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1. (25 points) Term Structure (Assume annual compounding.) You are given the following prices for US treasury STRIPS:
Bond Maturity in Years Price Spot Forward A 1 97.32 B 2 94.77 C 3 92.09 D 4 89.29
a. Use these prices to compute spot, forward and annuity rates for each maturity. Show me example calculations for spot, forward and annuity rates. b. Calculate the price of a four-year, 2% coupon bond (with annual coupons and identical payment dates as the zeros above) that would not allow arbitrage. c. What is the yield to maturity on the 4 year 2% coupon bond? d. If the bond is part b has a market price of 100, show how to earn arbitrage.
2. (25 points) You have a friend who is planning for their retirement and they are incredibly risk averse. They expect to live for 40 years and want to spend $100,000 (in today’s dol-lars) per year during their retirement years. They have asked you to help them construct a bond portfolio that meets their retirement objectives. Assume that inflation will average 3% annually over the next 40 years. a. In principle, what characteristics would you recommend for your friend to build into the design of their portfolio? Assume that you have all bonds of all maturi-ties available to you? This is an answer in words. b. Suppose that your client has saved $3,000,000 for their retirement and that the fol-lowing spot rates are found in the market today:
Maturity in Years Spot Rate 1-10 4.00% 11-20 5.00% 21-30 5.50% 31-40 5.75%
If your friend can only purchase 1 zero coupon bond today to fund his retirement which one and how much of it will you buy? Will this portfolio be a Ronco de-vice (`set it and forget it-)? c. If your friend can purchase two bonds for their investment portfolio what would you recommend to get the most out their retirement portfolio given the constraints they have on their behavior? d. Demonstrate how well your portfolio would perform if all rates permanently in-creased by 1.00% across the term structure. e. Demonstrate how a “twist” or change in slope of the term structure would impact your portfolio.