Currently a three-year zero-coupon treasury bond is traded at a price of $70.38. The Treasury plans to issue a three-year annual coupon bond, with a coupon rate of 10%. The face value of all treasury annual coupon bonds is $100.

(a) What is the yield to maturity of the three-year zero-coupon bond? (2 marks)

(b) At what price should the three-year coupon bond be selling for? (4 marks)

(c) A bond analyst comments that without calculation, he can infer whether the bond will sell above its face value or not. How can he do this? Provide a brief explanation. (3 marks)

(d) If two bonds have the same term to maturity, the same yield to maturity, and the same level of risk, the bonds should sell for the same price." Do you agree that this is correct? Provide a brief explanation. (3 marks)

(e) Lily manages a bond portfolio with the following Treasury bonds:

• 3 year zero-coupon bonds
• 3 year 10% coupon bonds
• 10 year zero-coupon bonds
• 10 year 10% coupon bonds

She believes that market interest rates are going to increase over the next several months. Accordingly, she is suggested to do the following. Comment on each suggestion and make your recommendations to Lily (e.g., whether or not to adopt the suggestion). (6 marks)

1. Sell the 3 year zero coupon bonds and buy the 10 year zero coupon bonds
2. Buy the 10 year zero coupon bonds and sell the 10 year 10% coupon bonds