4. A bond speculator currently has positions in two separate corporate bond portfolios: a long holding in Portfolio1 and a short holding in Portfolio 2. All the bonds have the same credit quality. Other relevant information on these positions includes Portfolio Bond Market Value ($ millions) Coupon Rate (%) Compounding Frequency Maturity (yrs) Yield to Maturity (%)1A $6.0 0.0% Annual 37.31% B 4.0 0.0 Annual 147.312 C 11.5 4.6 Annual 97.31 Treasury bond futures (based on $100,000 face value of 20-year T-bonds having an6 percent semi-annual coupon) with a maturity exactly six months from now are currently priced at 104-24 with a corresponding yield to maturity of 5.602 percent. The yield betas between the futures contract and Bonds A, B, and C are 1.13, 1.03, and 1.01, respectively. Finally, the modified duration for the T-bond underlying the futures contract is 11.769 years.

a. Calculate the modified duration (expressed in years) for each of the two bond portfolios. What will be the approximate percentage change in the value of each if all yields increase by 60 basis points on an annual basis?

-

b. Assuming that the bond speculator wants to hedge her net bond position, what is the optimal number of futures contracts that must be bought or sold? Start by calculating the optimal hedge ratio between the futures contract and the two bond portfolios separately and then combine them.

-