QUESTION 4 |A fund manager has a portfolio of two-year bonds with a total face value of $30 million. These bonds carry a 6% p.a. coupon, paid annually. The yield to maturity on these bonds is 9% p.a. (annual compounding). Concerned that a rise in interest rates will reduce the market value of his bond portfolio, the fund manager takes a position in the three-year New Zealand Government Stock futures contract (TYS) at a price of 92.00 (or 9200). The asset underlying this contract is three-year government stock with $100,000 face value, 8% p.a. coupon, paid semi-annually. The duration of this TYS contract is 2.726 years when yields are 8% p.a. (semi-annual compounding). p.a. = per annum a. Calculate the duration of the fund manager's bond portfolio (i.e., the two-year bond portfolio with a total face value of $30 million). b. Determine the duration-based hedge ratio for neutralising or hedging the risk of an interest rate rise. Also clearly state if any position in the futures contracts should be long or short