3. (25 marks) An investor holds 100,000 units of a bond whose features are summarized in the following table. He wishes to be hedged against a rise in interest rates. Maturity Coupon rate YTM Face value 5 Years 9% 8% $100 YTM 6 Years 7% 8% Face value $100 Characteristics of the hedging instrument, which is a bond here, are as follow: Maturity Coupon rate Coupon frequency and compounding frequency are assumed to be annual. a. Calculate the modified durations for the two bonds. b. What is the quantity of the hedging instrument that the investor has to sell? c. Suppose that the YTM increases instantaneously by 0.1%, what happens if the bond is not hedged? What happens if the bond is hedged as above?