Tài chính doanh nghiệp - Chapter 12: Futures contracts and portfolio management

© 2004 South-Western Publishing1Chapter 12Futures Contracts and Portfolio Management2OutlineThe concept of immunizationAltering asset allocation with futures3The Concept of ImmunizationIntroductionBond risksDuration matchingDuration shiftingHedging with interest rate futuresIncreasing duration with futuresDisadvantages of immunizing4IntroductionAn immunized bond portfolio is largely protected from fluctuations in market interest ratesSeldom possible to eliminate interest rate risk completely A portfolio’s immunization can wear out, requiring managerial action to reinstate the portfolioContinually immunizing a fixed-income portfolio can be time-consuming and technical5Bond RisksA fixed income investor faces three primary sources of risk:Credit riskInterest rate riskReinvestment rate risk6Bond Risks (cont’d)Credit risk is the likelihood that a borrower will be unable or unwilling to repay a loan as agreedRating agencies measure this risk with bond ratingsLower bond ratings mean higher expected returns but with more risk of defaultInvestors choose the level of credit risk that they wish to assume7Bond Risks (cont’d)Interest rate risk is a consequence of the inverse relationship between bond prices and interest ratesDuration is the most widely used measure of a bond’s interest rate risk 8Bond Risks (cont’d)Reinvestment rate risk is the uncertainty associated with not knowing at what rate money can be put back to work after the receipt of an interest checkThe reinvestment rate will be the prevailing interest rate at the time of reinvestment, not some rate determined in the past9Duration MatchingIntroductionBullet immunizationBank immunization10IntroductionDuration matching selects a level of duration that minimizes the combined effects of reinvestment rate and interest rate riskTwo versions of duration matching:Bullet immunizationBank immunization11Bullet ImmunizationSeeks to ensure that a predetermined sum of money is available at a specific time in the future regardless of interest rate movements12Bullet Immunization (cont’d)Objective is to get the effects of interest rate and reinvestment rate risk to offsetIf interest rates rise, coupon proceeds can be reinvested at a higher rateIf interest rates fall, proceeds can be reinvested at a lower rate13Bullet Immunization (cont’d)Bullet Immunization Example A portfolio managers receives $93,600 to invest in bonds and needs to ensure that the money will grow at a 10% compound rate over the next 6 years (it should be worth $165,818 in 6 years). 14Bullet Immunization (cont’d)Bullet Immunization Example (cont’d) The portfolio manager buys $100,000 par value of a bond selling for 93.6% with a coupon of 8.8%, maturing in 8 years, and a yield to maturity of 10.00%.15Bullet Immunization Example (cont’d)Panel A: Interest Rates Remain Constant Bullet Immunization (cont’d) Year 1Year 2Year 3Year 4Year 5Year 6$8,800$9,680$10,648$11,713$12,884$14,172 $8,800$9,680$10,648$11,713$12,884  $8,800$9,680$10,648$11,713   $8,800$9,680$10,648    $8,800$9,680          Interest$68,805     Bond      Total$165,817$8,800$97,92016Bullet Immunization (cont’d)Bullet Immunization Example (cont’d)Panel B: Interest Rates Fall 1 Point in Year 3  Year 1Year 2Year 3Year 4Year 5Year 6$8,800$9,680$10,648$11,606$12,651$13,789 $8,800$9,680$10,551$11,501$12,536  $8,800$9,592$10,455$11,396   $8,800$9,592$10,455    $8,800$9,592         Interest$66,568     Bond     Total$166,218$8,800$99,65017Bullet Immunization (cont’d)Bullet Immunization Example (cont’d)Panel C: Interest Rates Rise 1 Point in Year 3  Year 1Year 2Year 3Year 4Year 5Year 6$8,800$9,680$10,648$11,819$13,119$14,563 $8,800$9,680$10,745$11,927$13,239  $8,800$9,768$10,842$12,035   $8,800$9,768$10,842    $8,800$9,768         Interest$69,247     Bond      Total $165,477$8,800$96,23018Bullet Immunization (cont’d)Bullet Immunization Example (cont’d) The compound rates of return in the three scenarios are 10.10%, 10.04%, and 9.96%, respectively. 19Bank ImmunizationAddresses the problem that occurs if interest-sensitive liabilities are included in the portfolioE.g., a bank’s portfolio manager is concerned with the entire balance sheetA bank’s funds gap is the dollar value of its interest rate sensitive assets (RSA) minus its interest rate sensitive liabilities (RSL)20Bank Immunization (cont’d)To immunize itself, a bank must reorganize its balance sheet such that:21Bank Immunization (cont’d)A bank could have more interest-sensitive assets than liabilities:Reduce RSA or increase RSL to immunizeA bank could have more interest-sensitive liabilities than assets:Reduce RSL or increase RSA to immunize22Duration ShiftingThe higher the duration, the higher the level of interest rate riskIf interest rates are expected to rise, a bond portfolio manager may choose to bear some interest rate risk (duration shifting)23Duration Shifting (cont’d)The shorter the maturity, the lower the durationThe higher the coupon rate, the lower the durationA portfolio’s duration can be reduced by including shorter maturity bonds or bonds with a higher coupon rate24Duration Shifting (cont’d)Maturity CouponLowerHigherLowerAmbiguousDuration LowerHigherDuration HigherAmbiguous25Hedging With Interest Rate FuturesA financial institution can use futures contracts to hedge interest rate riskThe hedge ratio is:26Hedging With Interest Rate Futures (cont’d)The number of contracts necessary is given by:27Hedging With Interest Rate Futures (cont’d)Futures Hedging Example A bank portfolio holds $10 million face value in government bonds with a market value of $9.7 million, and an average YTM of 7.8%. The weighted average duration of the portfolio is 9.0 years. The cheapest to deliver bond has a duration of 11.14 years, a YTM of 7.1%, and a CBOT correction factor of 1.1529. An available futures contract has a market price of 90 22/32 of par, or 0.906875. What is the hedge ratio? How many futures contracts are needed to hedge?28Hedging With Interest Rate Futures (cont’d)Futures Hedging Example (cont’d) The hedge ratio is:29Hedging With Interest Rate Futures (cont’d)Futures Hedging Example (cont’d) The number of contracts needed to hedge is:30Increasing Duration With FuturesExtending duration may be appropriate if active managers believe interest rates are going to fallAdding long futures positions to a bond portfolio will increase duration31Increasing Duration With Futures (cont’d)One method for achieving target duration is the basis point value (BPV) methodGives the change in the price of a bond for a one basis point change in the yield to maturity of the bond32Increasing Duration With Futures (cont’d)To change the duration of a portfolio with the BPV method requires calculating three BPVs:33Increasing Duration With Futures (cont’d)The current and target BPVs are calculated as follows:34Increasing Duration With Futures (cont’d)The BPV of the cheapest to deliver bond is calculated as follows:35Increasing Duration With Futures (cont’d)BPV Method Example A portfolio has a market value of $10 million, an average yield to maturity of 8.5%, and duration of 4.85. A forecast of declining interest rates causes a bond manager to decide to double the portfolio’s duration. The cheapest to deliver Treasury bond sells for 98% of par, has a yield to maturity of 7.22%, duration of 9.7, and a conversion factor of 1.1223. Compute the relevant BPVs and determine the number of futures contracts needed to double the portfolio duration. 36Increasing Duration With Futures (cont’d)BPV Method Example (cont’d) 37Increasing Duration With Futures (cont’d)BPV Method Example (cont’d) 38Increasing Duration With Futures (cont’d)BPV Method Example (cont’d) The number of contracts needed to double the portfolio duration is: 39Disadvantages of ImmunizingOpportunity cost of being wrongLower yieldTransaction costsImmunization: instantaneous only40Opportunity Cost of Being WrongIf the market is efficient, it is very difficult to forecast changes in interest ratesAn incorrect forecast can lead to an opportunity cost of immunized portfolios41Lower YieldImmunization usually results in a lower level of income generated by the funds under managementBy reducing the portfolio duration, the portfolio return will shift to the left on the yield curve, resulting in a lower level of income42Transaction CostsCosts include:Trading feesBrokerage commissionsBid-ask spread Tax liabilities43Immunization: Instantaneous OnlyDurations and yields to maturity change every dayA portfolio may be immunized only temporarily44Altering Asset Allocation With FuturesTactical changesInitial situationBond adjustmentStock adjustmentNeutralizing cash45Tactical ChangesInvestment policy statements may give the portfolio manager some latitude in how to split the portfolio between equities and fixed income securitiesThe portfolio manager can mix both T-bonds and S&P 500 futures into the portfolio to adjust asset allocation without disturbing existing portfolio components46Initial SituationPortfolio market value = $175 millionInvested 82% in stock (average beta = 1.10) and 18% in bonds (average duration = 8.7; average YTM = 8.00%)The portfolio manager wants to reduce the equity exposure to 60% stock47Initial Situation (cont’d)48Initial Situation (cont’d)Stock Index Futures September settlement = 1020.00 Treasury Bond FuturesSeptember settlement = 91.05Cheapest to deliver bond:Price = 95%Maturity = 18 yearsCoupon = 9 %Duration = 8.60Conversion factor = 1.327549Initial Situation (cont’d)Determine:How many contracts will remove 100% of each market and interest rate riskWhat percentage of this 100% hedge matches the proportion of the risk we wish to retain50Bond AdjustmentUsing the BPV technique:51Bond Adjustment (cont’d)The number of contracts to completely hedge the bond portion of the portfolio is:Thus, the manager should buy 410 T-bond futures 52Stock AdjustmentFor this portfolio, the hedge ratio is:Selling 619 stock index futures would turn the stock into a synthetic T-bill53Stock Adjustment (cont’d)The current equity investment is $143,500,000The desired equity investment is $105,000,000, which is 26.83% less than the current level54Stock Adjustment (cont’d)We can use 26.83% of the stock index futures hedge ratio:55Stock Adjustment (cont’d)The portfolio manager can change the asset allocation from 82% stock, 18% bonds to 60% stock, 40% bonds byBuying 521 T-bond futures andSelling 166 stock index futures56Neutralizing CashIt is harder to “beat the market” with the downward bias in relative fund performance due to cashCash can be neutralized by offsetting it with long positions in stock index futuresCash can be neutralized by offsetting it with long positions in interest rate futures