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

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Liability-Driven Investing

F. M. Redington, a British actuary, coined the term “immunization” in 1952. In an influential address to the Society of Actuaries, he proposed that life insurance companies manage interest rate risk by matching what he called the “mean term” of assets to liabilities. He described immunization to occur when the first derivative of the value of assets given a change in the interest rate equals the first derivative of the value of liabilities and the second derivative of the value of assets exceeds the second derivative of the value of liabilities. To me, Redington and Macaulay (along with Irving Fisher, who first decomposed nominal rates into the real rate and inflation) are the fathers of bond math.

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