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An Introduction to Bond Markets, Fourth Edition by Moorad Choudhry

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Chapter 3
BOND INSTRUMENTS AND INTEREST-RATE RISK
Chapter 1 described the basic concepts of bond pricing. This chapter discusses the sensitivity of bond prices to changes in market interest rates and the key related concepts of duration and convexity.

DURATION, MODIFIED DURATION AND CONVEXITY

Most bonds pay a part of their total return during their lifetimes in the form of coupon interest. Because of this, a bond’s term to maturity does not reflect the true period over which its return is earned. Term to maturity also fails to give an accurate picture of the trading characteristics of a bond or to provide a basis for comparing it with other bonds having similar maturities. Clearly, a more accurate measure is needed.
 
A bond’s maturity gives little indication of how much of its return is paid out during its life or of the timing and size of its cash flows. Maturity is thus inadequate as an indicator of the bond’s sensitivity to moves in market interest rates. To see why this is so, consider two bonds with the same maturity date but different coupons: the higher-coupon bond generates a larger proportion of its return in the form of coupon payments than does the lower-coupon bond and so pays out its return at a faster rate. Because of this, the higher-coupon bond’s price is theoretically less sensitive to fluctuations in interest rates that occur during its lifetime. A better indication of a bond’s payment characteristics and interest-rate sensitivity might be the average time ...

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