Chapter 23 Removing Interest Rate Risk 1 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 2 Categories of Interest Rate Futures Contracts Short-term contracts Intermediate- and long-term contracts 3 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 4 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 5 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 6 Characteristics of U.S. Treasury Bills (cont’d) Standard convention: T -bill price = Face value - D iscount am o unt D iscount am ount = Face value ( D ays to m aturity ) A sk dis count 360 7 Characteristics of U.S. Treasury Bills (cont’d) The T-bill yield on a bond equivalent basis: Bond equivalent yield D iscount am ount D iscount price 365 D ays to m aturity 8 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 9 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? 10 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: D iscount am ount = Face value ( D ays to m aturity ) A sk dis count 360 $10, 000 ( 182 ) 0.053 360 $267.94 11 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 - D iscount am o unt $10, 000 $267.94 $9, 732.06 12 Characteristics of U.S. Treasury Bills (cont’d) Example (cont’d) Solution (cont’d): The bond equivalent yield is 5.52%: B ond equivalent yield D iscount am ount D iscount price $267.94 $9, 732.06 365 D ays to m aturity 365 182 5.52% 13 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) 14 Treasury Bill Futures Contracts (cont’d) Example Listed below is information regarding a T-bill futures contract. What is the price of the $1 million (par value) Tbills implied by the contract? Discount Open High Low Settle Change Settle Change Open Interest 92.49 92.49 92.48 92.48 -.01 +.01 7.52 250 15 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 16 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 17 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 18 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 19 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 20 Sample Conversion Factors 21 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 = (S ettlem ent price on pos ition day C onversion factor) + A ccrued interest 22 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 23 Cheapest to Deliver Calculation 24 Concept of Immunization Definition Duration matching Immunizing with interest rate futures Immunizing with interest rate swaps Disadvantages of immunizing 25 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 26 Duration Matching An independent portfolio Bullet immunization example Expectation of changing interest rates An asset portfolio with a corresponding liability portfolio 27 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 28 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 29 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 own will decrease – Our portfolio may end up below the target value 30 Bullet Immunization Example (cont’d) To hedge the interest rate risk, invest in a bond with a duration of 6 years. An example with an 8.8% coupon bond is shown on the next two slides: • Interest is paid annually • Market interest rates change only once, at the end of the third year 31 32 33 In General: 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 34 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) 35 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 w here $ A , L dollar value of rate-sensitive assets and liabilities D A , L dollar-w eighted average duration of assets and liabilities 36 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 37 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 (note that the first two points are usually more feasible than the last two) 38 Immunizing With Interest Rate Futures Financial institutions use futures to hedge interest rate risk If interest rates are expected to rise, go short T-bond futures contracts 39 Immunizing With Interest Rate Futures (cont’d) To hedge, first calculate the hedge ratio: H R C Fctd Pb D b Pf D f w here Pb price of bond portfolio as a perc entage of par D b duration of bond portfolio P f price of futures contract as a percenta ge D f duration of cheapest-to-deliver bond eligible for delivery C Fctd conversion factor for the cheapest-to-d eliver bond 40 Immunizing With Interest Rate Futures (cont’d) Next, calculate the number of contracts necessary given the hedge ratio: N um ber of contracts Portfolio value HR $100, 000 41 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? 42 Immunizing With Interest Rate Futures (cont’d) Example Solution: First calculate the hedge ratio: H R C Fctd Pb D b Pf D f 1.2786 0.945 7 0.9446875 10.92 0.8199 43 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: N um ber of contracts $18,900,000 0.8199 $100, 000 154.96 44 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 45 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 46 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 47 Disadvantages of Immunizing Opportunity cost of being wrong Lower yield Transaction costs Immunization is instantaneous only 48 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 49 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 50 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 51 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 52

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