固定收益证券的复习计算题

F i x e d-i n c o m e t r e a s u r yPpt31、公式：Practice QuestionSuppose currently, 1-year spot rate is 1% and marketexpects that 1-year spot rate next year would be 2%and1-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）2、Current YieldCompute the current yield for a 7% 8-year bond whose price is$. How about the current yield if price is $100, $106,respectively3、CaseConsider a 7% 8-year bond paying coupon semiannually which is sold for $. The present value using various discount rate is:A. What is the YTM for this bondB. How much is the total dollar return on this bondC. How much is the total dollar return if you put the same amount of dollars into a deposit account with the same annual yield4、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 %是年化利率（%要除以2）Ppt41、Fixed‐Coupon BondsPractice QuestionA. 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 rateC. 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 %, %, % and %, respectively.Infinite maturityPv=($100*10%/2)/(8%/2)(半年付息）Present Value PropertiesPractice QuestionA. 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%. Redo your calculation in part A and decompose the price change attributable to moving to maturity and to the increase in the discount rate.（期限与贴现率变化）3、Pricing a Bond between Coupon PaymentsPractice QuestionSuppose that there are five semiannual coupon payments remaining for a 10% coupon bond. Also assume the following:①Annual discount rate is 8%②78 days between the settlement date and the next coupon payment date③182 days in the coupon periodCompute the full price of this coupon bond. What is the clean price of this bond4、Valuation ApproachCaseA. Consider a 8% 10-year Treasury coupon bond. What is its fair value if traditional approach isused, 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 ratesC. Which approach is more accurate（准确）C、Arbitrage-Free Approach is more accuratePpt52、ConvexityConsider a 9% 20-year bond selling at $ to yield 6%. For a 20 bp change in yield, its price would either increase to $ or decrease to $.A. Compute the convexity for this bond.B. What is the convexity adjustment for a change in yield of 200 bpsC. If we know that the duration for this bond is , 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 Ppt61、Measuring Yield Curve RiskCase : Panel AConsider the following two $100 portfolios composed of2-year, 16-year, and 30-year issues, all of which are zero-coupon bonds:For simplicity, assume there are only three key rates—2years, 16 years and 30 years. Calculate the portfolio’s key rate durations at these three points and its effective duration.Case : Panel BConsider 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 the30-year rate shifts down 10 basis points.Scenario 3: The 2-year key rate shifts down 10 basis points andthe 30-year rate shifts up 10 basis points.How would the portfolio value change in each scenarioPpt7Consider a % 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.Ppt81、Valuing Callable and Putable BondsCase : Valuing a callable bond with singlecall priceConsider a % 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 . Calculate the fair price of this callable bond.2、Case : Valuing a callable bond with call scheduleConsider a % callable bond with 4 years remaining tomaturity, 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 . Calculate the fair price of this callable bond.3、Case : Valuing a putable bond Consider a % putable bond with 4 years remaining to maturity, putable in one year at $100. Assume the yieldvolatility is 10% and the appropriate binomial interest rate tree is same as Case . Calculate the fair price of this putable bond.Convertible BondsCase :Suppose that the straight value of a % ADC convertible bond is $ per $1,000 of par value and its market price is $1,065. The market price per share of common stock is $33 and the conversion ratio is shares per $1,000 of parvalue. Also assume that the common stock dividend is $ per share.公式：Minimum Value: the greater of its conversion price and its straight value.Conversion Price = Market price of common stock ×Conversion ratioStraight 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 ratioMarket Conversion Premium Per Share= Market conversion price – Market price of common stockMarket Conversion Premium Ratio= Market conversion premium per share ÷Market price of common stockPremium over straight value= (Market price of convertible bond/Straight value) – 1The higher this ratio, the greater downside risk and theless 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 ratioA. What is the minimum value of this convertible bondB. Calculate its market conversion price, market conversion premium per share and market conversion premium ratio.C. What is its premium payback periodD. Calculate its premium over straight value.Market price of common stock=$33,conversion ratio =Straight Value=$ ，market price of conversible bond = $1,065common stock dividend = $Coupon rate=%A、Conversion Price = Market price of common stock ×Conversion ratio=$33*=$the minimum value of this convertible bond=max{$,$}=$B、Market Conversion Price/Conversion ParityPrick= Market price of convertible security ÷Conversion ratio=$1065/=$Market Conversion Premium Per Share= Market conversion price – Market price of common stock= $ -$33= $Market Conversion Premium Ratio= Market conversion premium per share ÷Market price of common stock= $$33=%C、Premium Payback Period= Market conversion premium per share ÷Favorable income differential per share Favorable Income Differential Per Share= [Coupon interest – (Conversion ratio × Common stock dividend per share)] ÷Conversion ratioCoupon interest from bond = %×$1,000 =$Favorable income differential per share = ($ –×$ ÷= $Premium payback period = $$ = yearsD、Premium over straight value= (Market price of convertible bond/Straight value) – 1=$1,065/$ – 1 =%Ppt10No-Arbitrage Principle:no riskless profits gained from holding a combination of a forward contract position as well as positions in other assets.FP = Price that would not permit profitable riskless arbitrage in frictionless markets, that is:CaseConsider a 3-month forward contrac t on a zero-coupon bond with a face value of $1,000 that is currently quoted at $500, and assume a risk-free annual interest rate of 6%. Determine the price of the forward contract underthe no-arbitrage principle.Solutions.CaseSuppose the forward contract described in case 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 contrac t and how much the arbitrageprofit would be.CaseIf the forward contract described in case 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.Case :interest) that has just paid a coupon and will make another coupon payment in 182 days. The annual risk-free rate is 6%.Solutions. Remember that T-bonds make semiannual coupon payments, soCaseSolutions.The semiannual coupon on a single, $1,000 face-value7% bond is $35. A bondholder will receive one payment years from now years left to expiration of futures) and one payment 1 year from now yearsuntil expiration). Thus,Ppt11Payoffs and ProfitsCaseConsider 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, respectivelySolutions.A. If the spot price at expiration is $1,000, the payoff to the call option ismax{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 call option ismax{0, $920 - $900}=$20. So, the call is in the money and it will be exercised with a loss of $30. (why)C. If the spot price is $880 at expiration, the payoff to the call option is max{0, $880 - $900}=0. So, the call is out of money and it will not be exercise. The loss occurred would be $50.CaseConsider a European bond put option with an exercise price of $950. The put premium for this option is $50. At expiration, if the spot price for the underlying bond is $1,000, what is the put option’s payoff as well as itsgain/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, respectivelySolutions.A. If the spot price at expiration is $1,000, the payoff to the put option is max{0, $950 - $1,000}=0. So, the put is out of money and it will not be exercised. The loss occurred would be $50.B. If the spot price at expiration is $920, the payoff to the put option is max{0, $950 - $920}=$30. So, the put is in the money and it will be exercised with a loss of $20. (why)C. If the spot price is $880 at expiration, the payoff to the call option is max{0, $950 - $880}=$70. So, the put is in the money and it will not be exercise with a gain of $20.。