Problem 3 (20%) Suppose that you observe bond prices in the market as follows Bond Principal 100 100 100 100 100 Time to maturity (yrs) Coupon per year Bond price 0.25 0.50 1.00 1.50 2.00 Note: the coupon is paid every 6 months 0 0 0 8 12 1 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)