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Key Takeaways
- Define the price, spread or ratio being studied and the central value used as its reference.
- The reference average can be a moving average, a valuation ratio, a spread between two assets, or a long-run return, and the chosen average defines the strategy.
- Use a z-score or matching statistical bands to express deviation in units of the series’ standard deviation.
- Evaluate the selected series, holding period and trading rules together when testing a reversion strategy.
- Reversion and momentum use different directional rules. Select the strategy and reference horizon before the trade.
What is mean reversion?
Mean reversion is the movement of a series, such as a stock price, a valuation ratio or a two-asset spread, back toward a defined central value. As a trading strategy, it measures how far the series has moved from that reference and takes a position for a return toward it, with a set entry, target and exit. The reference, threshold and exit rules define the actual strategy.
A trading application starts with the series being studied, its reference sample and the time horizon of the position. Each kind of series needs its own construction, so specify it before calculating a deviation.
How to measure distance from the mean: the z-score
Subtract the reference mean from the observation and divide by the reference standard deviation. With a $100 mean and $4 standard deviation, $108 is +2 and $92 is −2.
The example holds those reference values fixed. A rolling calculation updates its mean and dispersion as observations enter and leave the window. Price can remain above an old reference while its rolling z-score changes.
RSI measures the balance of smoothed gains and losses. Use it for that quantity rather than treating it as another calculation of standard-deviation distance from the mean.
Formula
Reference z-score = (current observation − reference mean) ÷ reference standard deviation- Use the mean and positive standard deviation from the defined reference sample. Specify whether that sample stays fixed or rolls forward.
- A positive z means price sits above the average and a negative z means it sits below.
- Choose and test the signal threshold. A wider threshold changes which observations qualify; its effect on trade quality must be measured from the resulting record.
Mean reversion trade example: entry, target and stop
Use a fixed reference mean of $100 and reference standard deviation of $4. At $108, evaluate a short-entry scenario with a $100 target and a $110 stop-price scenario. Hold those reference values fixed throughout the displayed illustration.
- Deviation: $108 − $100 = $8
- Reference z-score: $8 ÷ $4 = +2.0
- Fixed two-standard-deviation levels: $92 and $108
- Target price gain for the short: $108 − $100 = $8 per share
- Stop-price loss: $110 − $108 = $2 per share
- Planned reward-to-risk ratio: $8 ÷ $2 = 4.0 before costs
The $108 observation is two reference standard deviations above $100. A short closed at $100 gains $8 per share; an exit at $110 loses $2 per share before costs. The statistical reference and the trade’s actual result are separate measurements.
Define the holding-time rule and whether the target updates during the trade. Record actual fills and costs separately from the reference calculations.
Log the reference, signal, entry, target, exit and net result for each trade, then compare the complete sample under the same rules to evaluate the strategy.
Mean reversion in pairs and relative-value spreads
For two assets, specify the hedge weights and the spread being evaluated. Before trading the spread, test it for stationarity and hedge its market exposure; a high historical correlation does neither. Test the constructed series and measure the portfolio’s actual sensitivities.
Use the event calendar and business context to identify the facts relevant to the chosen reference. Price and options activity feed the review; judge fundamental value separately from the trade result.
Risks and limitations of mean reversion
- When the series keeps trending away from an old average, the deviation widens instead of closing, and the $110 stop takes the example’s $2 loss. A rolling z-score also moves as the window updates, so recompute it before each entry.
- A different reference sample, window length or threshold changes which observations qualify, so fix all three before the test.
- The 4-to-1 reward-to-risk is planned before costs. A fill past the $110 stop, or costs on both legs, shrinks it, so measure the ratio on actual fills.
- For pairs, correlation between the legs is the starting screen. Test the constructed spread for stationarity and measure its directional market exposure before you trade it.
- Test rules that worked in one sample on separate observations. When reversion gives way to momentum in a new period or horizon, a rule fitted to the old sample fails.
Bottom line
Mean reversion trades the distance between a series and a defined central value, positioning for a move back toward it. Define the series, reference and z-score threshold before the trade, set a target and a separate stop, and judge the rules on a full sample after costs.
Clear answers
Frequently Asked Questions
Sources and Further Reading
- CFA Institute: Momentum, Mean-Reversion, and Social Media (Digest)
- NBER: Mean Reversion in Stock Prices, Evidence and Implications (Poterba and Summers)
- Fidelity Learning Center: Bollinger Bands
How entries are sourced, calculated and updated: editorial methodology.