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1、Fixed-income treasuryPpt31、公式：Practice Question 3.1Suppose 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 todays 2-year spot rate and 3-year spot rate.(已做答案）2、Current YieldCompute the current yield f
2、or a 7% 8-year bond whose price is$94.17. How about the current yield if price is $100, $106,respectively?3、uCase 3.1Consider 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 tot
3、al 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?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）Ppt41、FixedCoupon Bondsu Practice Questi
4、on 4.2A. 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 discounte
5、d 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 maturityPv=($100*10%/2)/(8%/2)(半年付息）Present Value PropertiesuPractice Question 4.4
6、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%. Redo your calculation in part A and decompose the price change att
7、ributable 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 PaymentsuPractice Question 4.6Suppose that there are five semiannual coupon payments remaining for a 10% coupon bond. Also assume the following: Annual discount rate is 8% 78 days betwe
8、en the settlement date and the next coupon payment date 182 days in the coupon periodCompute the full price of this coupon bond. What is the clean price of this bond? 4、Valuation ApproachuCase 4.1A. Consider a 8% 10-year Treasury coupon bond. What is its fair value if traditional approach isused, gi
9、ven 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）?C、Arbitrage-Free Approach is more accuratePpt52、ConvexityConsider a 9% 20-
10、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
11、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?Ppt61、Measuring Yield Curve RiskuCase 6.1: Panel AConsider the following two $100 portfolios composed of 2-year, 16-year, and 30-year issues, all of which ar
12、e zero-coupon bonds:For simplicity, assume there are only three key rates2years, 16 years and 30 years. Calculate the portfolios key rate durations at these three points and its effective duration.Case 6.1: Panel BConsider the following three scenarios:Scenario 1: All spot rates shift down 10 basis
13、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 scenario?Ppt7Consider a 6.5% option-f
14、ree 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 BondsuCase 8.1: Valuing a callable bond with singlecall priceConsider a 6.5% callable bond with 4 years remaining to
15、 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.2、Case 8.2: Valuing a callable bond with call scheduleConsider a 6.5% 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 6.4. Calculat
