a. Question 1 A Treasury bond has exactly 3 years to maturity. The coupon rate on this bond is 4% per year and coupons are paid annually. The face value of the Treasury Bond is 100 and the current market price is 95. Below are the prices of zero-coupon bonds with identical face value to the Treasury bond: Maturity (years) Price 1 90 2 86 3 80 Is the current market price for the Treasury bond fair? If the answer to the above is 'no', devise a trading strategy that can be used to generate profits, explaining your steps. Given the bond's fair value and its face value, what can one say about the yield to maturity on the bond? [10 marks] b. Smudge Ltd. has just issued a 2-year bond with face value 100 and a coupon rate of 4% per year. Coupons are paid semi-annually. The term structure of interest rates is flat at 3% per year. Derive the payoff structure of the bond and calculate its price. Calculate the bond's Macaulay duration. What does this figure imply for the interest rate sensitivity of the bond? What is the bond's modified duration? Estimate the new price of the Smudge Ltd. bond for an 150 basis points upward shift in the term structure. [10 marks] C. Briefly discuss the concept of convexity that is used in the estimation of bond price changes due to movements in yields. Give a derivation which justifies the use of convexity for this task. [5 marks]