A measurement of a bond’s price sensitivity to changes in interest rates. A high-duration bond, or one whose maturity date is a long way out in the future, is more sensitive to interest rate changes than a bond with a shorter maturity date. The duration is defined as the weighted average of the maturities of the bond’s cash flows, which include periodic interest rate payments and principal repayment cash flows. The weights are the proportionate share of the bond’s price that the cash flows in each time period represent.
Modified duration is a measure of Macaulay duration, which was named for Frederick Macaulay. It is calculated by dividing the yield maturity by the number of interest payments per year that have been adjusted to help estimate a bond’s price volatility. Modified duration allows an estimate of bond price changes for a small change in interest rates. For larger changes in interest rates, convexity is used. Convexity measures the way duration and price change when interest rates change. It does this through a mathematical formula that measures the curvature of the price-yield relationship.