A measurement of the change in the value of an instrument in response to a change in interest rates. The primary basis for comparing the effect of interest rate changes on prices of fixed income instruments. The formula shows the small difference between modified and Macaulay duration. Many applications are not sensitive to the difference, and modified and Macaulay duration numbers are often used interchangeably. Also called Adjusted Duration. See also Macaulay Duration, Duration, Effective Duration, Partial Duration, Option-Adjusted Duration.
Dmod = [ 1 / (1 + (y/f)) ] Dmac Where
Dmod = Modified Duration Dmac = Macaulay Duration y = yield to maturity f = frequency of coupon payment
If Macaulay Duration is 6, yield is 7% (.07), and the bond pays interest twice a year
Dmod = [ 1 / (1 + (.07/2)) ] 6 = 5.8 years
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