Assignment 2

Please show all your calculations. Providing the final answers only will not receive credits.

(1) A bond will mature in 15 years. It has a 4% coupon rate and will pay annual coupons. If the bond has a face value of $1,000 and a 4.5% yield to maturity, what should be the price of the bond today? What if YTM goes up to 5%? What if YTM goes up to 5.5%?

(2) What would be the price of the bond above in (1) if the coupons were paid semiannually?

(3) What is the relationship between the coupon rate of a bond and the yield to maturity in terms of the bonds price. In particular, when do we have a discount bond, a par bond, and a premium bond? Do not just state the relationship, but please explain the rational behind the relationship as if you are explaining this relationship to a novice of Finance.

(4) Both Bond X and Bond Y have 5% coupons, make semiannual payments, and have YTM of 4%. Bond X has five years to maturity, whereas Bond Y has 20 years to maturity. If the interest rates (YTM) suddenly rise by 2 percent point to 6%, what is the percentage change in the price of Bond X and Bond Y? Based on your answer, what can you say about the relationship between the interest rate risk and the time to maturity?