Question

Mustafa's portfolio consists of an annuity with monthly payments of $1,000 each month for five years and a $20,000 8% eight-year par-value bond bearing semiannual coupons. Calculate the Macaulay duration of the portfolio at 9%.

Answer 1

To calculate the Macaulay duration of the portfolio, calculate the present value of each cash flow and weight it according to the time it is received.

Step-by-step explanation:

To calculate the Macaulay duration of the portfolio, we need to calculate the present value of each cash flow and weight it according to the time it is received. For the annuity, we have monthly payments of $1,000 for five years. Using the present value formula, we can calculate the present value of the annuity. For the bond, we have semiannual coupon payments of $20,000 (8% of the par value) for eight years. Again, using the present value formula, we can calculate the present value of the bond. Finally, we calculate the weighted average of the present values of the annuity and the bond to find the Macaulay duration of the portfolio.