The Half-Life of mean reversion measures how quickly prices tend to return to their average level. A shorter half-life means faster reversion, which is generally more attractive for trading strategies.
The Ornstein-Uhlenbeck Process
Half-Life is calculated using the Ornstein-Uhlenbeck (OU) model, which describes mean-reverting processes mathematically. The OU process assumes prices are pulled back toward a mean level with a certain strength.
The Half-Life is derived from the speed parameter θ:
Practical Interpretation
A Half-Life of 10 bars means that, on average, half of any deviation from the mean will be corrected within 10 bars. Shorter half-lives indicate stronger, faster mean reversion.
- HL ≤ 50 bars - Score: 100 (fast reversion)
- HL = 100 bars - Score: 50 (moderate)
- HL ≥ 200 bars - Score: 0 (too slow)
Calculation Method
QuanterLab estimates Half-Life through linear regression:
- Calculate the spread between price and its moving average
- Regress the change in spread against the spread level
- The slope coefficient gives the reversion speed
- Convert to Half-Life using the formula above
Why Half-Life Matters
A security might be mean-reverting, but if the Half-Life is 500 bars, you'd have to hold positions for extended periods waiting for reversion. Shorter half-lives allow for:
- More frequent trading opportunities
- Reduced exposure time and risk
- Better capital efficiency
Half-Life is estimated from historical data and assumes the reversion process remains stable. Regime changes can alter the effective Half-Life significantly.
Platform Integration
Half-Life receives a 15% weight in the daily composite score. Securities with half-lives exceeding a maximum threshold (typically configurable based on timeframe) are filtered out as unsuitable for mean reversion strategies.
Further Reading
Foundational papers
- Vasicek, O. (1977). An Equilibrium Characterization of the Term Structure. Journal of Financial Economics, 5(2), 177–188.
- Avellaneda, M. & Lee, J.-H. (2010). Statistical Arbitrage in the U.S. Equities Market. Quantitative Finance, 10(7), 761–782.
Textbook references
- Hamilton, J. D. (1994). Time Series Analysis. Princeton University Press.
- Chan, E. P. (2013). Algorithmic Trading: Winning Strategies and Their Rationale. Wiley.
Related QuanterLab articles
Try it in QuanterLab
For tradable mean-reversion on daily bars, look for half-lives between 5 and 30 bars. Shorter is microstructure noise; longer is capital-intensive. The platform's OU half-life output is the right number to filter on.