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This illustrates that the convexity measure is effective for larger yield changes only. The example at right provides an illustration of the greater accuracy produced by combining the modiﬁed duration and convexity measures for larger yield shifts. The convexity measure increases with the square of maturity; it decreases as both coupon and yield rise. It is a function of modiﬁed duration, so index-linked bonds, which have greater duration than conventional bonds of similar maturities, also have greater convexity.
As noted earlier, the price change estimated using modiﬁed duration can be quite inaccurate; the convexity measure is the approximation of the size of the inaccuracy. Summing the two values—the price-change estimate using modiﬁed duration plus the convexity error adjustment—gives a more accurate picture of the actual magnitude of the price change. The estimated and adjusted values differ signiﬁcantly, however, only when the change in yield is very large. 64498. 92462 percent If the yield fell by 200 basis points, the convexity effect would be the same.
This is because the cash ﬂows received in the early years of the bond’s life have the greatest present values and therefore are given the greatest weight. That shortens the average time in which cash ﬂows are received. A zero-coupon bond’s cash ﬂows are all received at redemption, so there is no present-value weighting. Therefore, a zero-coupon bond’s duration is equal to its term to maturity. Duration increases as coupon and yield decrease. The lower the coupon, the greater the relative weight of the cash ﬂows received on the maturity date, and this causes duration to rise.
Bloomberg Securities Handbook