a. The duration of a bond portfolio can be calculated in one of the two ways:
i. A weighted average of time to receipt of the aggregate cash flows, and
ii. The weighted average of the individual bond duration in the portfolio.
b. It is extremely difficult to calculate the duration of the bond portfolio using the first method, as it requires the calculation of cash flow yield, and then make modifications to the same to determine the percentage changes in price.
c. The weighted average portfolio duration can be calculated by summing up the weighted average of the individual bonds within the portfolio. The formula for calculating the same is:
In the above equation, the sum of the weights of the individual bonds equals the weights of the portfolio. Such that,
and, the modified duration is:
where m is the periodicity of the coupon payments.