Chapter 23 Removing Interest Rate Risk

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Chapter 23Removing 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 (contd)

• Standard convention

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Characteristics of U.S. Treasury Bills (contd)

• 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 (contd)

• The T-bill yield on a bond equivalent basis

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Characteristics of U.S. Treasury Bills (contd)

• 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 T-bill on a bond equivalent basis?

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Characteristics of U.S. Treasury Bills (contd)

• Example (contd)
• Solution We must first compute the discount
  amount to determine the price of the T-bill

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Characteristics of U.S. Treasury Bills (contd)

• Example (contd)
• Solution (contd) With a discount of 267.94,
  the price of this T-bill is

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Characteristics of U.S. Treasury Bills (contd)

• Example (contd)
• Solution (contd) The bond equivalent yield is
  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 (contd)

• Example
• Listed below is information regarding a T-bill
  futures contract. What would you pay for this
  futures contract today?

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Treasury Bill Futures Contracts (contd)

• Example (contd)
• Solution First, determine the yield for the life
  of the T-bill
• 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 (contd)

• 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 (contd)

• 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 (contd)

• The invoice price is the amount that the
  deliverer of the bond receives when a particular
  bond is delivered against a futures contract

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Treasury Bond Futures Contracts (contd)

• 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 (contd)

• 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 bonds
  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 (contd)

• 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 (contd)

• 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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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 banks 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
(contd)

• A bank can immunize itself from interest rate
  fluctuations by restructuring its balance sheet
  so that

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An Asset Portfolio With A Liability Portfolio
(contd)

• 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
(contd)

• 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 (contd)

• To hedge, first calculate the hedge ratio

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Immunizing With Interest Rate Futures (contd)

• Next, calculate the number of contracts necessary
  given the hedge ratio

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Immunizing With Interest Rate Futures (contd)

• 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 (contd)

• Example
• Solution First calculate the hedge ratio

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Immunizing With Interest Rate Futures (contd)

• Example
• Solution Based on the hedge ratio, the bank
  manager needs to short 155 contracts to immunize
  the portfolio

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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 (contd)

• 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 (contd)

• 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 (contd)

• 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