1. Duration and Convexity Your research department reports continuously compounded interest rates as Maturity (Years) Interest Rate (%) 0.5 1.0 1.5 2.0 1.00 1.50 2.00 2.00 (a) Use these rates to compute the prices P(0,1) and P:(0,2) of one- and two-year zero coupon bonds, and the price Pc(0,2) of a two-year, 3% coupon bond. Coupons are paid semi- annually, and the face value of all bonds is 100. (b) Obtain the coupon bond's duration and convexity. (c) Suppose that the monthly changes in the interest rates have a mean of zero and a standard deviation of 0.5%. Obtain the monthly 95% Value at Risk and Expected Shortfall on the coupon bond. (d) Construct a hedge portfolio of 1 coupon bond and k one-year zero coupon bonds that has zero duration. What is the value of k? What is the convexity of the hedge portfolio? (e) Construct a hedge portfolio of 1 coupon bond, and ki one-year zero coupon bonds and k two-year zero coupon bonds, that has zero duration and convexity. What are the values of ki and k2? (f) Suppose that the yield curve shifts upward parallelly with dr-196. Recalculate PdO,2), P.(0,1) and P.(0,2) and use this to calculate the change in the values of the hedge portfolios constructed in (d) and (e). Comment on the result