Question

Consider a 3-ycar bond with a coupon rate of 10%, yield to maturity of 5% and a par value of £1,000. a. Calculate the bond duration, D, and the modified duration, MD. b. Let r denote the yield to maturity, Cz denote the payment in period t and P denote the bond price. Construct a formula for calculating the percentage change in P per unit change of r, that is Use your answer to Question 2b. to calculate the ar for the above discussed 3. year bond. In addition, explain your anticipated effect on the bond price if there is a one-unit increase of the yield to maturity. 2. [6 marks] dP/dr [2.5 marks] c. [4 marks]

Answer 1

Solution: (a) Calculation of Duration of Bond: Year Cash Flows 100 21 100 3 1100 PVF @ 5% 0.952 0.907 0.864 Present Value 95.24 90.7 950.4 1136.34 Proportion of the Bond Value 0.084 0.080 0.836 Proportion of the Bond Value * Time 0.084 0.160 2.509 2.753 Bond Duration = 2.75 years and Bond Price = 1136.34 Calculation of Modified Duration: Modified Duration - Duration/(1+ly/m)) = 2.75/(1+(5%/1) = 2.62 years Where, y = yield to maturity m = no. of compounding periods per year (b) The percentage change in Bond Price with unit change in yield is Convexity of the Bond. Hence, Convexity=px(+y+ Ela 41 (2+0)] Convexity (c) Convexity of the Bond = 9.69 If the yield increase by 1%, there will decrease in bond price by 2.62%. Therefore, Bond price will be f 1106.57 (1136.34-2.62% of 1136.34).