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?

(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?