Direct Answer
The curvature of a bond's price response to yield changes measured by repricing the bond under small upward and downward shifts in the benchmark curve. It captures embedded options such as calls or prepayments. Positive effective convexity means price gains from falling yields exceed losses from rising yields.
Effective Convexity: Formula, Meaning, Signals, Examples and How to Use It
How Is Effective Convexity Calculated?
The curvature of a bond's price response to yield changes measured by repricing the bond under small upward and downward shifts in the benchmark curve. It captures embedded options such as calls or prepayments.
Formula: Effective convexity = (P_down + P_up - 2 x P_0) / (P_0 x dy^2)
Inputs:
- Current price P_0
- Model price P_down after yields fall by dy
- Model price P_up after yields rise by dy
- Shift size dy
Worked example. With a price of 100, 107 after a 1 percentage point fall in yields and 93.5 after a 1 point rise, effective convexity is 50.0. The inputs are illustrative numbers, not market data.
Reading it. Positive effective convexity means price gains from falling yields exceed losses from rising yields. Callable bonds and mortgage securities can show negative convexity when yields fall.
Limits. The result depends on the valuation model, the volatility assumption and the size of the shift dy. Different models can give noticeably different values for the same security.
What is Effective Convexity?
The curvature of a bond's price response to yield changes measured by repricing the bond under small upward and downward shifts in the benchmark curve. It captures embedded options such as calls or prepayments.
How to use Effective Convexity
Positive effective convexity means price gains from falling yields exceed losses from rising yields. Callable bonds and mortgage securities can show negative convexity when yields fall. A reading alone is never a buy or sell signal; it needs context from price structure, volume, volatility and the broader market regime.
Strengths
- The second difference of three model prices captures the curvature that embedded options create, which closed-form convexity cannot.
- A negative value flags that price gains from falling yields are capped, as with callable bonds, which the sign of the number shows directly.
- Reproducible when the formula and data convention are fixed.
Weaknesses and limitations
- It is a ratio of small differences, so rounding in model prices is magnified when dy is small, making the result noisy.
- It is a local second-order measure, so across large yield moves the actual curvature of a bond with options can change sign.
- Correlated indicators can create false confidence by repeating the same underlying information.
Editorial and risk note
This page is educational content, not individualized investment advice. It should not imply guaranteed prediction, accuracy or outperformance.
Frequently Asked Questions
Is Effective Convexity a buy or sell signal?
No. Positive effective convexity means price gains from falling yields exceed losses from rising yields. The result depends on the valuation model, the volatility assumption and the size of the shift dy. A trade built on it still needs a trigger, an invalidation rule, a position size and realistic execution assumptions.
What is the best setting for Effective Convexity?
Effective Convexity is computed from current price P_0; model price P_down after yields fall by dy; model price P_up after yields rise by dy, so the choices that matter are the data convention and the window it is read over. Test those across instruments, regimes and out-of-sample periods instead of fitting one historical winner.
Can Effective Convexity be used by itself?
The result depends on the valuation model, the volatility assumption and the size of the shift dy. Different models can give noticeably different values for the same security. For that reason it is read next to measures of direction, participation, valuation, liquidity and risk, not alone.
Does Effective Convexity work on every timeframe?
The calculation (Effective convexity = (P_down + P_up - 2 x P_0) / (P_0 x dy^2)) can be run on any bar size, but behavior is not portable: a reading on a five-minute chart describes a very different market window from the same reading on a daily chart. Validate the exact timeframe before relying on it.
Why does Effective Convexity give false signals?
It is a ratio of small differences, so rounding in model prices is magnified when dy is small, making the result noisy. It is a local second-order measure, so across large yield moves the actual curvature of a bond with options can change sign. Lag, noise and regime changes add to this, because market participants react to new information after the reading is calculated.
How should Effective Convexity be backtested?
Rebuild Effective Convexity from current price P_0 using point-in-time data, write the rules before testing, include delisted securities where relevant, model realistic fills and costs, reserve a validation sample and compare with a simpler baseline.