Chapter 23
Removing Interest Rate Risk
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The first mistake is usually the cheapest mistake.
- A trader adage
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Outline
 Introduction
 Interest
rate futures contracts
 Concept of immunization
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Introduction
 A portfolio
is interest rate sensitive if its
value declines in response to interest rate
increases
• Especially pronounced:
– For portfolios with income as their primary
objective
– For corporate and government bonds
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Interest Rate
Futures Contracts
 Categories
of interest rate futures contracts
 U.S. Treasury bills and their futures
contracts
 Treasury bonds and their futures contracts
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Categories of Interest Rate
Futures Contracts
 Short-term
contracts
 Intermediate- and long-term contracts
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Short-Term Contracts
 The
two principal short-term futures
contracts are:
• Eurodollars
– U.S. dollars on deposit in a bank outside the U.S.
– The most popular form of short-term futures
– Not subject to reserve requirements
– Carry more risk than a domestic deposit
• U.S. Treasury bills
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Intermediate- and
Long-Term Contracts
 Futures
contract on U.S. Treasury notes is
the only intermediate-term contract
 The principal long-term contract is the
contract on U.S. Treasury bonds
 Special-purpose contracts:
• Municipal bonds
• U.S. dollar index
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U.S. Treasury Bills and
Their Futures Contracts
 Characteristics
of U.S. Treasury bills
 Treasury bill futures contracts
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Characteristics of
U.S. Treasury Bills
 U.S.
Treasury bills:
• Are sold at a discount from par value
• Are sold with 91-day and 182-day maturities at
a weekly auction
• Are calculated following a standard convention
and on a bond equivalent basis
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Characteristics of
U.S. Treasury Bills (cont’d)
 Standard
convention:
T-bill price = Face value - Discount amount
Discount amount = Face value  (
Days to maturity
)  Ask discount
360
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Characteristics of
U.S. Treasury Bills (cont’d)
 The
T-bill yield on a bond equivalent basis
adjusts for:
• The fact that there are 365 days in a year
• The fact that the discount price is the required
investment, not the face value
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Characteristics of
U.S. Treasury Bills (cont’d)
 The
T-bill yield on a bond equivalent basis:
Bond equivalent yield 
Discount amount
365

Discount price Days to maturity
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Characteristics of
U.S. Treasury Bills (cont’d)
Example
A 182-day T-bill has an ask discount of 5.30 percent. The
par value is $10,000.
What is the price of the T-bill? What is the yield of this Tbill on a bond equivalent basis?
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Characteristics of
U.S. Treasury Bills (cont’d)
Example (cont’d)
Solution: We must first compute the discount amount to
determine the price of the T-bill:
Discount amount = Face value  (
 $10, 000  (
Days to maturity
)  Ask discount
360
182
)  0.053
360
 $267.94
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Characteristics of
U.S. Treasury Bills (cont’d)
Example (cont’d)
Solution (cont’d): With a discount of $267.94, the price of
this T-bill is:
T-bill price = Face value - Discount amount
 $10, 000  $267.94
 $9, 732.06
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Characteristics of
U.S. Treasury Bills (cont’d)
Example (cont’d)
Solution (cont’d): The bond equivalent yield is 5.52%:
Discount amount
365
Bond equivalent yield 

Discount price Days to maturity
$267.94 365


$9, 732.06 182
 5.52%
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Treasury Bill
Futures Contracts
 T-bill
futures contracts:
• Call for the delivery of $1 million par value
• Of 90-day T-bills
• On the delivery date of the futures contract
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Treasury Bill
Futures Contracts (cont’d)
Example
Listed below is information regarding a T-bill futures
contract. What would you pay for this futures contract
today?
Discount
Open
High
Low
Settle
Change Settle
Change Open
Interest
92.43
92.43
92.41
92.42
-.01
+.01
7.52
250
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Treasury Bill
Futures Contracts (cont’d)
Example (cont’d)
Solution: First, determine the yield for the life of the Tbill:
7.52% x 90/360 = 1.88%
Next, discount the contract value by the yield:
$1,000,000/(1.0188) = $981,546.92
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Treasury Bonds and Their
Futures Contracts
 Characteristics
of U.S. Treasury bonds
 Treasury bond futures contracts
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Characteristics of U.S.
Treasury Bonds
 U.S.
Treasury bonds:
• Pay semiannual interest
• Have a maturity of up to 30 years
• Trade readily in the capital markets
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Characteristics of U.S.
Treasury Bonds (cont’d)
 U.S.
Treasury bonds differ from U.S.
Treasury notes:
• T-notes have a life of less than ten year
• T-bonds are callable fifteen years after they are
issued
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Treasury Bond
Futures Contracts
 U.S.
Treasury bond futures:
• Call for the delivery of $100,000 face value of
U.S. T-bonds
• With a minimum of fifteen years until maturity
(fifteen years of call protection for callable
bonds)
 Bonds
that meet these criteria are
deliverable bonds
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Treasury Bond
Futures Contracts (cont’d)
 A conversion
factor is used to standardize
deliverable bonds:
• The conversion is to bonds yielding 6 percent
• Published by the Chicago Board of Trade
• Is used to determine the invoice price
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Sample
Conversion Factors
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Treasury Bond
Futures Contracts (cont’d)
 The
invoice price is the amount that the
deliverer of the bond receives when a
particular bond is delivered against a futures
contract:
Invoice price = (Settlement price on position day  Conversion factor)
+ Accrued interest
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Treasury Bond
Futures Contracts (cont’d)
 Position
day is the day the bondholder
notifies the clearinghouse of an intent to
delivery bonds against a futures position
• Two business days prior to the delivery date
• Delivery occurs by wire transfer between
accounts
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Treasury Bond
Futures Contracts (cont’d)
 At
any given time, several bonds may be
eligible for delivery
• Only one bond is cheapest to delivery
– Normally the eligible bond with the longest duration
– The bond with the lowest ratio of the bond’s market
price to the conversion factor is the cheapest to
deliver
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Cheapest to
Deliver Calculation
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Concept of Immunization
 Definition
 Duration
matching
 Immunizing with interest rate futures
 Immunizing with interest rate swaps
 Disadvantages of immunizing
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Definition
 Immunization
means protecting a bond
portfolio from damage due to fluctuations in
market interest rates
 It
is rarely possible to eliminate interest rate
risk completely
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Duration Matching
 An
independent portfolio
 Bullet immunization example
 Expectation of changing interest rates
 An asset portfolio with a corresponding
liability portfolio
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An Independent Portfolio
 Bullet
immunization is one method of
reducing interest rate risk associated with an
independent portfolio
• Seeks to ensure that a set sum of money will be
available at a specific point in the future
• The effects of interest rate risk and
reinvestment rate risk cancel each other out
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Bullet Immunization Example
 Assume:
• You are required to invest $936
• You are to ensure that the investment will grow
at a 10 percent compound rate over the next 6
years
– $936 x (1.10)6 = $1,658.18
• The funds are withdrawn after 6 years
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Bullet Immunization
Example (cont’d)
 If
interest rates increase over the next 6
years:
• Reinvested coupons will earn more interest
• The value of any bonds we buy will decrease
– Our portfolio may end up below the target value
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Bullet Immunization
Example (cont’d)
 Reduce
the interest rate risk by investing in
a bond with a duration of 6 years
 One
possibility is the 8.8 percent coupon
bond shown on the next two slides:
• Interest is paid annually
• Market interest rates change only once, at the
end of the third year
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38
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Expectation of Changing
Interest Rates
 The
higher the duration, the higher the
interest rate risk
 To
reduce interest rate risk, reduce the
duration of the portfolio when interest rates
are expected to increase
• Duration declines with shorter maturities and
higher coupons
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An Asset Portfolio With
A Liability Portfolio
 A bank
immunization case occurs when
there are simultaneously interest-sensitive
assets and interest-sensitive liabilities
 A bank’s
funds gap is its rate-sensitive
assets (RSA) minus its rate-sensitive
liabilities (RSL)
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An Asset Portfolio With
A Liability Portfolio (cont’d)
 A bank
can immunize itself from interest
rate fluctuations by restructuring its balance
sheet so that:
$ A  DA  $ L  DL
where $ A, L  dollar value of rate-sensitive
DA, L
assets and liabilities
 dollar-weighted average duration
of assets and liabilities
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An Asset Portfolio With
A Liability Portfolio (cont’d)
 If
the dollar-duration value of the asset side
exceeds the dollar-duration of the liability
side:
• The value of RSA will fall to a greater extent
than the value of RSL
• The net worth of the bank will decline
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An Asset Portfolio With
A Liability Portfolio (cont’d)
 To
immunize if RSA are more sensitive than
RSL:
•
•
•
•
Get rid of some RSA
Reduce the duration of the RSA
Issue more RSL or
Raise the duration of the RSL
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Immunizing With
Interest Rate Futures
 Financial
institutions use futures to hedge
interest rate risk
 If
interest rate are expected to rise, go short
T-bond futures contracts
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Immunizing With
Interest Rate Futures (cont’d)
 To
hedge, first calculate the hedge ratio:
Pb  Db
HR  CFctd 
Pf  D f
where Pb  price of bond portfolio as a percentage of par
Db  duration of bond portfolio
Pf  price of futures contract as a percentage
D f  duration of cheapest-to-deliver bond eligible for delivery
CFctd  conversion factor for the cheapest-to-deliver bond
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Immunizing With
Interest Rate Futures (cont’d)
 Next,
calculate the number of contracts
necessary given the hedge ratio:
Portfolio value
Number of contracts 
 HR
$100, 000
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Immunizing With
Interest Rate Futures (cont’d)
Example
A bank portfolio manager holds $20 million par value in
government bonds that have a current market price of
$18.9 million. The weighted average duration of this
portfolio is 7 years. Cheapest-to-deliver bonds are
8.125s28 T-bonds with a duration of 10.92 years and a
conversion factor of 1.2786.
What is the hedge ratio? How many futures contracts
does the bank manager have to short to immunize the
bond portfolio, assuming the last settlement price of the
futures contract was 94 15/32?
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Immunizing With
Interest Rate Futures (cont’d)
Example
Solution: First calculate the hedge ratio:
HR  CFctd 
Pb  Db
Pf  D f
0.945  7
 1.2786 
0.9446875 10.92
 0.8199
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Immunizing With
Interest Rate Futures (cont’d)
Example
Solution: Based on the hedge ratio, the bank manager
needs to short 155 contracts to immunize the portfolio:
$18,900,000
Number of contracts 
 0.8199
$100, 000
 154.96
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Immunizing With
Interest Rate Swaps
 Interest
rate swaps are popular tools for
managers who need to manage interest rate
risk
 A swap
enables a manager to alter the level
of risk without disrupting the underlying
portfolio
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Immunizing With
Interest Rate Swaps (cont’d)
 A basic
interest rate swap involves:
• A party receiving variable-rate payments
– Believes interest rates will decrease
• A party receiving fixed-rate payments
– Believes interest rates will rise
 The
two parties swap fixed-for-variable
payments
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Immunizing With
Interest Rate Swaps (cont’d)
 The
size of the swap is the notional amount
• The reference point for determining how much
interest is paid
 The
price of the swap is the fixed rate to
which the two parties agree
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Immunizing With
Interest Rate Swaps (cont’d)
 Interest
rate swaps introduce counterparty
risk:
• No institution guarantees the trade
• One party to the swap pay not honor its
agreement
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Disadvantages of Immunizing
 Opportunity
cost of being wrong
 Lower
yield
 Transaction costs
 Immunization is instantaneous only
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Opportunity Cost
of Being Wrong
 With
an incorrect forecast of interest rate
movements, immunized portfolios can
suffer an opportunity loss
 For
example, if a bank has more RSA than
RSL, it would benefit from a decline in
interest rates
• Immunizing would have reduced the benefit
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Lower Yield
 The
yield curve is usually upward sloping
 Immunizing
may reduce the duration of a
portfolio and shift fund characteristics to the
left on the yield curve
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Transaction Costs
 Buying
and selling bonds requires
brokerage commissions
• Sales may also result in tax liabilities
 Commissions
with the futures market are
lower
• The futures market is the method of choice for
immunizing strategies
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Immunization Is
Instantaneous Only
 A portfolio
is theoretically only immunized
for an instant
• Each day, durations, yields to maturity, and
market interest rates change
 It
is not practical to make daily adjustments
for changing immunization needs
• Make adjustments when conditions have
changed enough to make revision cost effective
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