A fund manager manages a portfolio of two-year bonds with a total market value of $2 million. These bonds carry a 4% p.a. coupon paid semi-annually. Concerned that the volatile fluctuation in the interest rates will affect the market value of her bond portfolio, the fund manager would like to take a position in the three-year New Zealand Government Stock futures contract (TYS) at a price of 92.00 (or 9200 implying an 8% p.a. yield-to-maturity) to hedge the interest rate risk. The asset underlying this TYS contract is three-year government stock with $100,000 face value, 8% p.a. coupon, paid semi-annually. Assume that the yield curve is flat at 8% (semi-annual compounding), that is, yields for all maturities are 8% and that the duration of TYS contract is 2.726 years when yields are 8% p.a.. (a) The duration of the two-year bonds is years and the bond manager needs to the TYS contract for hedging the risk of interest rate (b) The duration-based optimal number of TYS contracts for hedging the interest rate risk for the bond portfolio is Note: Please provide your answer as a positive number with two decimal points in the format of xx.xx (for example, if the answer is 12.345, type in 12.35)