Performance & Risk Metrics
Hurst Exponent
A statistical measure between 0 and 1 that quantifies the long-memory and mean-reversion properties of a time series, with values above 0.5 indicating trending behavior and values below 0.5 indicating mean-reversion.
The Hurst Exponent, derived from the rescaled range analysis pioneered by hydrologist Harold Hurst, detects persistent or anti-persistent patterns in a return series. A value of 0.5 means a pure random walk; values approaching 1.0 point to trending, momentum-driven behavior; values near 0.0 mark strong mean reversion. It is a way to ask whether a series has memory or whether each move is independent of the last.
Knowing whether a series trends or mean-reverts shapes how you trade it: a trending series favours momentum rules, a mean-reverting one favours fade-the-move rules. Computing the exponent over rolling windows can flag a regime shift, when a series that used to trend starts reverting. Treat the estimate with care, since it is noisy on short windows and sensitive to the method used.
Formula
- R/S
- Rescaled range statistic, the ratio of adjusted range to standard deviation over a time period N
- N
- Number of observations or time steps in the analyzed series