---
title: "Half-Life of Mean Reversion: Formula"
description: "The half-life of mean reversion is the expected time for a deviation from the long-run mean to shrink by half. It is estimated from the autoregressive speed..."
canonical: https://www.getswoopr.com/indicators/statistical-and-quantitative/half-life-of-mean-reversion/
source: "Swoopr Investment: https://www.getswoopr.com"
---

## Direct Answer



> Half-Life of Mean Reversion is a statistical & quantitative measure used to quantify statistical properties, relationships, normalization, or model residuals. The production page must define the exact calculation convention before interpreting higher or lower readings, because platform and provider implementations can differ.





      


# Half-Life of Mean Reversion: Formula, Meaning, Signals, Examples and How to Use It



## How Is Half-Life of Mean Reversion Calculated?

The half-life of mean reversion is the expected time for a deviation from the long-run mean to shrink by half. It is estimated from the autoregressive speed of the series and is used to judge how quickly a spread tends to revert.

**Formula:** `Regress change on lagged level: dX = a + b * X[t-1] + e; half-life = -ln(2) / ln(1 + b), approximately -ln(2) / b for small b`

**Inputs:**

- Spread or level series
- Regression slope b
- Sample window

**Worked example.** A regression slope of -0.05 per bar implies a half-life of 13.5 bars. The inputs are illustrative numbers, not market data.

**Reading it.** Short half-lives mean deviations close quickly, long half-lives mean slow reversion. It is only meaningful when the slope b is between -1 and 0, since a non-negative slope implies no reversion.

**Limits.** The estimate is imprecise in short samples and can change a lot as the window moves. Treating it as stable assumes the process is stationary, which may fail.


      

## Indicator overview





| Attribute | Value |
| --- | --- |
| Category | Statistical & Quantitative |
| Asset classes | Cross-asset, Portfolios, Pairs, Time series |
| Output type | Line/scalar |
| Parameters | Varies by implementation; document exact settings on use |






## What is Half-Life of Mean Reversion?



Half-Life of Mean Reversion is a statistical & quantitative measure used to quantify statistical properties, relationships, normalization, or model residuals. The production page must define the exact calculation convention before interpreting higher or lower readings, because platform and provider implementations can differ.



For Swoopr, the canonical profile separates definition, calculation, interpretation and decision use. That keeps readers from collapsing a descriptive metric into a trading strategy. An indicator can describe trend, momentum, volatility, participation, positioning or risk without providing a complete entry, exit, sizing or portfolio decision.




## What does it measure?



Half-Life of Mean Reversion measures specific market properties in the Statistical & Quantitative domain. The practical value is repeatability: the same inputs and formula can be applied across a defined dataset, allowing users to compare readings through time or across instruments when the calculation convention is held constant.




## How to read Half-Life of Mean Reversion



Interpretation depends on the market property being measured. A descriptive reading is not automatically predictive. The same numerical state can lead to different outcomes in a strong trend, quiet range, event-driven gap or illiquid market. Always combine with context from price structure, volume, and broader market regime before drawing conclusions.




## Strengths



- Stating the speed as a time in bars is easier to interpret than the raw regression coefficient b.
- The half-life formula is closed form once the regression is fitted, so it needs only one coefficient.
- Reproducible when the formula and data convention are fixed.




## Weaknesses and limitations



- If b is estimated at or above zero, the formula gives an undefined or negative half-life, which signals no reversion in the sample.
- Small changes in b near zero produce very large changes in the half-life, so the value is highly nonlinear in the estimate.
- 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. Where multiple valid definitions exist, Swoopr states the alternatives and the reason for selecting its primary convention.







## Frequently Asked Questions


        



Is Half-Life of Mean Reversion a buy or sell signal?




No. Short half-lives mean deviations close quickly, long half-lives mean slow reversion. The estimate is imprecise in short samples and can change a lot as the window moves. 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 Half-Life of Mean Reversion?




Half-Life of Mean Reversion takes these inputs: spread or level series; regression slope b; sample window. There is no universal best setting for the tunable ones, so test them across instruments, regimes and out-of-sample periods and favor stable parameter regions over one historical winner.










Can Half-Life of Mean Reversion be used by itself?




The estimate is imprecise in short samples and can change a lot as the window moves. Treating it as stable assumes the process is stationary, which may fail. For that reason it is read next to measures of direction, participation, valuation, liquidity and risk, not alone.










Does Half-Life of Mean Reversion work on every timeframe?




The calculation (Regress change on lagged level: dX = a + b * X[t-1] + e; half-life = -ln(2) / ln(1 + b), approximately -ln(2) / b for small b) 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 Half-Life of Mean Reversion give false signals?




If b is estimated at or above zero, the formula gives an undefined or negative half-life, which signals no reversion in the sample. Small changes in b near zero produce very large changes in the half-life, so the value is highly nonlinear in the estimate. Lag, noise and regime changes add to this, because market participants react to new information after the reading is calculated.










How should Half-Life of Mean Reversion be backtested?




Rebuild Half-Life of Mean Reversion from spread or level series 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.










## References

- [Physical Review: On the Theory of the Brownian Motion (1930)](https://doi.org/10.1103/PhysRev.36.823)



S




Swoopr Editorial Team



The Swoopr Editorial Team produces independent investment education, research, and tools for understanding markets, evaluating opportunities, and managing risk. All content is educational only and does not constitute personalized investment advice.



See our [editorial policy](https://www.getswoopr.com/legal/editorial-policy/) and [corrections policy](https://www.getswoopr.com/legal/corrections-policy/).