Price a bond, see its Macaulay and modified duration, and visualize the price yield curve alongside the straight line duration approximation to see convexity in action.
| Yield Shift | Duration Only Estimate | Duration + Convexity Estimate | Actual Price Change |
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A bond's price is the present value of its future cash flows, its coupon payments and final face value repayment, discounted at the current market yield. As that yield changes, the price moves in the opposite direction: higher yields mean lower prices, and lower yields mean higher prices. Duration measures how sensitive that price is to a small change in yield, while convexity captures how that sensitivity itself changes as yields move further, which is why the actual price curve bends rather than following a straight line. Every slider on this page has a matching number field: drag to explore, or type exact figures if you already know your numbers.
Macaulay duration is the weighted average time until a bond's cash flows are received, measured in years, where each cash flow is weighted by its present value. Modified duration adjusts that figure to directly estimate percentage price sensitivity to a yield change, and is what most practitioners mean when they informally say a bond's duration. A bond with a modified duration of seven means its price will move roughly seven percent for a one percentage point change in yield, in the opposite direction.
Duration alone assumes a straight line relationship between yield and price, which is a reasonable approximation for small yield changes but increasingly inaccurate for larger ones. The true relationship curves, and that curvature is what convexity measures. Because bond price convexity is positive for most ordinary bonds, the duration only estimate understates how much a bond gains in price when yields fall, and overstates how much it loses when yields rise. This is exactly what the chart above illustrates: the actual gold curve sits above the dashed straight line estimate at every point except where they touch at the current yield.
Two bonds can have the same duration but different convexity, and the one with higher convexity will generally outperform in both rising and falling rate environments, which is why convexity is treated as a desirable property, all else equal. This is a foundational concept in fixed income portfolio management and immunization strategies, where duration and convexity are matched against a set of future liabilities to protect a portfolio from interest rate risk.
Bond pricing, yield to maturity, duration, and convexity are core fixed income topics on CFA Level 1 and are tested in more depth on CFA Level 2, particularly around duration based immunization strategies. These same concepts appear in the products sections of the SIE exam and Series 7, and in the fixed income planning content on the CFP exam.
When the market yield exactly matches the coupon rate, the bond's fixed payments are worth exactly what an investor requires, so the bond trades at par, meaning its price equals its face value. If the yield rises above the coupon rate the bond trades at a discount, and if the yield falls below the coupon rate it trades at a premium.
Duration is a weighted average of when cash flows arrive. A bond with a longer maturity has cash flows, especially the large final face value repayment, arriving further in the future, which pulls the weighted average time further out and increases both Macaulay and modified duration.
A higher coupon rate returns more cash to the investor earlier through larger coupon payments, which pulls more weight toward the earlier years and shortens the weighted average time to receive the bond's value, lowering duration relative to a lower coupon bond of the same maturity.
Yes. Each slider has a paired number input. Type directly into any gold field to enter a precise figure, and the slider along with all results update immediately.
Bond pricing, duration, and convexity show up directly on CFA and FINRA exams. Practice for free.
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