2. Bond Arbitrage Suppose three bonds are currently traded in the market. Bond 1 is a pure discount (zero-coupon) bond that matures in one year, has a face value of $10,000, and a yieldto-maturity of 1.75%. Bond 2, maturing in two years with a face value of $10,000, is a coupon bond with annual coupons and a 4% coupon rate. Bond 2 trades at par. Bond 3 is a pure discount (zero-coupon) bond that matures in three years, has a face value of $10,000, and has a price of $9,000. (a) What is the term structure of spot rates (i.e. r1,r2 and r3 )? (b) What are the yield to maturities of Bonds 2 and 3 ? (c) Suppose that the government is issuing a new level coupon bond, bond 4, which matures in three years, and has a face value of $10,000, annual coupons at 10% coupon rate. Suppose its price is $11,500. Can you make an arbitrage profit in this situation? If so, how? Describe your strategy carefully. What is the arbitrage profit? 5 (d) Now suppose that there are transaction fees for buying/selling. In particular, you pay a 1% fee when going long (e.g., you pay $1 for each $100 of bonds that you buy), and pay a fee of 2% when going short (e.g., you pay a $2 fee for each $100 you short). What is your arbitrage profit, if any? 2. Bond Arbitrage Suppose three bonds are currently traded in the market. Bond 1 is a pure discount (zero-coupon) bond that matures in one year, has a face value of $10,000, and a yieldto-maturity of 1.75%. Bond 2, maturing in two years with a face value of $10,000, is a coupon bond with annual coupons and a 4% coupon rate. Bond 2 trades at par. Bond 3 is a pure discount (zero-coupon) bond that matures in three years, has a face value of $10,000, and has a price of $9,000. (a) What is the term structure of spot rates (i.e. r1,r2 and r3 )? (b) What are the yield to maturities of Bonds 2 and 3 ? (c) Suppose that the government is issuing a new level coupon bond, bond 4, which matures in three years, and has a face value of $10,000, annual coupons at 10% coupon rate. Suppose its price is $11,500. Can you make an arbitrage profit in this situation? If so, how? Describe your strategy carefully. What is the arbitrage profit? 5 (d) Now suppose that there are transaction fees for buying/selling. In particular, you pay a 1% fee when going long (e.g., you pay $1 for each $100 of bonds that you buy), and pay a fee of 2% when going short (e.g., you pay a $2 fee for each $100 you short). What is your arbitrage profit, if any