A note on Macaulay’s formula for duration

Macaulay duration approximates the yield elasticity of bond price. Since its introduction in 1938 researchers have sought a more accurate formula. This article demonstrates Macaulay’s formula gives accurate results if applied appropriately. A bond with maturity n has n solutions for yield, one orthodox and (n-1) unorthodox. Conventional analysis ignores the distinction, which means a shift in yield shifts all yields at once. In contrast, an other-things-being-equal shift in the orthodox yield, holding the unorthodox yields constant, permits the successful application of Macaulay’s formula. This finding questions the conventional focus on the orthodox yield alone.