18-1
Chapter 18
Interest Rate Risk Management:
Index Futures, Options, Swaps and Other
Derivatives
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18-2
Stock Index Futures
 They are instruments for hedging exposure
to changes in the market value of equity
portfolios.
 Their value is pegged to movements in one
of several aggregate measures of stock
market performance.
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18-3
Characteristics of Stock Index Futures
 They differ from other types of futures
contracts in that it is not possible to make or
take physical delivery of an index.
• If closure does not occur before the delivery
month, the contract’s settlement level is the
same as the level of the index on a given date in
either March, June, September, or December.
 The value of the contract is calculated as the
level of the index multiplied by an
established amount, usually $500.
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18-4
 They are subject to daily trading limits.
 The price volatility of each index futures
contract is greater than the price volatility of
the underlying index.
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18-5
Number of Contracts
 Beta is a relative measure of volatility.
 A portfolio of stocks underlying a market
index is assumed to have a beta of 1.
 If a portfolio to be hedged has a beta greater
or less than 1, changes in the value of the
hedged portfolio will be more or less than
changes in the index underlying the futures
contract.
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18-6
The number of futures contracts (NF) is given by:
Value of Stock Portfolio
NF 
 Bp
Futures Index  $Multiplie r
where:
Bp = the beta of the portfolio to be hedged
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18-7
The Use of Stock Index Futures Illustrated
Suppose that a pension fund manager holds a stock
portfolio of $450 million in January, and the NYSE
index is at 600.24. The equity markets have been in
an upswing, but the surge is expected to end soon.
The manager chooses to sell NYSE stock index
futures. The previous day’s index settlement level
on March futures contract was 602.75
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18-8
THE SHORT HEDGE: PORTFOLIO BETA OF 1.0 (FORECAST: BEAR MARKET)
A short hedge with index futures is used when falling securities prices are forecasted.
The profit on the futures position can be used to offset losses in a portfolio of stocks.
Cash Market
Futures Market
January
NYSE Index: 600.24
Stock portfolio value:
$450,000,000
March
Market decline = 2.5%
NYSE Index: 585.23
Stock portfolio value:
$450,000,000(1 - 0.025 )= $438,750,000
NYSE Index settlement level 602.75
Sell 1,493 contractsa
602.75 × $500 × 1,493 = $449,952,875
NYSE Index settlement level:
602.75(1 - 0.025) = 587.68
Close out position buying 1,493 contracts:
587.68 × $500 × 1,493 = $438,703,120
Cash Market Loss
January value
March value
Loss
Futures Market Gain
$450,000,000
438,750,000
($ 11,250,000)
January sale
March purchase
Gain
$449,952,875
438,703,120
$ 11,249,755
Net Loss ($245)
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18-9
Cash Market Loss
January value
March value
Loss
Futures Market Gain
$450,000,000
438,750,000
($ 11,250,000)
January sale
March purchase
Gain
$449,952,875
438,703,120
$ 11,249,755
Net Loss ($245)
600.24  $500
NF 
1  1,493
a
$450 Million
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18-10
THE SHORT HEDGE: PORTFOLIO BETA OF 1.3 (FORECAST: BEAR MARKET)
Short hedges with index futures must take into account the market risk (as measured by
beta) of the hedged portfolio. Portfolios with high betas must be hedged with a larger
number of index futures contracts than portfolios with lower betas.
Cash Market
January
NYSE Index: 600.24
Stock portfolio value:
$450,000,000
March
Market decline = 2.5%
Stock portfolio value change:
-2.5% × 1.3 = 3.25%
Stock portfolio value:
$450,000,000(1 - 0.0325) = $435,375,000
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Futures Market
NYSE Index settlement level 602.75
Sell 1,941 contractsa
602.75 × $500 × 1,941 = $584,968,875
NYSE Index settlement level:
602.75(1 - 0.025) = 587.68
Close out position buying 1,941 contracts:
587.68 × $500 × 1,941 = $570,343,440
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18-11
Cash Market Loss
January value
March value
Loss
Futures Market Gain
$450,000,000
435,375,000
($ 14,625,000)
January sale
March purchase
Gain
$584,968,875
570,843,440
$ 14,625,435
Net Gain $435
600.24  $500
NF 
1.3  1,941
a
$450 Million
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18-12
Index Arbitrage
 Index Arbitrage is the simultaneous trading of
stock and stock index futures to profit from
changes in the spread between the two.
 Arbitragers are not attempting to use futures to
offset adverse changes in a portfolio held in the
normal course of operations.
 Arbitragers attempt to profit from fluctuations in
the basis.
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18-13
INDEX ARBITRAGE
Index arbitrage is the simultaneous trading of index futures and stocks composing the
underlying index. Computer programs are used to determine when stocks and futures are
bought and sold to profit from temporary price discrepancies in the two markets.
Cash Market
Futures Market
February 26
MMI: 311.74
Buy 2,000 shares of each MMI stock
Value = $2,749,000
If Prices Increase by March 21
MMI increase = 5.23%
MMI: 328.07
Stock portfolio value:
$2,893,000
MMI settlement level 313.55
Sell 18 contracts
313.55 × $500 × 18 = $2,821,950
MMI settlement level:
328.07, an increase of 4.631%
Close out position buying 18 contracts:
328.07 × $500 × 18 = $2,952,630
Cash Market Gain
3/21 value
2/26 value
Gain
$2,893,000
2,749,000
$ 144,000
Futures Market Loss
2/26 sale
3/21 purchase
Loss
$2,821,950
2,952,630
($ 130,680)
Net Gain $13,320
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18-14
Cash Market
If Prices Decrease by March 21
MMI decrease= 5.23%
MMI: 295.41
Stock portfolio value:
$2,605,000
Futures Market
MMI settlement level:
295.41, a decrease of 5.785%
Close out position buying 18 contracts:
295.41 × $500 × 18 = $2,658,690
Cash Market Loss
3/21 value
2/26 value
Loss
$2,605,000
2,749,000
($ 144,000)
Futures Market Gain
2/26 sale
3/21 purchase
Gain
$2,821,950
2,658,690
$ 163,260
Net Gain $19,260
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18-15
Options Defined
 An option is an agreement giving its holder
the right to buy or sell a specified asset,
over a limited time period, at a specified
price (exercise price or strike price).
 An option writer creates the option and
stands ready to buy or sell the asset when
the holder wishes to make a transaction.
 Options are traded on organized exchanges.
 Options are available on financial assets and
on futures contracts.
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18-16
Differences Between Options and Futures
 An option does not obligate the holder to
undertake the purchase or sale.
 The holder may choose not to exercise the
option to buy or sell.
 American options can be exercised at any
point during their lives.
• With futures, an exchange of securities takes
place only on the specified delivery date.
• Futures are similar to European options which
can be exercised only at expiration.
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18-17
Call Options
 A call option is an agreement in which the option
writer sells the holder the right to buy a specified
asset on or before a future date.
 The buyer of the call expects the price of the
asset to increase over the life of the option,
eventually exceeding the exercise price.
 The value of the option rises as the price of the
asset rises.
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18-18
Put Options
 A put option is an agreement in which the
option writer sells the holder the right to sell
a specified asset on or before a future date
at the strike price.
 The buyer of the put expects the price of the
asset to fall below the strike price.
 The value of the option rises as the price of
the asset declines.
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18-19
Option Premiums
 It is the price paid to purchase the option.
 It reflects the cost of the option.
 If the option is not exercised, the cost of the
option is the option premium.
 Since a large asset price change is necessary
to cover the cost of the premium, it is better
to hedge instruments with large expected
price changes with options.
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18-20
Market Forecasts and Option Hedges
 Falling stock prices or rising interest rates
suggest the use of puts.
 Rising stock prices or falling interest rates
suggest the use of calls.
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18-21
Hedging With Options: An Illustration
Suppose that in June, 2002, the bond portfolio manager for a
large insurance firm forecasts a sharp decline in interest rates
over the next 3 months. The insurance company is expecting a
large inflow from sales of insurance policies in August. The
manager wants to hedge the opportunity loss on the investment
of those premiums.
However, the manager of a money market fund holds the
opposite expectations for interest rate movements. She is
willing to write a call option on T-bond futures contracts.
Suppose T-bond futures for September delivery are currently
trading at 75.5% of par. The call option has a strike price of
76, a premium of $1,187.50 and an expiration of August 2002.
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18-22
HEDGING WITH OPTIONS ON T-BOND FUTURES CONTRACTS
An option provides the opportunity to limit losses to the amount of the option premium
if forecasts are incorrect. If forecasts are correct, gains on a hedge can be used to offset
losses in cash markets.
Treasury Bond Call Option
Premium:
$1,187.50
Strike price:
76
Expiration date:
August 2002
Security:
Treasury bond futures contract for September delivery
$100,000 face value
Current market value: 75.5
Scenario 1: Interest Rate Increase
T-bond futures contract value: < 76
Call option not exercised.
Results of the hedge: -$1,187.50 (premium)
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18-23
Scenario 2: Interest Rates Fall Slightly
T-bond futures contract market value: 77
Call option exercised. Contract purchased at 76 and sold at 77.
Result of hedge
$1,000.00
Profit from futures trade [(77-76) = 1 or 1% of face value]
- 1,187.50
Premium
($187.50)
Loss
Scenario 3: Interest Rates Fall Significantly
T-bond futures contract market value: 81
Call option exercised. Contract purchased at 76 and sold at 81.
Result of hedge
$5,000.00
Profit from futures trade [(81-76) = 5 or 5% of face value]
- 1,187.50
Premium
$3,812.50
Gain
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18-24
HEDGING WITH T-BOND FUTURES CONTRACTS
Futures hedges also provide opportunities to gain if forecasts are correct. If forecasts
are incorrect, however, losses on a futures position can be larger than losses on
comparable hedging strategies.
The Long Hedge
Treasury bond futures contract for September delivery
$100,000 face value
Current market value: 75.5
Scenario 1: Interest Rates Increase
T-bond futures contracts market value: 70
Position closed at loss of 5.5 of contract.
Results of hedge: -$5,500 loss
Scenario 2: Interest Rates Fall Slightly
T-bond futures contract market value: 77
Pos. closed at profit of 1.5 of contract.
Results of the hedge: $1500 profit
Scenario 3: Interest Rates Fall Significantly
T-bond futures contract market value: 81
Position closed at profit of 5.5 of contract.
Results of the hedge: $5,500 profit
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18-25
Interest Rate Swaps
 A swap agreement is an exchange of cash
flows between two parties.
 Parties in a swap agreement are referred to
as counterparties.
 In the simplest interest rate swap one
counterparty exchanges a fixed-rate
payment obligation for a floating-rate one,
while the other counterparty exchanges
floating for fixed.
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18-26
Exchange of Obligations in an Interest Rate Swap
S&L Pays Interest on $50
Million at 8.5%
8.5% Fixed-Rate
Obligation in Eurodollar
Markets
Savings
Association
Variable Rate
Obligation on Deposits
Commercial Bank
Counterparty
Bank Pays Interest on $50 Million at
LIBOR + 0.25%
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18-27
Details on Interest Rate Swaps
 Initially, the floating rate will probably be
lower than the fixed rate.
 The relationship could change over the life
of the swap as interest rate levels fluctuate.
 The differential between the floating-rate
and fixed-rate can be viewed as the
insurance premium paid to transfer interest
rate risk exposure to the counterparty
accepting the floating-rate obligation.
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18-28
Important Factors in a Swap: Maturity and
Interest Rate Index
 Long-term interest rate swaps are available
but short-term swaps are more popular.
 Termination clauses are usually included in
agreement.
• The party who unwinds the swap pays a
penalty.
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18-29
 Many participants make agreements to
reverse a swap in the event of unfavorable
rate movement.
 The LIBOR rate is the predominant index
used in swap transactions.
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18-30
Important Interest Rate Factors: Brokers and
Dealers and Credit Risk
 Many large institutions in the U.S., U.K.
and Japan serve as broker/dealers.
 As brokers, institutions bring two parties
together.
 As dealers they may take the counterparty
position in an agreement.
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18-31
COMPARING INTEREST RATE FUTURES AND INTEREST RATE SWAPS
These comparisons show that swaps are more flexible hedging tools than futures, but
futures markets are large, more well-developed, and more standardized.
Feature
Futures
Swaps
Maturities available
1½ to 2 years
1 month to 20 years
Costs
Margins and commissions
Brokers’/dealers’ fees
Size of hedge available
Standardized contract values
Any amount over $1m
Contract expiration date
Fixed quarterly cycle
Any dates
Difficulty of management
Complex
Simple
Termination positions
Closed out with opposite
contract
Organized exchanges
Unwound or reversed
Transactions completed through
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Commercial or
investment banks
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18-32
Swap Options and Futures
 A call swaption gives the buyer an
opportunity to enter into a swap agreement
in the future to receive a fixed rate and pay
a floating rate.
 A put swaption gives the buyer the right to
make a future swap agreement to receive a
floating rate and pay a fixed rate.
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18-33
 A swap future is a futures contract in which
the “cash instrument” is a generic, plain
vanilla swap with a 3 to 5 year life.
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18-34
Interest Rate Caps, Floors, and Collars
 The purchaser of an interest rate cap pays a
premium for the right to limit the cost of its
liabilities to a specific rate.
 For a premium, the purchaser of an interest
rate floor owns the right to receive interest
payments at the strike level.
 Interest rate collars require the purchase
and/or sale of caps and floors, hedging
against increases and decreases in rates.
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18-35
Other Derivatives
 Option Contracts for Insured Losses from
Catastrophic Events
 Total Return Swaps
 Credit Swaps
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18-36
 A dealer in the intermediary role guarantees
the continuation of the cash flows for the
swap, even if one counterparty defaults.
 The financial strength of the counterparties
is important to the dealer.
 The financial strength of the dealer is
important to the counterparties.
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