Duration and Bond Return Approximation: The Quasi-Convexity Effect

Abstract

Duration is often applied to relate bond price changes to changes in the yield to maturity (or key interest rates). As the relationship between bond price and yield is non-linear, convexity characteristics can be used to improve the linear first order approximation. In this paper, we show that knowledge of a bond’s duration (or key rate durations) allows a better price return approximation than is suggested in the literature. The proposed approximations may be helpful in Value-at-Risk analyses where duration (and convexity) approximations are used as fast alternatives for full revaluation. Our main approximation formula is based on only duration but incorporates quasi-convexity characteristics. This signifies a substantial improvement in approximation accuracy, even for substantial yield changes. The approximants based on duration and convexity are virtually exact, even for extreme yield changes.