Bond Duration Calculator

Macaulay duration is the present-value-weighted average time, in years, until you receive all of a bond's cash flows. It treats the bond as a stream of payments and asks: on average, when do you get your money back? Modified duration takes that figure and divides it by (1 + the per-period yield), which converts a measure of time into a measure of price sensitivity. Macaulay tells you when, modified tells you how much the price moves when yields shift. For a 10-year bond yielding 5% semiannually, Macaulay duration might be 7.99 years and modified duration 7.79 years.

Modified duration is a first-order estimate of percentage price change for a small yield move. The rule of thumb: percentage price change is approximately negative modified duration times the change in yield. A bond with a modified duration of 7 falls roughly 7% in price if yields rise by 1 percentage point (100 basis points), and rises about 7% if yields fall by the same amount. The estimate is most accurate for small moves of 25 to 50 basis points. For larger moves, convexity adds a meaningful correction because the real price-yield relationship is curved, not linear.

Longer maturity means the bulk of the cash flow, the face value redemption, sits further out in the future. That stretches the weighted-average time to receipt and amplifies the present-value impact of any yield change, because the discount factor compounds across more periods. A 2-year Treasury might have a duration near 1.9 years, while a 30-year Treasury easily runs 18 to 20 years. The same 100 basis point rate move that nudges the 2-year price by about 2% can hit the 30-year price by 18% or more, which is why long bonds are the most rate-sensitive part of the fixed-income market.

Convexity is the second-order correction to the duration estimate. It captures the fact that bond prices do not move in a perfectly straight line with yields. Prices fall less than duration predicts when yields rise, and prices rise more than duration predicts when yields fall. The full price-change estimate is approximately negative modified duration times the yield change plus one-half times convexity times the yield change squared. For a small move convexity barely matters, but for a 200 or 300 basis point move it adds a noticeable cushion. All else equal, higher convexity is good for the bondholder because it improves the asymmetry of returns.

A zero-coupon bond has exactly one cash flow: the face value at maturity. Macaulay duration is the weighted-average time to cash flows, and with only one cash flow the average collapses to its date. A 10-year zero has a Macaulay duration of exactly 10 years. Coupon bonds always have a duration shorter than maturity because the coupons in between pull the weighted average forward. This also means zero-coupon bonds are the most rate-sensitive bonds at any given maturity, which is why pension funds and insurers use long-dated zeros to match liabilities decades out.