FINANCE 361 Question 4 (17 marks) The following is a list of (annualized) yields to maturity for risk-free zero-coupon bonds. Maturity (Years) 2 3 4 5 Zero Coupon Spot Rates 3.0% 3.5% 4.0% 5.0% 5.5% a) Calculate the single annualized forward rate that applies between the end of year 2 and the end of year 5. (3 marks) b) Calculate one-year holding period returns for buying two-year, three-year, four-year, and five-year zero-coupon bond now and selling them in one year assuming that the yield curve will be the same in one year. That is, fill in the blanks in the table below: Maturity Spot Rates Maturity in Spot Rates in One-year holding (Years) now one year one year period Return 3.0% 0 NA 3% 2 3.5% 3% 3 4.0% 2 3.5% ? 4 5.0% 3 4.0% 5 5.5% 4 5.0% now ? ? ? (4 marks) c) A friend of yours proposes a one-year pure yield swap strategy based on your answer in part b). The strategy would buy the bonds with the highest one-year holding period return and finance the purchase by shorting the bonds with the lowest one-year holding period return. The strategy will surely generate a positive return and is self-financed, so it is easy money, your friend claims. Do you agree? Why or why not? Briefly explain. (4 marks) d) (Unrelated to parts a)-c)) You are interested in buying a new fixed rate annual coupon bond issued by a BBB-rated company. The bond offers a coupon rate of 6%, has a maturity of exactly five years and a face value of $100. If the price of the bond is $95, what is its Z-spread given the yield curve above? (Hint: You will need a numerical optimizer such as Excel Solver.) (6 marks) (Total for Question: 17 marks) FINANCE 361 Question 4 (17 marks) The following is a list of (annualized) yields to maturity for risk-free zero-coupon bonds. Maturity (Years) 2 3 4 5 Zero Coupon Spot Rates 3.0% 3.5% 4.0% 5.0% 5.5% a) Calculate the single annualized forward rate that applies between the end of year 2 and the end of year 5. (3 marks) b) Calculate one-year holding period returns for buying two-year, three-year, four-year, and five-year zero-coupon bond now and selling them in one year assuming that the yield curve will be the same in one year. That is, fill in the blanks in the table below: Maturity Spot Rates Maturity in Spot Rates in One-year holding (Years) now one year one year period Return 3.0% 0 NA 3% 2 3.5% 3% 3 4.0% 2 3.5% ? 4 5.0% 3 4.0% 5 5.5% 4 5.0% now ? ? ? (4 marks) c) A friend of yours proposes a one-year pure yield swap strategy based on your answer in part b). The strategy would buy the bonds with the highest one-year holding period return and finance the purchase by shorting the bonds with the lowest one-year holding period return. The strategy will surely generate a positive return and is self-financed, so it is easy money, your friend claims. Do you agree? Why or why not? Briefly explain. (4 marks) d) (Unrelated to parts a)-c)) You are interested in buying a new fixed rate annual coupon bond issued by a BBB-rated company. The bond offers a coupon rate of 6%, has a maturity of exactly five years and a face value of $100. If the price of the bond is $95, what is its Z-spread given the yield curve above? (Hint: You will need a numerical optimizer such as Excel Solver.) (6 marks) (Total for Question: 17 marks)
