Question 3 (12 Marks). A portfolio contains 50% of Bond I, 20% of Bond II, 20% of Bond III and 10% of Bond IV. Details of the four bonds are given below: I. II. 10-year zero coupon government bond, par value $1000, current price = $613.91 10-year zero coupon corporate bond, par value $1000, default premium= 2.5% 5 year 15% coupon corporate bond, par value $1000, annual coupon payments, default premium = 9% and YTM for similar government bond is 6% III. IV. 5 year 15% government coupon bond, par value $1000, annual coupon payments, YTM=6% a. Find the prices of Bond II, Bond III, and Bond IV. (2 marks) b. What are the Macaulay's durations of Bond III and Bond IV? (4 marks) c. What is the duration of the portfolio? (2 mark) d. What is the convexity of Bond I? (2 marks) e. If Bond I's yield increases by 1.5%, what is the price of Bond I based on duration- with-convexity rule? (2 marks)