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QUESTION 6. [{CALC'NS a + b + c + d. = (1 + 1 + 1) + (3 + 3) + (2 + 2 + 2) + 1 = 16 Marks} + { REC'NS e. = 2 Marks)] A Briefly explain the following concepts relating to bond portfolio management. i. Duration. Convexity. Immunisation. B. Illustrate your answer to A. above with the calculation of the duration and convexity of a bond with a face value of $1,000, term to maturity of 3 years, a coupon rate of 6% per annum, payable yearly, and a yield to maturity of 4% per annum. [NOTE: As a by-product of these calculations, you should calculate the current market price of the bond, which price should be used as a base or starting point to your answers required in C. 1. and C. ii. below.] C. Calculate the expected price of the bond described in B. above, if the yield to maturity fell immediately to 3% per annum, by each of the following 3 methods. 1. The duration adjustment method. 11. The duration-with-convexity adjustment method. The present value of future cash flows method. D. Which of the methods listed in C. above is most accurate? Why? E. Explain how a pension fund can use zero-coupon bonds to immunize its obligation to pay out $10 million a year in pensions in perpetuity, if the forecast long-term interest/ discount rate is 5% a year forever