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# Yield Duration

We can derive specific formulas for the various duration statistics by calculating carefully the first partial derivative of the bond pricing equation 6.1 with respect to a change in the yield per period. As much fun as it is to do the calculus and work though the ensuing algebra, the step-by-step process is relegated to the Technical Appendix. A general formula for the Macaulay duration statistic is shown in equation 6.13.

Here the coupon rate per period is denoted c, where c = PMT/FV.

Let's go back to the 4%, annual payment, 4-year corporate bond priced at 99.342 to yield 4.182% that we first saw in Chapter 3. Suppose that one ...

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