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

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Chapter 9: Bond Portfolios

I first saw the relationship linking Macaulay duration, convexity, cash flow dispersion, and the yield to maturity (i.e., equation 9.7) in Olivier de la Grandville, Bond Pricing and Portfolio Analysis: Protecting Investors in the Long Run (MIT Press, 2001).

The idea of using the basis-point-value-weighted average of the yields to maturity as a good approximation for the portfolio cash flow yield is from Kenneth D. Garbade, Fixed Income Analytics (MIT Press, 1996). The same point is made in a thorough collection of articles on fixed-income management, Quantitative Management of Bond Portfolios (Princeton University Press, 2007), by Lev Dynkin, Anthony Gould, Jay Hyman, Vadim Konstantinovsky, and Bruce Phelps.

I do not ...

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