Problem 3 (20%) Suppose that you observe bond prices in the market as follows Bond Principal Time to maturity (yrs) Coupon per year 100 0.25 0 100 0.50 0 100 1.00 0 100 1.50 8 100 2.00 12 Note: the coupon is paid every 6 months Bond price 97.0 95.0 90.0 96.0 102.0 (1) Calculate the zero rate for 1 and 1.5 years. (2) Calculate the half-year forward rate in one year, f(0,1,1.5). (3) Suppose a financial institution holds a bond liability with duration of 1.5 years. The institution worries about interest rate changes and wants to use the 1.5-year and 2-year bonds in the table to hedge the risk. Explain briefly how to use these two bonds to construct a hedging portfolio (calculation is not required)