Hong Life CalculatorsUnderstanding the bond price change from duration — concept and principle
Duration tells you how sensitive a bond's price is to a change in interest rates. This calculator uses modified duration, and optionally convexity, to estimate the percentage price change and the new price when yields move by a given number of percentage points.
How it is calculated
With modified duration D, convexity C and yield change Δy written as a decimal (1 point = 0.01):
- Duration effect = −D × Δy
- Convexity effect = ½ × C × Δy²
- Price change ≈ −D × Δy + ½ × C × Δy²
- New price ≈ current price × (1 + price change)
Leave convexity at 0 for the simple duration estimate. Use the convexity in the same convention your data source quotes, since some quote it divided by 100.
The principle
A bond's price is the present value of its future cash flows. When yields rise, every cash flow is discounted more heavily and the price falls. Macaulay duration, introduced by Frederick Macaulay in 1938, is the weighted average time until those cash flows arrive. Modified duration (Macaulay duration ÷ (1 + yield per period)) is the slope of the price–yield curve: the percentage price change for a small yield change. That curve is not a straight line but bends upward, so duration alone overstates losses and understates gains for large moves. The convexity term adds that curvature back, a second-order Taylor approximation.
Worked example
- Modified duration 7.2, convexity 0, yield change +1 point, so Δy = 0.01, price $1,000.
- Duration effect = −7.2 × 0.01 = −7.2%.
- Convexity effect = ½ × 0 × 0.01² = 0%.
- Price change ≈ −7.2%, new price ≈ 1,000 × (1 − 0.072) = $928.00.
With a convexity of 60, the convexity effect would be ½ × 60 × 0.0001 = +0.3%, giving about −6.9% and $931.
How to read the result
Duration is a rule of thumb: a duration of 7 means about 7% price change per 1 point of yield. Short-term bonds often have durations of 1–3, while long government bonds can exceed 15. Higher duration means more price swing in both directions. For a fund, look up its effective duration in the fact sheet.
Common mistakes
- Entering the yield change as 1 for one basis point; 1 here means one percentage point, which is 100 basis points.
- Using Macaulay duration as if it were modified duration.
- Trusting the linear estimate for very large rate moves.
Frequently asked questions
If yields rise 1% and duration is 7, how much does the price fall?
About 7%, slightly less once convexity is taken into account.
Why do long bonds have higher duration?
Their cash flows arrive further in the future, so discounting changes affect them more.
Does duration matter if I hold to maturity?
Price swings matter less, since you receive face value at maturity if the issuer pays, but the market value of your holding still moves in between.
Sources: Macaulay, F. R. (1938). Some Theoretical Problems Suggested by the Movements of Interest Rates, Bond Yields and Stock Prices in the United States since 1856. NBER · Fabozzi, F. J. Bond Markets, Analysis, and Strategies