# Exercise Solution 1.6

For portfolios with fixed cash flows, Macaulay’s (1938) weighted-average maturity formula may be used. With this formula, the present value of each cash flow is multiplied by its time to maturity. The results are summed and divided by the portfolio’s present value.

Alternatively, and more generally, a portfolio’s duration may be measured by calculating its present value twice: once assuming a positive 5 basis point parallel shift in the (continuously compounded) yield curve and again assuming a negative 5 basis point parallel shift. Duration is calculated by subtracting the first result from the second, multiplying by 1,000, and dividing by the portfolio’s present value (which may be calculated based upon the current yield curve or approximated by averaging the two previously calculated present values).

The purpose of this exercise is to illustrate the distinction between risk measures and risk metrics. Here, we have described two different risk measures, both of which support the same risk metric.