Properties and Limitations of Duration as a Measure of Time Structure of Bond and Interest Rate Risk

Headnote

ABSTRACT

The purpose of this study is to examine the main features of duration as a measure of, both, time structure of a bond and interest rate risk. The study concludes that, as a measure of the time structure of a bond, duration has four properties: (1) the duration of a bond is always equal or less than its maturity. (2) For a zero coupon bond, duration equals its maturity. (3) The duration increases as the maturity increase then decreases in nonlinear steps to reach zero at the final maturity date. (4) As maturity increases, the duration tends to be closed to the perpetuity duration. In addition, duration measures the elasticity of the market price of an asset (liability) with respect to the market discount rate. Finally, as a measure of bond's interest rate risk, duration has three features: (1) Duration of a bond decreases as the coupon rates rises. (2) Duration decreases as the yield to maturity rises. (3) Duration represents an accurate measure of interest rate elasticity of the bond price. There are, however, many limitations to duration as a measure of the risk of a bond portfolio.

JEL Classification: G12.

Key Words: Duration; Bonds; Interest Rate; Risk.

(ProQuest: ... denotes formulae omitted.)

1. INTRODUCTION

The concept of duration discovered by Frederick Macaulay (1938) while searching for a correct measure of the life of a bond. He proposed a measure of duration to represent the "essence of the time element of a loan". Hicks (1939), independently, derived the equivalent average period measuring bond price elasticity with respect to a discount rate. In recent years, duration revived and has become an increasingly common technique of fixed income securities for matching portfolios and as a mean to estimate the volatility or sensitivity of the portfolio's market value to changes in interest rates (Altman and Nammacher, 1987).

Many characteristics, usefulness, and limitations of duration as an immunization tool, for non zero price assets, have been reviewed by Bierwag, Kaufman and Khang (1978) and Ingersoll, Skelton, and Weil (1978). Nevertheless, this essay will discuss the main features of duration as a measure of, both, the time structure of a bond and the interest rate risk.

Duration measures have been widely promoted as a technique that investors...