Mean Reversion

Overview



Mean reversion is the tendency of asset to reverse price direction. That is, after a move up, it will move down, or after a move down, it will move up. A mean reversion trader bets against the most recent price move.

A price move is measured over a set period. Mean reversion traders will measure the price move over a pre-defined period, and then bet that the move over the next period will be opposite that of the prior period.

Formalization



A mean reverting time series is a series where the change in the series is negatively correlated with the difference of the current value and the series mean. Stated as an equation
{% \Delta X_{t+1} = -\alpha(X_t - \mu) + \epsilon_{t+1} %}
where
{% \Delta X_{t+1} := X_{t+1} - X_{t} %}
Mean reversion is typically detected through running an OLS Regression on the equation given above, or through the use of autocorrelation chart, which should show some stable negative correlations among the first few terms.

Return Efficiency



The total variation of an assets price moves over a period of time is given by
{% Total \, Variation = \sum_i | \Delta Price_i | %}
The efficiency of a price move can be defined as the difference of the price from the start to end, divided by the total amount of variation. for example, if the price difference over a month is measured, and then divided by the total "distance" that the asset has moved over the same period (sum of all the back and forth movements), the result will give the percentage of the total movements that resulted in the final return.
{% Efficiency = \frac{\Delta Price}{Total \, Variation} %}
Many assets show a large amount of variation relative to the total return. Mean reversion traders seek to profit from the back and forth movements of the asset, even those assets which are trending.

Note, mean reversion does not just assume a large volatility. Random walks can have large volatility. The mean reversion trade assumes that the volatility is so large that the asset must mean

As a general rule, mean reversion works best with frequent trading, for example, daily.

Strategies and Indicators



  • Mean Reversion over defined Period - Defines a period, and then bets against the move that ocurred in that period. As an example, a daily mean reversion strategy would sell any asset that went up during the day, and buy anything that went down.
  • Large Move Reversion - bet against any large marge in an asset over a defined period. Requires that a threshold be set. As an example, buy any stock that has decreased in value by 2% or move over a given day.
  • Large Move in Conjunction with Trend - Take a bet against any large move that moves opposite to the current trend. As an example, buy any stock that decreases by 2% or more in a given day as long as the price is above the 200-day moving average.

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