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I 'or the measure of duration under discussion, duration is additive only if there is a flat yield curve, which is hat we have assumed.

Notice that the duration for coupon paying bonds is less than the maturity. Up to now we have assumed that the yield curve is flat and that a shift takes place in the flat yield curve. There are many other assumptions that could be made. Different assumptions change the definition of duration. We have set out several of these in Appendix A at the end of the chapter. Researchers have compared these measures to see which seems to be the most accurate representation of a bond's sensitivity to a change in interest rates. The surprising result is that the one we have presented in this chapter, which was the first one ever derived and is certainly the simplest, seems to do well in explaining unanticipated returns: Its performance and simplicity helps explain why this measure is the one most widely used in practice.

Table 21.2 shows the duration on a number of bonds with different maturities and different coupons. Notice how the duration of a bond is much shorter than its maturity, especially for bonds with long maturities.

Equation (21.3) shows that the duration of a bond is affected by the maturity of the bond, its coupon, and the interest rate. Holding changes in other variables constant:

.1. An increase in the coupon lowers duration. This is illustrated in Table 21.2, and the logic behind it is easy to understand. As the coupon is increased, the value of the earlier cash flows increases relative to the present value of the terminal cash flow. This increases the weight of the early cash flows and lowers duration.

2. An increase in the interest rate lowers duration. The greater the interest rate, the less important are cash flows far in the future relative to near term flows. The greater the weight on near term flows, the lower the duration.

3. In general, the longer the maturity, the greater the duration. This is illustrated in Table 21.2.4

While this ends our presentation of the concept of duration, we return to duration and use it as a tool in bond portfolio management in the later section of the chapter.

Table 21.2 Duration of Bonds with Different Maturities and Coupons"

Years to Maturity

Table 21.2 Duration of Bonds with Different Maturities and Coupons"

Years to Maturity

Coupon

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