Hurst Exponent Calculator

Why the Hurst exponent matters

Most quant edge comes from picking the right strategy for the right asset and the right regime. Momentum strategies bleed money on mean-reverting assets; mean-reversion strategies get steamrolled by trends. The Hurst exponent gives you one number that tells you which regime an asset is in, so you can stop running the wrong playbook.

The math in 60 seconds

Take a time series. Split it into chunks of size n. Inside each chunk, compute the cumulative deviation from the mean, take its range (max minus min), and divide by the chunk's standard deviation. Average those across chunks — that is the rescaled range R/S(n). Repeat for many values of n. Plot log(R/S(n)) versus log(n) and fit a line. The slope is the Hurst exponent.

For a true random walk (geometric Brownian motion), this slope is exactly 0.5. For a process with persistent long-term trends, the slope is above 0.5. For a process that reverts to its mean, the slope is below 0.5. The exponent therefore directly measures the long-memory of the series.

What Hurst values look like in real markets

• S&P 500 (daily, multi-decade): H ≈ 0.55-0.60 — slightly trending, which is why long-only buy-and-hold and trend-following both work over long horizons.
• Major FX pairs (EUR/USD, USD/JPY): H ≈ 0.48-0.52 — close to random walk. This is consistent with the difficulty of beating spot FX systematically.
• Short-term interest rates: H often below 0.4 — strongly mean-reverting, which is why carry and roll-down strategies work here.
• Single-name equities: H ≈ 0.40-0.55 with high variance — many show short- term mean reversion (intraday) but mild trending (multi-month).
• Crypto majors (BTC, ETH): H ≈ 0.55-0.70 historically — strongly trending, which is why CTA-style trend strategies have outperformed in crypto.

How to use Hurst in a research workflow

1. Choose the right return frequency. The Hurst exponent of an asset can be different on daily, weekly, and monthly data. Pick the frequency at which your strategy will trade.
2. Compute on rolling windows. A single H over 10 years averages across multiple regimes and tells you very little. Compute H on a rolling 1-2 year window and chart it through time. Watch for crossings of 0.5.
3. Use H as a strategy switch. If your toolkit includes both momentum and mean-reversion, route capital based on the current rolling H. Many systematic shops do exactly this.
4. Validate with out-of-sample tests. The H value can mislead on small samples. Always confirm any strategy choice by walk-forward backtesting on data the H was not measured on.

Limitations and caveats

• Small samples are noisy. Below ~100 observations, H estimates can be off by ±0.1 or more. Always check R-squared.
• Non-stationarity inflates H. A series with a strong trend can produce H > 1.0. Run Hurst on returns, not raw prices, to avoid this.
• Regime changes are common. An H value computed yesterday may not apply tomorrow. Markets shift between trending and mean-reverting regimes constantly.
• Hurst is not a profit predictor. It tells you the asset has structure consistent with a strategy style — not that the strategy will be profitable after transaction costs.

Related calculators

For other regime-detection metrics, see the Sharpe ratio calculator and probabilistic Sharpe ratio calculator. For risk-of-ruin assessment of strategies you choose based on Hurst, see the drawdown calculator and value-at-risk calculator. For sizing positions, see the Kelly criterion calculator.