what is modified duration 
modified duration is a formula that expresses the measurable change in the value of a security in response to a change in interest rates modified duration follows the concept that interest rates and bond prices move in opposite directions this formula is used to determine the effect that a 100 basis point 1 change in interest rates will have on the price of a bond formula and calculation of modified durationmodified duration macaulay duration 1 n ytm where macaulay duration weighted average term to maturity of the cash flows from a bond ytm yield to maturity n number of coupon periods per year begin aligned text modified duration frac text macaulay duration 1 overset text ytm n textbf where text macaulay duration text weighted average term to qquad text maturity of the cash flows from a bond text ytm text yield to maturity n text number of coupon periods per year end aligned modified duration 1 nytmmacaulay duration where macaulay duration weighted average term tomaturity of the cash flows from a bondytm yield to maturityn number of coupon periods per year modified duration is an extension of the macaulay duration which allows investors to measure the sensitivity of a bond to changes in interest rates macaulay duration calculates the weighted average time before a bondholder receives the bond s cash flows in order to calculate modified duration the macaulay duration must first be calculated the formula for the macaulay duration is macaulay duration t 1 n pv cf t market price of bond where pv cf present value of coupon at period t t time to each cash flow in years n number of coupon periods per year begin aligned text macaulay duration frac sum n t 1 text pv times text cf times text t text market price of bond textbf where text pv times text cf text present value of coupon at period t text t text time to each cash flow in years n text number of coupon periods per year end aligned macaulay duration market price of bond t 1n pv cf t where pv cf present value of coupon at period tt time to each cash flow in yearsn number of coupon periods per year here pv cf is the present value of a coupon at period t and t is equal to the time to each cash flow in years this calculation is performed and summed for the number of periods to maturity 