固定收益证券的复习计算题

Fixed income treasury Ppt3 1 公式 Practice Question 3 1 Suppose currently 1 year spot rate is 1 and marketexpects that 1 year spot rate next year would be 2 and 1 year spot rate in 2 years would be 3 Compute today s 2 year spot rate and 3 year spot rate 已做答案 已做答案 2 CurrentCurrent YieldYield Compute the current yield for a 7 8 year bond whose price is 94 17 How about the current yield if price is 100 106 respectively 3 Case 3 1 Consider a 7 8 year bond paying coupon semiannually which is sold for 94 17 The present value using various discount rate is A What is the YTM for this bond B How much is the total dollar return on this bond C How much is the total dollar return if you put the same amount of dollars into a deposit account with the same annual yield 2 4 Forward Rates 注 6 month bill spot rate is 3 是年化利率 3 要除以 2 1 year bill spot rate is 3 3 是年化利率 3 3 要除以2 3 Ppt4 1 Fixed Coupon Bonds Practice Question 4 2 A What is the value of a 4 year 10 coupon bond that pays interest semiannually assuming that the annual discount rate is 8 What is the value of a similar 10 coupon bond with an infinite maturity 无期限 B What is the value of a 5 year zero coupon bond with a maturity value of 100 discounted at an 8 interest rate C Compute the value par 100 of par value of a 4 year 10 coupon bond assuming the payments are annual and the discount rate for each year is 6 8 7 2 7 6 and 8 0 respectively Infinite maturity Pv 100 10 2 8 2 Pv 100 10 2 8 2 半年付息 4 PresentPresent ValueValue PropertiesProperties Practice Question 4 4 A Suppose the discount rate for the 4 year 10 coupon bond with a par value of 100 is 8 Compute its present value B One year later suppose that the discount rate appropriate for a 3 year 10 coupon bond increases from 8 to 9 RedoRedo youryour calculationcalculation in part A and decomposedecompose thethe priceprice change attributable toto movingmoving toto maturitymaturity and toto thethe increaseincrease inin thethe discountdiscount raterate 期限与贴现率变化 期限与贴现率变化 5 3 Pricing a Bond between Coupon Payments Practice Question 4 6 Suppose that there are five semiannual coupon payments remaining for a 10 coupon bond Also assume the following Annual discount rate is 8 78 days between the settlement date and the next coupon payment date 182 days in the coupon period Compute the full price of this coupon bond What is the clean price of this bond 4 Valuation Approach Case 4 1 A Consider a 8 10 year Treasury coupon bond What is its fair value if traditional approach is used given yield for the 10 year on the run Treasury issue is 8 B What is the fair value of above Treasury coupon bond if arbitrage free approach is used given the following annual spot rates C Which approach is more accurate 准确 6 C Arbitrage Free Approach is more accurate 7 Ppt5 8 2 ConvexityConvexity Consider a 9 20 year bond selling at 134 6722 to yield 6 For a 20 bp change in yield its price would either increase to 137 5888 or decrease to 131 8439 A Compute the convexity for this bond B What is the convexity adjustment for a change in yield of 200 bps C If we know that the duration for this bond is 10 66 what should the total estimated percentage price change be for a 200 bp increase in the yield How about a 200 bp decrease in the yield 9 Ppt6 1 MeasuringMeasuring YieldYield CurveCurve RiskRisk Case 6 1 Panel A Consider the following twotwo 100 100 portfoliosportfolios composed of 2 year2 year 16 year16 year and 30 30 yearyear issues all of which are zero coupon bonds For simplicity assume there are onlyonly threethree keykey ratesrates 2years2years 1616 yearsyears and 3030 yearsyears Calculate thethe portfolio sportfolio s keykey raterate durationsdurations atat thesethese threethree pointspoints and itsits effectiveeffective duration duration Case 6 1 Panel B Consider the following three scenarios Scenario 1 All spot rates shift down 10 basis points Scenario 2 The 2 year key rate shifts up 10 basis points an the 30 year rate shifts down 10 basis points Scenario 3 The 2 year key rate shifts down 10 basis points and the 30 year rate shifts up 10 basis points How would the portfolio value change in each scenario 10 Ppt7 Consider a 6 5 option free bond with 4 years remaining to maturity If the appropriate binomial interest rate tree is shown as below calculate the fair price of this bond 11 Ppt8 1 ValuingValuing CallableCallable andand PutablePutable BondsBonds Case 8 1 Valuing a callable bond with single call price Consider a 6 5 callable bond with 4 years remaining to maturity callable in one year at 100 Assume the yield volatility is 10 and the appropriate binomial interest rate tree is same as Case 6 4 Calculate the fair price of this callable bond 12 2 Case 8 2 Valuing a callable bond with call schedule Consider a 6 5 callable bond with 4 years remaining to maturity callable in one year at a call schedule as below Assume the yield volatility is 10 and the appropriate binomial interest rate tree is same as Case 6 4 Calculate the fair price of this callable bond 13 3 Case 8 3 Valuing a putable bond Consider a 6 5 putable bond with 4 years remaining to maturity putable in one year at 100 Assume the yield volatility is 10 and the appropriate binomial interest rate tree is same as Case 6 4 Calculate the fair price of this putable bond Vapppppppplue of a Cappppppp 14 ConvertibleConvertible BondsBonds Case 9 1 Suppose that the straight value of a 5 75 ADC convertible bond is 981 9 981 9 per 1 000 1 000 of par value and its marketmarket priceprice isis 1 065 1 065 The market price per share of commoncommon stockstock isis 33 33 and thethe conversionconversion ratioratio isis 25 3225 32 shares per 1 000 of parvalue Also assume that thethe commoncommon stockstock dividenddividend isis 0 90 0 90 per share ptionption 公式 Minimum Value the greater of its conversion price and its straight value Conversion Price Market price of common stock Conversion ratio Straight Value Investment Value present value of the bond s cash flows discounted at the required return on a comparable option free issue Market Conversion Price Conversion ParityPrick Market price of convertible security Conversion ratio Market Conversion Premium Per Share Market conversion price Market price of common stock Market Conversion Premium Ratio Market conversion premium per share Market price of common stock Premium over straight value Market price of convertible bond Straight value 1 The higher this ratio the greater downside risk and the less attractive the convertible bond Premium Payback Period Market conversion premium per share Favorable income differential per share Favorable Income Differential Per Share Coupon interest Conversion ratio Common stock dividend per share Conversion ratio 15 A What is thethe minimumminimum valuevalue ofof thisthis convertibleconvertible bondbond B Calculate its marketmarket conversionconversion priceprice marketmarket conversionconversion premiumpremium perper shareshare and marketmarket conversionconversion premiumpremium ratioratio C What is its premiumpremium paybackpayback periodperiod D Calculate its premiumpremium overover straightstraight valuevalue pppp Market price of common stock 33 conversionconversion ratioratio 25 3225 32 Straight Value 981 9 981 9 marketmarket priceprice ofof conversibleconversible bondbond 1 065 1 065 commoncommon stockstock dividenddividend 0 90 0 90 Coupon rate 5 75 A Conversion Price Market price of common stock Conversion ratio 33 25 32 835 56 thethe minimumminimum valuevalue ofof thisthis convertibleconvertible bond max bond max 835 56 981 9 981 9 B Market Conversion Price Conversion ParityPrick Market price of convertible security Conversion ratio 1065 25 32 42 06 Market Conversion Premium Per Share Market conversion price Market price of common stock 42 06 33 9 06 Market Conversion Premium Ratio Market conversion premium per share Market price of common stock 9 06 33 27 5 C Premium Payback Period Market conversion premium per share Favorable income differential per share Favorable Income Differential Per Share 16 Coupon interest Conversion ratio Common stock dividend per share Conversion ratio Coupon interest from bond 5 75 1 000 57 50 Favorable income differential per share 57 50 25 32 0 90 25 32 1 37 Premium payback period 9 06 1 37 6 6 years D Premium over straight value Market price of convertible bond Straight value 1 1 065 981 5 1 8 5 Ppt10 No ArbitrageNo Arbitrage PrinciplePrinciple no riskless profits gained from holding a a combinationcombination ofof a a forwardforward contractcontract positionposition as well as positionspositions inin otherother assetsassets FP Price that would not permit profitable riskless arbitrage in frictionless markets that is Case 10 1 Consider a 3 month3 month forwardforward contraccontract on a zero coupon bond with a face value of 1 000 that is currently quoted atat 500 500 and assume a risk 17 free annual interest rate of 6 Determine thethe priceprice ofof thethe forwardforward contractcontract under the no arbitrage principle Solutions Solutions Case 10 2 Suppose the forward contract described in case 10 1 is actually trading at 510 which is greater than the noarbitrage price Demonstrate how an arbitrageur can obtain riskless arbitrage profit from this overpriced forward contract and how much the arbitrage profit would be Case 10 3 If the forward contract described in case 10 1 is actually trading at 502 which is smaller than the no arbitrage price Demonstrate how an arbitrageur can obtain riskless arbitrage profit from this underpriced forward contract and how much the arbitrage profit would be 18 Case 10 4 Calculate the price of a 250 day forward contract on a 7 U S Treasury bond with a spot price of 1 050 including accrued interest that has just paid a coupon and will make another coupon payment in 182 days The annual risk free rate is 6 Solutions Solutions Remember that T bonds make semiannual coupon payments so Case 10 6 Solutions Solutions The semiannual coupon on a single 1 000 face value7 bond is 35 A 19 bondholder will receive one payment 0 5 years from now 0 7 years left to expiration of futures and one payment 1 year from now 0 2 years until expiration Thus Ppt11 Payoffs and Profits Case 11 1 Consider a European bond call option with an exercise price of 900 The call premium for this option is 50 At expiration if the spot price for the underlying bond is 1 000 what is the call option s payoff as well as its gain loss Is this option in the money out of money or at the money Will you exercise this option How about your answers if the spot price at expiration is 920 and 880 respectively Solutions A If the spot price at expiration is 1 000 the payoff to the call option is max 0 1 000 900 100 So the call is in the money and it will be exercised with a gain of 50 B If the spot price at expiration is 920 the payoff to the ca