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