17-1
Chapter 17
Interest Rate Risk Management:
Interest Rate and Foreign Currency Futures
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17-2
Financial Institutions and Financial Futures:
Data on Use
 By mid-1997, the notional amount of
derivatives held by financial institutions
was $15.8 trillion or 68% of the $23.3
trillion total derivatives outstanding.
• Amount held was also four times the industry’s
total assets.
 Twenty-five very large banks held 98.6% of
the total bank-held derivatives and 98.1% of
interest rate derivatives.
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17-3
 Unfavorable regulatory and accounting
rules for futures partially explains the low
level of participation by other banks.
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17-4
Futures Contracts Defined
 A futures contract is a commitment to buy
or sell a specific commodity of designated
quality at a specified price and date in the
future (delivery date).
 Categories of futures contracts
• Agricultural products
• Metallurgical products
• Interest-bearing assets (financial futures)
• Stock indexes and other market indexes
(financial futures)
• Foreign currencies (financial futures)
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17-5
Hedging versus Speculation
 Futures can be used to hedge or avoid risk
by reducing the uncertainty about future
price movements for a particular
commodity.
 Futures can be used to speculate by
accepting the risk of price fluctuations with
the intention of profiting from them.
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17-6
Role of the Clearinghouse
 Futures trading is conducted through a
clearing house.
 The clearinghouse guarantees the
performance of the contract and assumes
the responsibility for the creditworthiness of
the buyer.
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17-7
 At the end of each day, the clearinghouse
settles all accounts, paying profits earned by
some traders and collecting payments due
from others.
 Because the contracts are standardized and
default risk is assumed by the
clearinghouse, the original owner of a
futures contract can easily offset or cancel
the contract before its delivery date.
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17-8
The Developing Global Marketplace
 Since 1985, 18 international markets for
trading futures opened in strategic locations
around the world.
 Many recent exchanges have developed as
electronic, computer-based systems versus
the traditional “open outcry” trading in the
U.S.
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17-9
 Several international markets also offer
greater flexibility, such as the option to settle
positions in a variety of currencies.
 Automation and flexibility in European
markets has challenged the dominance of
futures trading in U.S. markets.
 CBOT and CME responded by creating
Globex, a computerized futures trading
system.
• Globex has not been as successful as anticipated.
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17-10
The Margin
 Traders are required to post an initial
margin to support position.
 The margin can be in the form of cash, bank
letter of credit, or short-term Treasury
securities.
 The initial margin is usually no more than
5% of the face value of the contract.
 The margin is set by the exchange.
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17-11
 The margin depends on:
• type of contract;
• whether a trader is a hedger or a speculator; and
• price volatility of the underlying instrument.
 Contracts are “marked to market” each day.
• Losses on a given day are charged to the
trader’s margin account.
• If the charges reduce the balance in the account
below the required minimum, additional cash
must be deposited in the margin account.
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17-12
Limits on Price Changes
 The exchanges set a maximum amount by
which the price of a contract is allowed to
change.
 When the limit is reached on a given day,
the price cannot move farther.
 Subsequent trades will take place only if
they are within the limits.
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17-13
Interest Rate Changes and the Value of
Futures Contracts
 The market value of the futures contract
depends on the market value of the
underlying commodity.
 The market value of underlying interestearning financial assets moves inversely
with changes in market yields.
 Therefore, the market value of a financial
futures contract also changes inversely with
respect to interest rates.
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17-14
FEATURES OF SELECTED INTEREST RATE CONTRACTS
Interest rate futures are available on a variety of underlying instruments. Face values and
other specifications differ, and the choice of contracts depends on the cash instrument to
be hedged.
Name of
Contract
Underlying Instrument
Face Value
of Contract
Daily
Price Limit
T-bill future
13-week T-bill
$1 million
None
3-month
Eurodollar
futures
None, settled in cash
based on prevailing
rate on 3-month
Eurodollar time deposit
2-year, 5-year, 10-year
T-notes
8% T-bonds, minimum
maturity of 15 years
None, settled in cash
based on Bond Buyer
Municipal Bond Index
$1 million
None
$100,000 or
$200,000
$100,000
Varies 1 to
3 points
3 points
$1,000 times
value of
index
$3,000
T-note futures
T-bond futures
Municipal
Bond Index
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Standard
Delivery Months
Mar., Jun.,
Sept., Dec.
Mar., Jun.,
Sept., Dec.
Mar., Jun.,
Sept., Dec.
Mar,. Jun.,
Sept., Dec.
Mar., Jun.,
Sept., Dec.
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17-15
30-day
interest rate
futures
LIBOR
None, settled in cash
$5 million
based on monthly
averages of daily
fed funds rate
None, settled in cash
$3 million
based on the prevailing
LIBOR rate on 1-month
Eurodollar time deposit
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150 basis points
from previous
settlement price
Every Month
None
First 6 consecutive months
beginning with
current month
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17-16
Short Hedge
 A trader sells a futures contract, incurring
an obligation either to:
• deliver the underlying securities at some future
point; or
• close the futures contract out before the
delivery date by purchasing an offsetting
contract.
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17-17
 A trader will profit with a short hedge if
interest rates rise while holding the contract.
• The trader will be able to buy the securities for
delivery at a lower price in the spot market than
the selling price agreed upon in the contract.
• If the contract is closed out, the contract selling
price will be higher than the purchase price.
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17-18
Long Hedge
 A trader buys a futures contract, incurring
an obligation either to
• take delivery of the securities at the preestablished price on some future date; or
• sell the contract, closing out the position
through the clearinghouse before delivery.
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17-19
 A trader will profit from a long hedge if
interest rates fall.
• A trader that takes delivery can sell the
securities at a higher price in the spot market
than the purchase price written into the futures
contract.
• If the contract is closed out before the delivery
date, the contract selling price will be higher
than the purchase price.
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17-20
Long Hedge Illustrated
Suppose that, in June 2001, the manager of a money
market portfolio expects interest rates to decline.
New funds, to be received and invested in 90 days
(September 2001), will suffer from the drop in
yields, and the manager would like to reduce the
effects on portfolio returns.
The manager expects an inflow of $10 million in
September. The discount yield currently available on
91-day T-bills is 10%.
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17-21
THE LONG HEDGE (FORECAST: FALLING RATES)
A long hedge is chosen in anticipation of interest rate declines and requires the
purchase of interest rate futures contracts. If the forecast is correct, the profits on
the hedge will help to offset the losses in the cash market.
I.
Cash Market
June
T-bill discount yield at 10%
Price of 91-day T-bill, $10m par:
$9,747,222a
September
T-bill discount yield at 8%
Price of 91-day T-bill, $10m par:
$9,797,778
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Futures Market
Buy 10 T-bill contracts for September
delivery at 10% discount yield.
Value of Contracts:
$9,750,000b
Sell 10 T-bill contracts at 8%
discount yield
Value of contracts
$9,800,000
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17-22
II.
Cash Market Loss
Futures Market Gain
June Cost
September Cost
Loss
September Sale
June Purchase
Gain
$9,747,222
9,797,778
($ 50,556)
Net Loss:($556)c
$9,800,000
9,750,000
$ 50,000
III.
Effective Discount Yield with the Hedge
$10,000,000  ($9,797,778  $50,000) 360


$10,000,000
91
a At
9.978%
a discount yield of 10%, the price of a 91-day T-bill is:
 0.10(91) 
P0  $10,000,000 1 
 $9,747,222
360 

b T-bill
futures contracts are standardized at 90-day maturities, resulting in a price different from the
one calculated in the cash market.
c
Excludes transactions cost, brokers’ fees, and the opportunity cost of the margin deposit.
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17-23
Short Hedge Illustrated
Suppose that in September a financial institution
wants to hedge $5 million in short-term CDs whose
owners are expected to roll them over in 90 days. If
market yields go up, the thrift must offer a higher
rate on its CDs to remain competitive, reducing
NIM. Losses can be reduced by selling T-bill futures
contracts. CD rates are expected to increase from
7% to 9%.
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17-24
THE SHORT HEDGE (FORECAST: RAISING RATES)
A short hedge is chosen in anticipation of interest rate increases and requires the
sale of interest rate futures contracts. If the forecast is correct, the profits on the
hedge will help to offset the losses in the cash market.
I.
Cash Market
September
CD rate: 7%
Interest cost on $5m in deposits:
$87,500
December
CD rate: 9%
Interest cost on $5m in deposits:
$112,500
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Futures Market
Sell 5 T-bill contracts for December
delivery at 7% discount yield.
Value of Contracts:
$4,912,500
Buy 5 T-bill contracts at 9%
discount yield
Value of contracts
$4,887,500
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17-25
II.
Cash Market Loss
Futures Market Gain
September Interest
$ 87,500
December Interest
112,500
Loss
($ 25,000)
Net Benefit of Hedge: $0a
September Sale
December Purchase
Gain
$4,912,500
4,887,500
$ 25,000
III.
Net Interest Cost and Effective CD Rate
$112,500  $25,000  $87,500
$87,500
360

 .07 or 7%
$5,000,000 91
a Excludes
transactions cost, brokers’ fees and the opportunity cost of the margin
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17-26
The Basis
 It influences the type and number of contracts
to be bought or sold.
Basis  PSt  PFt
where:
PSt = spot price of the underlying financial asset at
time t
PFt = price of the futures contract at time t
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17-27
What Is a Perfect Hedge?
 It is a hedge in which the cash market loss
is exactly offset by the futures market profit.
 It requires the hedger to predict the basis
accurately and adjust the size of the hedge
accordingly.
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17-28
What Is Basis Risk?
 It is the possibility of unexpected changes in
the relationship between spot and futures
market prices.
 Basis risk results from the fact that cash and
futures market yields, although closely
related, are not perfectly correlated.
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17-29
Basis Risk Illustrated Using the Long Hedge
Example
The cost of the number of securities bought or sold
(Q) in the cash market at the close of the hedge is
given by
QPSt
= 10($979,777.80) = $9,797,778
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17-30
The cost of the futures market transaction at the close
of the hedge is the difference from the proceeds of the
sale at t=1 minus the cost of the purchase at t=0.
Q(PF1 )  Q(PF0 )  Q(PF1  PF0 )
10($980,000-$975,000) = $50,000
The net cost is given by
QPS1  Q(PF1  PF0 )  Q(PS1  PF1 )  QPF0
10($979,777.80 - $980,000) + 10($975,000) = $9,747,778
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17-31
 The basis at the time the position is closed out,
(PS1 - PF1), determines the success or failure of
the hedge.
 Neither PS1 nor PF1 is known at the time the
hedge is undertaken.
 As the basis fluctuates, so does the potential
gain or loss on the hedge.
 Basis risk exposure on the futures position may
be lower than the price risk in the cash market,
especially when the cash and futures
instruments are identical or closely related.
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17-32
The Cross Hedge and Basis Risk
 Whenever a futures hedge is constructed on
an instrument other than the cash market
security, the hedge is considered a cross
hedge.
• Example: hedging a corporate bond portfolio
with T-bond futures.
 Cross hedges have greater basis risk than
when the same security is involved in both
sides of the transaction.
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17-33
 If a short-term instrument was hedged with
a futures contract on long-term securities, or
vice versa, the basis risk would be even
greater.
 A perfect hedge is difficult to achieve with a
cross hedge.
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17-34
Choosing the Optimal Number of Futures
Contracts
 A hedge ratio (HR) must first be estimated.
Cov(PS , PF )
HR 
σ 2 PF
where:
Cov(PS,PF) = covariance between changes in spot prices
and changes in futures prices
2PF =
variance of changes in futures prices
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17-35
 As defined, the HR is the beta coefficient obtained
by regressing the past price changes in the cash
instrument to be hedged against past price changes
in a futures instrument.
 The number of futures contracts to be purchased
or sold, (NF), is given by:
V  HR
NF 
F
where:
V= the total market value of the securities to be hedged
F= the market value of a single futures contract
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17-36
Suppose that a portfolio manager anticipating a
decline in interest rates over the next three months,
wishes to protect the yield on an investment of $15
million in T-bills and that a T-bill futures contract is
now selling for $989,500. If the hedge ratio between
the T-bills and the T-bill futures contracts has been
estimated through regression analysis to be .93, how
many contracts should be used in the hedge?
V  HR $15,000,000  0.93
NF 

 14.098
F
$989,500
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17-37
Factors Affecting the Outcome of the Hedge
 Differences in the past covariance and the
covariance during the hedge.
 It is not possible to trade fractional amounts
of futures contracts so that the hedger must
adjust the number of contracts obtained
from the equation to a whole number.
• In the example the hedger would buy 14
contracts.
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17-38
Macro Hedges at Depository Institutions
 Used to hedge the entire funding gap or
duration gap.
 With a negative funding gap (i.e., a positive
duration gap), if interest rates rise, the
institution’s NII and the market value of its
equity falls.
• Hedge the loss by taking a short position in
futures that would produce a gain to offset the
institutions expected loss.
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17-39
 With a positive funding gap (i.e., a negative
duration gap), an institution is exposed to
losses if interest rates fall.
• The loss could be hedged by taking a long
position in futures that would produce a gain to
offset the expected loss.
 Macro hedges require:
• a detailed knowledge of a bank’s total exposure
to interest rate risk; and
• a relatively large transaction in the futures
market.
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17-40
Comparison of Forward and Futures Currency
Markets
 Forward contracts are not standardized and
are custom-tailored for the needs of the
trader.
 Futures contracts are available in standard
denominations and maturities for a few
currencies.
 Forward contracts expose the holder to
default risk while the clearinghouse
assumes the risk in futures contracts.
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17-41
 There is no secondary market for forward
contracts, exposing the holder to liquidity
risk.
 Futures contracts are marked to market
daily, requiring a margin account.
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17-42
Currency Futures Illustrated
Suppose a U.S. bank made a formal commitment on
December 24, 1998 to loan a German customer 1
million marks on January 24, 1999. At that time, the
bank plans to convert dollars into marks, but
management recognized the risk of exchange rate
fluctuations over the period. Of particular concern
was a possible decline in the value of the dollar
which would result in a higher cost for the mark.
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17-43
HEDGING WITH CURRENCY FUTURES CONTRACTS
(FORECAST: FALLING DOLLAR)
Currency futures contracts may be used to protect against a decline in the value of the
dollar. A long hedge, requiring the purchase of currency futures results in a gain if the
value of the dollar falls against the currency on which the futures contract is written,
but results in a loss when the value of the dollar strengthens.
I. Hedging in December
Cash Market
Futures Market
December 24
Dollars required to purchase 1 million
Buy 8 March contracts at $0.6001
marks at $0.5945 = $594,500
Value of Contracts:
125,000 × 8 × $0.6001 = $600,100
Results in January
January 24
Dollars required to purchase 1 million
Sell 8 March contracts at $0.6730
marks at $0.6725 = $672,500
Value of contracts:
125,000 × 8 × $0.6730 = $673,000
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17-44
II. Net Results of Hedge in January
Cash Market Gain
Future Market Loss
December “cost”
January cost
Loss
$594,500
December purchase
672,500
January sale
($ 78,000)
Gain
Net Effect ($5,100)
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$600,100
673,000
$ 72,900
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