buy or sell a product
but is not obligated to do so. They have the
choice to not exercise the option.
The second main difference is that the holder of
the option pays an initial price for the right to
buy or sell.
Option Terminology
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Call Option – the right to buy an asset at some
point in the future for a designated price.
Put Option – the right to sell an asset at some
point in the future at a given price
Option Terminology
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Expiration Date The last day the option can be
exercised (American Option)
also
called the strike date,
maturity,
and exercise
date
Exercise Price
The price specified in the
contract
American Option Can be exercised at any time up
to the expiration date
European Option Can be exercised only on the
expiration date
Option Terminology
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Long position: Buying an option
Long Call: Bought the right to buy the asset
Long Put: Bought the right to sell the asset
Short Position: Writing or Selling the option
Short Call - Agreed to sell the other party the
right to buy the underlying asset, if the other
party exercises the option you deliver the
asset.
Short Put - Agreed to buy the underlying
asset from the other party if they decide to
exercise the option.
Risk to the Writer of the Option
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The writer of the call option accepts all of the
risk since the buyer will not exercise if there
would be a loss.
Call Option Profit
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Call option – as the price of the asset increases
the option is more profitable.
Once the price is above the exercise price (strike
price) the option will be exercised
If the price of the underlying asset is below the
exercise price it won’t be exercised – you only
loose the cost of the option.
The Profit earned is equal to the gain or loss on
the option minus the initial cost.
Profit Diagram Call Option
(Long Call Position)
Profit
S-X-C
S
Cost
X
Spot Price
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Example: Naked Call Option
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Assume that you can purchase a share of stock
in one month with an exercise price of $100.
Assume that the option is currently at the money
(the current price of the stock is also $100) and
selling for $3.
What are the possible payoffs if you bought the
option and held it until maturity?
Five possible results
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The price of the stock at maturity of the option is
$100. The buyer looses the entire purchase
price, no reason to exercise.
The price of the stock at maturity is less than
$100. The buyer looses the $3 option price and
does not exercise the option.
Five Possible Results continued
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The price of the stock at maturity is greater than
$100, but less than $103. The buyer will
exercise the option and recover a portion of the
option cost.
The price of the stock is equal to $103. The
buyer will exercise the option and recover the
cost of the option.
The price of the stock is greater than $103. The
buyer will make a profit of S-$100-$3.
Profit Diagram Call Option
(Long Call Position)
Profit
S-100-3
103
-3
100
S
Spot Price
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Profit Diagram Call Option
(Short Call Position)
Profit
X
C+X-S
S Spot Price
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Put option payoffs
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The writer of the put option will profit if the
option is not exercised or if it is exercised and
the spot price is less than the exercise price plus
cost of the option.
In the previous example the writer will profit as
long as the spot price is less than $103.
What if the spot price is equal to $103?
Put Option Profits
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Put option – as the price of the asset decreases
the option is more profitable.
Once the price is below the exercise price (strike
price) the option will be exercised
If the price of the underlying asset is above the
exercise price it won’t be exercised – you only
loose the cost of the option.
Profit Diagram Put Option
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Profit
X-S-C
Spot Price
S
Cost
X
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More Terminology
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In - the - money options
when the spot price of the underlying asset for a call
(put) is greater (less) than the exercise price
Out - of - the - money options
when the spot price of the underlying asset for a call
(put) is less (greater) than the exercise price
At – the - money options
when the exercise price and spot price are equal.
Swap Introduction
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An agreement between two parties to exchange cash
flows in the future.
The agreement specifies the dates that the cash flows
are to be paid and the way that they are to be
calculated.
A forward contract is an example of a simple swap. With
a forward contract, the result is an exchange of cash
flows at a single given date in the future.
In the case of a swap the cash flows occur at several
dates in the future. In other words, you can think of a
swap as a portfolio of forward contracts.
Mechanics of Swaps
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The most common used swap agreement is an
exchange of cash flows based upon a fixed and
floating rate.
Often referred to a “plain vanilla” swap, the
agreement consists of one party paying a fixed
interest rate on a notional principal amount in
exchange for the other party paying a floating
rate on the same notional principal amount for a
set period of time.
In this case the currency of the agreement is the
same for both parties.
Notional Principal
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The term notional principal implies that the
principal itself is not exchanged. If it was
exchanged at the end of the swap, the exact
same cash flows would result.
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An Example
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Company B agrees to pay A 5% per annum on a
notional principal of $100 million
Company A Agrees to pay B the 6 month LIBOR
rate prevailing 6 months prior to each payment
date, on $100 million. (generally the floating rate
is set at the beginning of the period for which it
is to be paid)
The Fixed Side
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We assume that the exchange of cash flows
should occur each six months (using a fixed rate
of 5% compounded semi annually).
Company B will pay:
($100M)(.025) = $2.5 Million
to Firm A each 6 months.
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Summary of Cash Flows
for Firm B
Date
3-1-98
9-1-98
3-1-99
9-1-99
3-1-00
9-1-00
3-1-01
LIBOR
4.2%
4.8%
5.3%
5.5%
5.6%
5.9%
6.4%
Cash Flow
Received
2.10
2.40
2.65
2.75
2.80
2.95
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Cash Flow
Net
Paid
Cash Flow
2.5
2.5
2.5
2.5
2.5
2.5
-0.4
-0.1
0.15
0.25
0.30
0.45
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Swap Diagram
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LIBOR
Company A
Company B
5%
Offsetting Spot Position
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Assume that A has a commitment to borrow at a fixed rate of
5.2% and that B has a commitment to borrow at a rate of
LIBOR + .8%
Company A
Borrows (pays)
5.2%
Pays
LIBOR
Receives
5%
Net
LIBOR+.2%
Company B
Borrows (pays) LIBOR+.8%
Receives
LIBOR
Pays
5%
Net
5.8%
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Swap Diagram
5.2%
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LIBOR
Company A
LIBOR +.2%
5%
Company B
LIBOR+.8%
5.8%
The swap in effect transforms a fixed rate liability
or asset to a floating rate liability or asset (and
vice versa) for the firms respectively.
Options on Futures
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Options on futures are as popular or even more
popular than on the actual asset.
Options on futures do not require payments for
accrued interest.
The likelihood of delivery squeezes is less.
Current prices for futures are readily available, they
are more difficult to find for bonds.
Useful Concepts / Terminology
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The language of derivative markets can be
confusing. Some basic principles apply to all of
the markets and instruments that we will cover.
Risk Preferences
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Risk Loving vs. Risk Neutral vs. Risk Adverse
Assume you are faced with two equally likely
outcomes:
A gain of $10 and a loss of $5.
How much would you be willing to pay to accept
the risk of the possible loss?
Risk Preferences
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Risk Neutral: If you are willing to pay $2.50, you
are willing to pay a “fair price” to accept the risk.
(If you repeated the event over and over on
average you would receive your $2.50)
Risk Averse: If you are willing to pay less than
2.50 lets say 2.00, you are risk averse. The $.50
represents a risk premium, the additional return
you expect to earn for accepting the risk. The
lower the amount you are willing to pay the more
risk averse you are.
Short Selling
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The investor is selling an asset that he / she does
not want.
This is accomplished by borrowing an asset from
a broker and selling it. The anticipation is that
the price of the asset will decline. The investor is
obligated to buy back the asset in the future and
return it to the broker.
Short selling of derivatives is much simpler than
short selling stock. Often selling short can offset
risk in other positions.
Risk Preferences
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In pricing derivative products we often will
assume that the participants are risk neutral. In
other words the value of the securities represent
their “fair price”
Risk and Return
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Generally, increased risk results in increase return.
Based on the idea of a “risk free” rate which is the return
you require on an investment with a guaranteed payoff.
In derivative markets the value of the assets will often be
priced based on the use of a risk free rate. In a perfect
world the derivative contract would eliminate the risk
associated with the fluctuation in the underlying asset.
Therefore the combination of the two provides a risk free
return and provide a return comparable to the risk free rate.
Market Efficiency
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Market efficiency occurs when the price of an
asset reflects it “true economic value”. You can
think of this as the theoretical fair value of the
asset (think about the CAPM providing a fair
value…).
A good portion of the class is placed on valuing
derivatives, just like valuing of assets you have
done in other classes. The value or price of the
derivative will assume that markets are efficient.
Types of Traders
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Hedger - A participant in a derivatives transaction
who is attempting to decrease the risk associate
with a spot position by taking the opposite
position in a derivatives market.
Speculator- Unlike hedgers speculators are
attempting to profit from the future movement of
the market.
Arbitrageurs
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Fin 288
Participants who can lock in an immediate profit
by simultaneously entering into transactions in
two or more markets.
A basic assumption throughout the course is that
arbitrage opportunities do not exist. The basis
for this argument is that if they did exist, the
laws of supply and demand will quickly eliminate
them as participants attempt to take advantage
of the opportunity – the quicker arbitrage
opportunities leave the market the more efficient
the market is.
Arbitrage and the Law of one price
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Drake University
Fin 288
Assume you have two stocks A and B. There are two
possible outcomes one month from now.
1) If the first outcome occurs Stock A is worth $100 and
Stock B is worth $50
2) If the second outcome occurs, Stock A is worth $80
and stock B is worth $40.
From the example it looks like one share of stock A is
worth two shares of stock B. In other words by buying
two shares of stock B today you should be able to get
the same outcome as one share of stock A.
Law of one Price
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Drake University
Fin 288
What if stock A is selling for $85 today and B is
selling for $39
You could sell short stock A and receive $85 use
the proceeds to buy two shares of B (total cost
$78) and have a positive cash flow of $7. In one
month you could sell your two shares of B and
buy one of A returning it to the broker -- You are
ahead the $7 plus any interest you received.
Market Reaction
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Drake University
Fin 288
If this condition existed the price of stock B
would increase (everyone buys it) the price of A
would decrease (everyone is short selling it).
The two prices would move until the opportunity
no longer exists. This is sometimes referred to
as the law of one price (the arbitrage opportunity
must be eliminated quickly)
The Law of One Price
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Drake University
Fin 288
Assuming the law of one price is correct:
Investors will prefer more wealth to less
If two investment opportunities have the same
outcome they must have the same price
An investment that produces the same return
in all states is risk free and should earn the
risk free rate.
Investors will prefer an opportunity if it
produces a higher return in at least one state
and equivalent returns in all other states.
Storage, Delivery, and Settlement
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Drake University
Fin 288
Storing an asset entails risk since the spot price
of the commodity fluctuates. This risk can be
eliminated through the use of derivatives,
implying that in the absence of storage costs the
investment should earn the risk free rate.
Similarly since at expiration the contract is
identical to a spot transaction the mechanism for
delivery of a commodity and settlement of the
contract (via delivery or cash) plays a key role in
determining the price of the derivative.