The inaccuracy of duration on its own can be overcome by combining duration and convexity measures. By combining the two we can get an accurate description of the value response of the cash flow to changes in interest rates. If the required interest rate used to value a set of cash flows is increased, the convexity is decreased. The result of positive convexity is that the present value of the cash flows increases or decreases in the appropriate direction as the discount rate is raised or lowered If the discount rate is raised, the PV of the cash flow falls. The rate of fall in the PV of the cash flows is reduced as the discount rate increases and the duration is shortened.
Convexity falls as the interest rate rises.
For a given discount rate and maturity for the cash flows, the smaller the coupon or interest payments, the greater the convexity. Therefore, a zero coupon instrument with a five year maturity will have the largest convexity since it has all its cash flow payments at the end of its life. The result is that for a given modified duration, zero coupon bonds have the highest convexity. Duration on its own will be reasonably accurate for small changes in the interest rate, but becomes less useful if the interest rate changes are larger. When used with convexity there is much more accuracy in the predictions.