4. Hedging of Interest Rate Risk (30 points). Capital Management owns Treasury bonds with a face value of $100 million, an annual coupon of 5%, a maturity of 3 years, and a yield-to-maturity of 5%. The fund also has liabilities with a face value of $95 million, an annual coupon of 4%, a maturity of 2 years, and a yield-to-maturity of 2.9%. a) (5 points) Calculate the market values of Capital Management's assets and liabilities. b) (10 points) Capital Management is concerned that interest rates in the economy will increase in the future, leading to a long-term loss to the fund's equity value. The fund considers duration hedging of assets and liabilities. Specifically, Capital Management wants to: sell a fraction of its assets at a current high market price; use the proceeds to buy zero-coupon Treasury bonds with a maturity of 1 year. The 1- year spot rate is 1%. What fraction of its assets should Capital Management sell? Capital Management considers convexity hedging of assets c) (8 points, difficult) Still concerned, and liabilities. It wants to: sell a fraction of its assets; MSINO103 3 use the proceeds to buy zero-coupon Treasury bonds with maturities of 1 and 2 years. The 1-year spot rate is still 1%, while the 2-year spot rate is 2.94%. What fraction of its assets should Capital Management sell now? 4. Hedging of Interest Rate Risk (30 points). Capital Management owns Treasury bonds with a face value of $100 million, an annual coupon of 5%, a maturity of 3 years, and a yield-to-maturity of 5%. The fund also has liabilities with a face value of $95 million, an annual coupon of 4%, a maturity of 2 years, and a yield-to-maturity of 2.9%. a) (5 points) Calculate the market values of Capital Management's assets and liabilities. b) (10 points) Capital Management is concerned that interest rates in the economy will increase in the future, leading to a long-term loss to the fund's equity value. The fund considers duration hedging of assets and liabilities. Specifically, Capital Management wants to: sell a fraction of its assets at a current high market price; use the proceeds to buy zero-coupon Treasury bonds with a maturity of 1 year. The 1- year spot rate is 1%. What fraction of its assets should Capital Management sell? Capital Management considers convexity hedging of assets c) (8 points, difficult) Still concerned, and liabilities. It wants to: sell a fraction of its assets; MSINO103 3 use the proceeds to buy zero-coupon Treasury bonds with maturities of 1 and 2 years. The 1-year spot rate is still 1%, while the 2-year spot rate is 2.94%. What fraction of its assets should Capital Management sell now