The Variance Ratio test is a statistical method for detecting whether a time series follows a random walk or exhibits mean-reverting characteristics. It complements the Hurst Exponent by providing an independent measure of mean reversion tendency.
The Concept
In a random walk, variance increases linearly with time. If you look at 5-day returns, their variance should be approximately 5 times the variance of 1-day returns. The Variance Ratio tests this relationship.
Interpretation
- VR < 1.0 - Mean reversion: variance grows slower than expected
- VR = 1.0 - Random walk: variance grows as expected
- VR > 1.0 - Momentum/trending: variance grows faster than expected
When the Variance Ratio is below 1.0, it indicates that returns tend to reverse—an up day is more likely to be followed by a down day, and vice versa. This is exactly the behavior mean reversion strategies seek to exploit.
Platform Implementation
QuanterLab calculates the Variance Ratio using a 5-period lag. The scoring converts VR values to a 0-100 scale:
- VR ≤ 0.7 - Score: 100 (strong mean reversion)
- VR = 1.0 - Score: 50 (neutral)
- VR ≥ 1.3 - Score: 0 (momentum behavior, not suitable)
Combined with Hurst Exponent
While both metrics detect mean reversion, they use different mathematical approaches. A security showing low Hurst Exponent AND low Variance Ratio provides stronger evidence of mean-reverting behavior than either metric alone.
In the daily composite score, Variance Ratio receives a 15% weight, contributing to the overall assessment alongside Hurst (25%), RSI win rate (25%), and other factors.
Advantages of Variance Ratio
- Simple to calculate and interpret
- Independent validation of Hurst Exponent findings
- Directly measures the core property mean reversion exploits
Further Reading
Foundational papers
- Lo, A. W. & MacKinlay, A. C. (1988). Stock Market Prices Do Not Follow Random Walks: Evidence from a Simple Specification Test. Review of Financial Studies, 1(1), 41–66.
Textbook references
- Campbell, J. Y., Lo, A. W. & MacKinlay, A. C. (1997). The Econometrics of Financial Markets. Princeton University Press.
- Tsay, R. S. (2010). Analysis of Financial Time Series (3rd ed.). Wiley.
Related QuanterLab articles
Try it in QuanterLab
Variance ratio < 1 confirms mean-reversion tendency; combine it with Hurst < 0.5 in the MR Scanner. Names that pass both filters are stronger candidates than names passing only one.