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Chapter 23 Removing Interest Rate Risk Prof. Rushen Chahal Prof. Rushen Chahal 1 The first mistake is usually the cheapest mistake. - A trader adage Prof. Rushen Chahal 2 Outline • Introduction • Interest rate futures contracts • Concept of immunization Prof. Rushen Chahal 3 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 Prof. Rushen Chahal 4 Interest Rate Futures Contracts • Categories of interest rate futures contracts • U.S. Treasury bills and their futures contracts • Treasury bonds and their futures contracts Prof. Rushen Chahal 5 Categories of Interest Rate Futures Contracts • Short-term contracts • Intermediate- and long-term contracts Prof. Rushen Chahal 6 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 Prof. Rushen Chahal 7 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 Prof. Rushen Chahal 8 U.S. Treasury Bills and Their Futures Contracts • Characteristics of U.S. Treasury bills • Treasury bill futures contracts Prof. Rushen Chahal 9 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 Prof. Rushen Chahal 10 Characteristics of U.S. Treasury Bills (cont’d) • Standard convention: T-bill price = Face value - Discount amount Days to maturity Discount amount = Face value ( ) Ask discount 360 Prof. Rushen Chahal 11 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 Prof. Rushen Chahal 12 Characteristics of U.S. Treasury Bills (cont’d) • The T-bill yield on a bond equivalent basis: Discount amount 365 Bond equivalent yield Discount price Days to maturity Prof. Rushen Chahal 13 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 T-bill on a bond equivalent basis? Prof. Rushen Chahal 14 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: Days to maturity Discount amount = Face value ( ) Ask discount 360 182 $10, 000 ( ) 0.053 360 $267.94 Prof. Rushen Chahal 15 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 Prof. Rushen Chahal 16 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% Prof. Rushen Chahal 17 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 Prof. Rushen Chahal 18 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 7.52 +.01 250 Prof. Rushen Chahal 19 Treasury Bill Futures Contracts (cont’d) Example (cont’d) 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 Prof. Rushen Chahal 20 Treasury Bonds and Their Futures Contracts • Characteristics of U.S. Treasury bonds • Treasury bond futures contracts Prof. Rushen Chahal 21 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 Prof. Rushen Chahal 22 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 Prof. Rushen Chahal 23 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 Prof. Rushen Chahal 24 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 Prof. Rushen Chahal 25 Sample Conversion Factors Prof. Rushen Chahal 26 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 Prof. Rushen Chahal 27 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 Prof. Rushen Chahal 28 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 Prof. Rushen Chahal 29 Cheapest to Deliver Calculation Prof. Rushen Chahal 30 Concept of Immunization • Definition • Duration matching • Immunizing with interest rate futures • Immunizing with interest rate swaps • Disadvantages of immunizing Prof. Rushen Chahal 31 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 Prof. Rushen Chahal 32 Duration Matching • An independent portfolio • Bullet immunization example • Expectation of changing interest rates • An asset portfolio with a corresponding liability portfolio Prof. Rushen Chahal 33 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 Prof. Rushen Chahal 34 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 Prof. Rushen Chahal 35 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 Prof. Rushen Chahal 36 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 Prof. Rushen Chahal 37 Prof. Rushen Chahal 38 Prof. Rushen Chahal 39 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 Prof. Rushen Chahal 40 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) Prof. Rushen Chahal 41 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 assets and liabilities DA , L dollar-weighted average duration of assets and liabilities Prof. Rushen Chahal 42 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 Prof. Rushen Chahal 43 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 Prof. Rushen Chahal 44 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 Prof. Rushen Chahal 45 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 Prof. Rushen Chahal 46 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 Prof. Rushen Chahal 47 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? Prof. Rushen Chahal 48 Immunizing With Interest Rate Futures (cont’d) Example Solution: First calculate the hedge ratio: Pb Db HR CFctd Pf D f 0.945 7 1.2786 0.9446875 10.92 0.8199 Prof. Rushen Chahal 49 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 Prof. Rushen Chahal 50 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 Prof. Rushen Chahal 51 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 Prof. Rushen Chahal 52 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 Prof. Rushen Chahal 53 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 Prof. Rushen Chahal 54 Disadvantages of Immunizing • Opportunity cost of being wrong • Lower yield • Transaction costs • Immunization is instantaneous only Prof. Rushen Chahal 55 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 Prof. Rushen Chahal 56 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 Prof. Rushen Chahal 57 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 Prof. Rushen Chahal 58 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 Prof. Rushen Chahal 59

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