A. Yields on short-term bonds tend to be more volatile than yields on long-term bonds. Suppose that you have estimated that the yield on 20-year bonds changes by 10 basis points for every 15-basis-point move in the yield on 5-year bonds. You hold a $1 million portfolio of 5-year maturity bonds with modified duration 4 years and desire to hedge your interest rate exposure with T-bond futures (20 year maturity), which currently have modified duration 9 years and sell at F0 = $95. How many futures contracts should you sell? The par value of the T-bond futures is $100,000

B. A manager is holding a $1 million bond portfolio with a modified duration of 8 years. She would like to hedge the risk the portfolio by short-selling T-bonds futures. The modified duration of T-bonds in the futures contract is 10 years. How many dollars' worth of T-bonds should she sell to minimize the variance of her position?