Back

Learn yieldcurve.pro

Duration

Duration measures how much a bond's price changes when interest rates move. It is expressed in years but functions as a risk metric: a bond with a duration of 8 years will lose approximately 8% of its value for every 1 percentage point rise in yields.

Two related measures are commonly used:

  • Macaulay duration is the weighted-average time to receive a bond's cash flows, where the weights are the present values of each payment. For a par bond with semiannual coupons, Macaulay duration approximates (1 + y/2) / (y/2) x (1 - 1/(1 + y/2)^(2n)), where y is the yield and n is the maturity in years.
  • Modified duration adjusts Macaulay duration for the compounding frequency: modified duration = Macaulay / (1 + y/2). This gives the percentage price change per 1% yield change.

Duration increases with maturity and decreases with coupon rate. A 10-year Treasury at par has a modified duration around 8.2 years, while a 30-year bond has roughly 16.4 years.

Portfolio managers use duration to manage interest rate risk. A duration-neutral portfolio is constructed so that gains from one position offset losses from another when rates move. Understanding duration is essential for evaluating how yield curve shifts affect portfolio value.

FAQ

What is the difference between Macaulay and modified duration?

Macaulay duration is the present-value-weighted average time until a bond's cash flows are received, expressed in years. Modified duration adjusts that figure for compounding so it can be read directly as a percentage price change per 1% yield change. Modified duration = Macaulay / (1 + y/k), where k is the number of coupon payments per year.

How do I estimate the price impact of a yield change using duration?

Multiply the bond's modified duration by the negative of the yield change. A bond with a modified duration of 7.5 will lose about 7.5% of its market value if yields rise by 1 percentage point, and gain a similar amount if yields fall by 1 point. The estimate is most accurate for small yield moves; for larger moves, convexity adds a meaningful second-order correction.

Why does duration fall as coupon rate rises?

Higher coupons return more of the bond's cash flows earlier in its life, which shortens the present-value-weighted average maturity. A zero-coupon bond has the longest duration for its maturity (duration equals maturity), while a high-coupon bond of the same maturity has a noticeably shorter duration and therefore less interest rate sensitivity.

View chart →


Related Terms

  • Convexity — A measure of how a bond's duration changes as yields move, capturing the curvature of the price-yield relationship.
  • DV01 — The dollar value of a 1 basis point yield change for a bond position. Used to size hedges and compare interest rate exposure across different securities.
  • Yield Curve — A line plotting Treasury yields across maturities from 1-month bills to 30-year bonds. The global benchmark for risk-free rates and the term structure of interest rates.

Back