1. The term structure is flat at 6%. A bond has 10 years to maturity and coupon rate 8%. Coupon payments are semiannual, par values are 100, and interest rates are expressed as semiannual APRs. (a) Compute the bond price. (b) Compute the bond's Macaulay and modified duration. (c) Suppose the term structure moves up by 5 basis points (1 basis point = 0.01%), still staying flat. What is the bond's new price? (d) Compute the approximate price change using duration, and compare it to the actual price change. (e) Compute the bond's convexity. (f) Suppose the term structure moves up to 7% (still staying flat). What is the bond's new price? (g) Compute the approximate price change using duration, and compare it to the actual price change. (h) Compute the approximate price change using duration and convexity. Comment on the accuracy of the approximation. 2. You just sold to a client a custom-made 31-year bond which pays a single coupon of 1M 30 years from now and 2M at maturity. You would like to hedge this liability. Assume that the term structure is currently flat at 5%. (a) Your first idea is to synthetically replicate the liability. Construct the hedging portfolio consisting of the following bonds paying annual coupons: Bond Coupon rate (%) Maturity A 0 31 years B 4 30 years C 6 30 years The par values of the three bonds are 100. 1 (b) You consider instead duration-based hedging. Assume that you have 10- and 15- year zero-coupon bonds available, with par values 100. Construct the hedging portfolio of the two bonds that has the same market value and the same interest- rate sensitivity (measured using the duration model) as your liability. (C) Suppose the interest rate fell to 4.8%. Would your hedging portfolio computed in part (b) remain the same? If not, explain why not and comment on the composition of the new hedging portfolio relative to the old one. (No computations are necessary.) (d) What are the advantages of synthetic replication (option described in part (a)) relative to approximate hedging (option described in part (b))? Why might one use approximate hedging instead