QUESTION 6 (use Excel question) Assume you have six different bonds:

B1 - A two-year bond with a nominal rate of 2 % per annum

B2 - A three-year bond with a nominal rate of 2.5 % per annum

B3 - A five-year bond with a nominal rate of 3 % per annum

B4 - An eight-year bond with a nominal rate of 4 % per annum

B5 - A ten-year bond with a nominal rate of 4 % per annum

B6 - A twenty-year bond with a nominal rate of 5 % per annum All these bonds pay annual coupons and have face values of $2,500. Calculate their Present Values, Macauley Durations and Convexities using a YTM of 3% (YTM = 0.03).

QUESTION 7 (use Excel question) Suppose a fund manager is committed to making annual payments of $25,000 for the next 20 years (an annuity) and they use a discount rate of 0.03 or 3 % pa.

(a) What is the Present Value of these payments?

(b) To fund these payments the fund manager must invest in the six bonds described in QUESTION 6. Assume she is trying to minimize transaction costs; use the figures in QUESTIONS 6 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.

QUESTION 8 (use Excel) For the portfolio described in QUESTIONS 6 and 7 and the methods outlined in the course notes on Mathematical Programming; that is, using the solver in excel, find the portfolio of bonds that the fund manager must invest in to immunize the portfolio. That is, the two streams of payments and receipts need to have the same Present Value, their Macaulay Durations must be equal, the diversification conditions should be satisfied and the Convexityreceipts (Assets) needs to be greater than the Convexitypayments (Liabilities). However, finding the immunized portfolio should be done in stages - reporting the different number bonds held at each step: (i) The stream of payments and receipts need to have the same Present Value. (ii) Add the constraint that the Macaulay Durations must be equal. (iii) Now include the diversification condition of holding a minimum of five of each bond. (iv) Lastly, include the second order condition of Convexityreceipts > Convexitypayments, so that all four constraints are now being applied.