Fixed Income Markets: Management, Trading and Hedging, 2nd Edition

CHAPTER 2 Bond Instruments and Interest-Rate Risk

In the introductory chapter, we described traditional concepts in bond pricing. This chapter is a continuation of the first, and we discuss here the sensitivity of bond prices to changes in market interest rates, the key concepts of duration and convexity. The analysis is again the traditional approach; for present-day purposes when one speaks of “duration” or modified duration the interest risk exposure measure used is generally a per basis point measure.

DURATION, MODIFIED DURATION, AND CONVEXITY

Bonds pay a part of their total return during their lifetime, in the form of coupon interest, so that the term to maturity does not reflect the true period over which the bond’s return is earned. Additionally, if we wish to gain an idea of the trading characteristics of a bond and compare this to other bonds of, say, similar maturity, term to maturity is insufficient, and so we need a more accurate measure. A plain-vanilla coupon bond pays out a proportion of its return during the course of its life, in the form of coupon interest. If we were to analyse the properties of a bond, we should conclude quite quickly that its maturity gives us little indication of how much of its return is paid out during its life, nor any idea of the timing or size of its cash flows, and hence its sensitivity to moves in market interest rates. For example, if comparing two bonds with the same maturity date but different coupons, the higher-coupon bond ...