For this question, assume bonds make semi-annual coupon payments and interest compounds semi-annually. Consider the following term structure of U.S. interest rates: Annual Yield Maturity 0.5-year spot rate 1-year spot rate 1.5-year spot rate 2-year spot rate 2.5-year spot rate 3-year spot rate 5.00% 5.00% 5.00% 3.00% 3.00% 2.00% a) (4 points) What is the price and yield-to-maturity of a zero-coupon Treasury bond with face value of $5000 and 1.5 years to maturity? b) (6 points) What is the price and yield-to-maturity of a 1.5-year Treasury bond with an annual coupon rate of 6%, face value of $5000, and 1.5 years to maturity? c) (5 points) Assume that the bonds listed below from A-E are the only securities that you could invest in today (i.e. you do not have any other investment opportunities). Assume that the same term structure of interest rates from parts a) and b) applies to all of these bonds and they have the following additional characteristics: A. A bond with 1 year to maturity and an 6% coupon rate. B. A bond with 1 year to maturity and a 8% coupon rate. C. A zero-coupon bond with 1.5 years to maturity (Bond from part a) D. A bond with 1.5 years to maturity and 4% coupon rate. E. A bond with 1.5 years to maturity and 6% coupon rate (Bond from part b) If you are worried that market interest rates might increase unexpectedly, which bond should you purchase and why? d) (6 points) Select the bond from part c) that you would choose if you found out in the morning that the term structure of interest rates will shift down by 1% (each spot-rate will decrease by 1%) later today? Assume that you know you know this with 100% probability but others have yet to find out). What will be your % gain (or loss) if you buy this bond before the interest rate change and sell the bond at the end of the day (after the interest rate declines)? e) (6 points) What is the price and yield-to-maturity of a Detroit Municipal Bond with 1.5 years left on its maturity, face value of $5000, and an annual coupon rate of 6%, if the credit spread on this bond is 2.5%? For this question, assume bonds make semi-annual coupon payments and interest compounds semi-annually. Consider the following term structure of U.S. interest rates: Annual Yield Maturity 0.5-year spot rate 1-year spot rate 1.5-year spot rate 2-year spot rate 2.5-year spot rate 3-year spot rate 5.00% 5.00% 5.00% 3.00% 3.00% 2.00% a) (4 points) What is the price and yield-to-maturity of a zero-coupon Treasury bond with face value of $5000 and 1.5 years to maturity? b) (6 points) What is the price and yield-to-maturity of a 1.5-year Treasury bond with an annual coupon rate of 6%, face value of $5000, and 1.5 years to maturity? c) (5 points) Assume that the bonds listed below from A-E are the only securities that you could invest in today (i.e. you do not have any other investment opportunities). Assume that the same term structure of interest rates from parts a) and b) applies to all of these bonds and they have the following additional characteristics: A. A bond with 1 year to maturity and an 6% coupon rate. B. A bond with 1 year to maturity and a 8% coupon rate. C. A zero-coupon bond with 1.5 years to maturity (Bond from part a) D. A bond with 1.5 years to maturity and 4% coupon rate. E. A bond with 1.5 years to maturity and 6% coupon rate (Bond from part b) If you are worried that market interest rates might increase unexpectedly, which bond should you purchase and why? d) (6 points) Select the bond from part c) that you would choose if you found out in the morning that the term structure of interest rates will shift down by 1% (each spot-rate will decrease by 1%) later today? Assume that you know you know this with 100% probability but others have yet to find out). What will be your % gain (or loss) if you buy this bond before the interest rate change and sell the bond at the end of the day (after the interest rate declines)? e) (6 points) What is the price and yield-to-maturity of a Detroit Municipal Bond with 1.5 years left on its maturity, face value of $5000, and an annual coupon rate of 6%, if the credit spread on this bond is 2.5%
