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Notice, however, that the interval of time from the settlement date (now)
until each payment is included in the numerator. The denominator is a pre-
sent value factor, and the remaining term is the particular cash flow. For
this reason, duration is sometimes described as the present value weighted
time to maturity of the cash flows.
Macaulay duration is usually modified by dividing the entire expres-
sion by (1 + r). Equation (11.4) is derived by dividing equation (11.3) by
(1 + r):
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The convenient feature of this modified duration is that it equals the per-
cent change in price (in particular, the dirty price) caused by a change in
yield of 1 percent (or 100 basis points). For example, a bond with a
coupon of 5.5 percent and duration of 5 will decline from 100 to approxi-
mately 95 if rates rise from 5.5 percent to 6.5 percent.
Figure 11.2 shows the price sensitivity of a five-year bond. The Excel
function MDURATION reports that the modified duration of a bond with
a 5.5 percent semiannual coupon is 4.320 at a yield of 5.5 percent. The
Risk Management and Hedge Funds
HEDGE FUND COURSE
FIGURE 11.2
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