Bond duration

Duration measures how sensitive a bond's price is to a change in interest rates, expressed as a number of years. A bond with a duration of 7 will lose roughly 7% of its value for each one-percentage-point rise in yields, and gain roughly the same for a one-point fall, as a first approximation.

Macaulay duration is the weighted-average time until a bond's cash flows are received, weighted by their present value; modified duration adjusts this to directly approximate the percentage price change per unit change in yield, %ΔPrice ≈ -Modified duration × Δyield. Duration differs from a bond's maturity: a 30-year bond with large coupon payments can have a shorter duration than a 10-year zero-coupon bond, because more of its value is returned sooner.

Duration is the standard tool for managing interest-rate risk in a bond portfolio, and matching the duration of assets and liabilities is a core technique in pension and insurance management. Its main limitation is that it is a linear approximation: for large rate moves, the true price change curves away from the duration estimate, an effect called convexity, so duration alone understates gains and overstates losses for big swings in the yield curve, and it does not by itself capture credit spread risk.