2. Consider the following two corporate bonds with same rate of Aaa. Face value Maturity in year 1000 1.0 1000 1.0 Coupon rate 2.5% 3.5% a. Find the modified duration in years of the first bond if its yield to maturity is 2.5%. (4 marks) b. If the duration and the convexity of a bond portfolio are 0.7 and 200 respectively, find the approximate percentage change of the portfolio value if the interest rate increases by 40 basis points. (4 marks) c. Consider the following one-year transition matrix for the bonds. Rating at beginning of year Aaa A Aaa 0.970 0.040 0.005 Rating at end of year Aa 0.025 0.900 0.030 A 0.005 0.060 0.965 What is the probability of downgrade in the second bond of the portfolio? (2 marks)