when the yield is continuously compounded, Macaulay duration and modified duration are equal.
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Bond duration - Wikipedia, the free encyclopedia percentage derivative of price with respect to yield. Modified duration applies when a bond or other asset is considered as a function of yield. In this case one can measure the logarithmic derivative with respect to yield:
It turns out that <span>when the yield is expressed continuously compounded, Macaulay duration and modified duration are equal.
First, consider the case of continuously compounded yields. If we take the derivative of price or present value, expression (2), with respect to the continuously compounded yield we see
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