Please answer this question about hedging with bond futures!

A fund manager has a portfolio of 2-year 5% coupon bonds with a total face value of $30 million. The coupons are paid semi-annually. Concerned that a rise in interest rates will reduce the market value of the bond portfolio, the fund manager intends to hedge with bond futures contracts. Assume there are: 3-year government stock futures contract (TYS) and 10-year government tock futures contract (TEN) available along with the following contract information.

	TYS	TEN
Term	3	8
Face Value	$100,000	$100,000
Coupon (p.a.)	9% s.a.	9% s.a.

Note s.a. stands for semi-annual coupon payments

Both the TYS and TEN contracts are traded at a price of 91.00 (or 9100 implying a yield to maturity of 9% p.a.) Assume that the yield curve is flat at 9% (semi-annual compounding) at all maturities, and the durations of the TYS and TEN contracts are 2.6950 and 6.7966 years when the yields are 9% p.a. respectively.

Question part 1: Specify which bond futures contract (TYS or TEN) is better to hedge interest risk from the fund managers point of view, and explain briefly.

Question part 2: Using the appropriate bond futures contract to determine the duration-based hedge ratio. Also clearly state if any position in the futures contract should be long or short. (Fractional contracts are disallowed and should be round to nearest integer).

Question part 3: Show the impact of the hedge if all yields drop from 9% to 7% instantaneously by calculating 1) profit/loss from the futures position as outlined in part 2 and 2) the change in the market value of the bond portfolio.