Convexity
The curvature of the relationship between a bond's price and its yield. Because the relationship is a curve and modified duration is a straight line tangent to it, the duration estimate is imprecise, and increasingly so as the move grows.
Example
On a 5-year 4% bond, modified duration predicts a 44.52 fall per 1,000 for a 100 basis point rise; the exact repricing is 43.29, so the estimate overstates the loss by 1.22.
Important
The error runs one way: the duration estimate overstates losses when yields rise and understates gains when they fall. Treating the approximation as exact makes a large move look worse than the arithmetic says.
Related terms
- Duration — The present-value-weighted average time until a bond's cash flows are received (Macaulay duration), and by extension the measure of how much its price moves when yields change. Modified duration is Macaulay duration divided by one plus the yield.
- Interest-rate risk — The risk that prevailing yields move and reprice a bond you already hold, because its fixed coupon must now compete with newly issued bonds paying a different rate.
- Yield to maturity — The single discount rate at which the present value of a bond's remaining cash flows equals its current price. It has no closed-form solution for a multi-period bond and is found numerically.
Lessons that explain it
All 578 terms in the Investing glossary