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BOND MATH: The Theory Behind the Formulas by Donald J. Smith

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Yield Duration and Convexity Relationships

We can derive the relationship between changes in the yield to maturity and the change in the market value of a standard fixed-income bond using a bit of algebra and calculus. Equation 6.1 is a general bond pricing equation very similar to equation 3.9 in Chapter 3.

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The periodic coupon payments (PMT) and the principal (FV) to be redeemed in full at maturity are discounted at the yield per period (y). The settlement date is t days into the T-day period and there are N periods to maturity counting from the beginning of the current period. Here the present value of the future cash flows is the market value ...

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