Problem 2 (Required, 25 marks) There are 3 bonds available in the market. The information of these 3 bonds is summarized in the following table: Time to Annual coupon Face value maturity rate (Frequency) Bond A 2 years Zero coupon 100 Bond B 4 years 6% (annual) 100 Bond C 8 years 3% (annual) 100 We assume that the term structure is flat and the annual effective interest rate is currently 5%. An investor has $10000 currently and wishes to invest his wealth for 5 years. The investor decides to invest the capital into 2 of these 3 bonds. To minimize the potential interest rate risk, the investor constructs the portfolio such that the internal rate of return of the investment can be maintained at 5% (or at least 5%). (a) Determine all portfolios which can achieve the investment goal of the investor. (b) Among the portfolio obtained in (a), which portfolio should the investor choose? Explain your answer. (c) An investor selected the portfolio derived in (b). Suppose that the interest rate drops to 4% after 1 year and the investor rebalances the portfolio using bond A and bond C (so that the portfolio remains immunized), describe the portfolio. (Hint for (c): To do so, you need to recalculate the Macaulay duration of bond A and bond Cat time 1 using the new interest rate (also the yield rate in this case) is 4%.) Problem 2 (Required, 25 marks) There are 3 bonds available in the market. The information of these 3 bonds is summarized in the following table: Time to Annual coupon Face value maturity rate (Frequency) Bond A 2 years Zero coupon 100 Bond B 4 years 6% (annual) 100 Bond C 8 years 3% (annual) 100 We assume that the term structure is flat and the annual effective interest rate is currently 5%. An investor has $10000 currently and wishes to invest his wealth for 5 years. The investor decides to invest the capital into 2 of these 3 bonds. To minimize the potential interest rate risk, the investor constructs the portfolio such that the internal rate of return of the investment can be maintained at 5% (or at least 5%). (a) Determine all portfolios which can achieve the investment goal of the investor. (b) Among the portfolio obtained in (a), which portfolio should the investor choose? Explain your answer. (c) An investor selected the portfolio derived in (b). Suppose that the interest rate drops to 4% after 1 year and the investor rebalances the portfolio using bond A and bond C (so that the portfolio remains immunized), describe the portfolio. (Hint for (c): To do so, you need to recalculate the Macaulay duration of bond A and bond Cat time 1 using the new interest rate (also the yield rate in this case) is 4%.)
