# solution

Using Excel to do this question

Assume you have six different bonds:

â€¢ B1 â€“ A two-year bond with a nominal rate of 2 % per annum

â€¢ B2 â€“ A four-year bond with a nominal rate of 2.5 % per annum

â€¢ B3 â€“ A five-year bond with a nominal rate of 3.5 % per annum

â€¢ B4 â€“ A seven-year bond with a nominal rate of 4 % per annum

â€¢ B5 â€“ A ten-year bond with a nominal rate of 4.5 % per annum

â€¢ B6 – A twenty-year bond with a nominal rate of 5 % per annum

All these bonds pay annual coupons and have face values of \$4,500. Calculate their Present Values, Macauley Durations and Convexities using a YTM of 4% (YTM = 0.04).

QUESTION 9: (5 + 7 = 12 marks)

Using Excel to do this question

Suppose a fund manager is committed to making annual payments of \$45,000 for the next 20 years (an annuity) and they use a discount rate of 0.04 or 4 % pa. 5

a. What is the Present Value of these payments? Calculate the Macauley Duration and Convexity.

b. To fund these payments the fund manager must invest in the six bonds described in QUESTION 8. Assume she is trying to minimize transaction costs; use the figures in QUESTIONS 8 to write the equations that would need to be satisfied to immunize the annuity described in this question. Note that the fund manager is concerned that the application of these conditions could result in only one or two different types of bonds being held. As this is considered risky she introduces a diversification condition whereby she must hold a minimum of Five of each of B1, B2, B3, B4, B5 and B6. This condition will also need to be considered in your equations.

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