Duration measures a bond's sensitivity to changes in interest rates and is used to assess interest rate risk. The higher the duration, the more sensitive the bond or bond fund is to changes in interest rates. Various methods have been developed to measure duration, including modified duration, among others.
$$Modified\, duration \mmlToken{mo}[linebreak="auto"]{=} \frac{Macaulay\, duration}{\left( 1+ \frac{YTM}{n}\right)}$$
YTMβ yield to maturity;
nβ number of coupon payments per year.
Modified duration measures how sensitive a bond's price is to a change in interest rates.
Macaulay duration measures the weighted average time to receive cash flows, while modified duration adjusts that value to estimate price sensitivity to yield changes.