May 27

Duration metrics summarized in easy worksheet

by David Harper, CFA, FRM, CIPM

In the EditGrid spreadsheet below (which is a workable calculator), I illustrate the three durations we care about for the FRM (Macaulay, modified/effective, and DV01)...

The bond is a 30-year zero coupon and the key input is the yield (yellow background). Note the chart: the blue line is the price-yield curve (displaying typical convexity) and the green line is the duration-based tangent line. Here are the key points:

For a zero coupon bond, Macaulay duration (as the weighted average time to receipt of cash flows) equals time to maturity.
The modified duration = Macaulay / (1+yield/k) where k = periods per year. In this case, k = 2, so given a yield of 4%, modified duration = -30/(1+4%/2) = -29.41
The dollar value of the '01 (DV01) = (Price)(Duration)/10,000. See how DVO1 and duration differ really by units. But also, DV01 is a function of price. That's why DV01 is not simply, necessarily an increasing function of maturity (but duration is).
The slope of the line is not really duration. It is actually duration * Price. Or, put another way, the slope of the line is -DV01*10,000

Here is the spreadsheet: