Duration and Bond Return Approximation: The Quasi-Convexity Effect

29 Pages Posted: 4 Jul 2009

See all articles by Winfried G. Hallerbach

Winfried G. Hallerbach

Fintelligence CCT; EDHEC Business School - Department of Economics & Finance

Date Written: July 29, 2001

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.

Keywords: approximation, bonds, interest rates, convexity, duration, key rate duration

JEL Classification: C13, C51, E49

Suggested Citation

Hallerbach, Winfried George, Duration and Bond Return Approximation: The Quasi-Convexity Effect (July 29, 2001). Available at SSRN: https://ssrn.com/abstract=1429763 or http://dx.doi.org/10.2139/ssrn.1429763

Winfried George Hallerbach (Contact Author)

Fintelligence CCT ( email )

Salernes, Var 83690
France

EDHEC Business School - Department of Economics & Finance ( email )

France

HOME PAGE: http://https://www.edhec.edu/

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