What is Bond Duration? Measuring Interest Rate Risk

Duration is a measure of the sensitivity of the price of a bond to a change in interest rates. It is expressed as a number of years.

Bond Duration is a time-weighted measure of a bond's cash flows. It serves two purposes: it represents the weighted average time until an investor receives the bond’s cash flows, and it quantifies the bond's price sensitivity to interest rate changes. For every 1% change in interest rates, a bond’s price will change by approximately 1% in the opposite direction for every year of duration.

The most common form is Macaulay Duration, calculated as: $D_{mac} = \frac{\sum_{t=1}^{n} t \times PV(C_t)}{P}$, where $t$ is the time period, $C_t$ is the cash flow, and $P$ is the current bond price. To find the price sensitivity specifically, quants use Modified Duration: $D_{mod} = \frac{D_{mac}}{1 + y/k}$, where $y$ is the yield to maturity and $k$ is the compounding frequency per year.

A bond's duration is influenced by its maturity and its coupon rate. A zero-coupon bond has a Macaulay duration exactly equal to its time to maturity. For coupon-paying bonds, duration is always less than the time to maturity because the investor receives some payments early. In 2021, as interest rates sat near zero, 'long-duration' assets like 30-year Treasury bonds were highly sensitive to the first signs of inflation, leading to significant price volatility when the 10-year yield began to climb.