Economics
Bond Duration: Price Sensitivity to Interest Rates
Quick fact
A bond with a duration of 5 years will see its price drop approximately 5% for every 1% increase in interest rates.
Why this is interesting
You buy a bond expecting steady income, but market interest rates move. How much will your bond's price change?
Read the full explanation
Understanding Bond Duration: Price Sensitivity to Interest Rates
Imagine two bonds: one pays all its interest in five years, and another pays small amounts each year for ten years. The first bond’s price is more sensitive to rate changes because you have to wait longer for your money. Duration captures this by measuring the average time you must wait to receive the bond’s cash flows, weighted by their present values. A higher duration means greater price swings when rates change. For a zero-coupon bond, duration equals its maturity. For a coupon-paying bond, duration is less than maturity because some cash flows come earlier.
A deeper explanation
Duration works because bond prices and yields move inversely. Mathematically, Macaulay duration is the weighted average time to receive each cash flow, where weights are the present value of each payment divided by the bond’s total price. Modified duration refines this: it approximates the percentage price change for a 1% change in yield. The formula is Modified Duration = Macaulay Duration / (1 + Yield). This approximation is linear, but real price-yield curves are convex (curved). For small rate changes, duration works well; for large changes, convexity correction is needed. Duration is crucial for portfolio immunization—structuring a bond portfolio so that its value is insensitive to small interest rate shifts—and for comparing bonds across different coupons and maturities.