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 is2.726 yearswhen 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 clearlystateif any position in the futures contracts should be "long" or "short".