Mean reversion — the return-to-the-mean strategy

Mean reversion proposes a reduction in distance from a specified reference. That reference and the object returning to it must be named and tested. A low RSI, band touch or low ADX does not identify a compulsory buy. A moving average can instead catch an unchanged price, so “reached the mean” need not mean a profitable trade. The worked example below separates those outcomes.

Specify what is supposed to revert

Mean reversion is a hypothesis about a specified series returning toward a reference, not a law that every price must obey. Define the series, units, window and any hedge coefficient before testing it. A moving average can move with price, and high correlation does not prove that a chosen difference will revert, as the diagram demonstrates.

Distinguish the price level, deviation from a moving reference and a model spread between instruments, such as P−βQ. This model spread is not the broker’s Bid–Ask spread. Correlation alone does not establish its stability. Trend-following systems test continuation rules instead; neither style’s name establishes future direction.

Two standard deviations can define a descriptive price envelope. It does not assign a return probability to a moving twenty-bar band or prove that price will revert. The chosen reference, window and entry rule need their own validation.

Describe distance and its calculation convention

Stationarity concerns properties of a specified process, including mean, variance and autocorrelation structure. Stationary changes do not by themselves make the level stationary. Cointegration is another hypothesis: the augmented Engle–Granger implementation in statsmodels tests a no-cointegration null under I(1) input assumptions. A fitted coefficient or test result from one sample does not establish future stability or net trading returns; do not estimate on later data and use it as if known earlier.

Traditional Bollinger Bands use a simple average with a standard-deviation-based width; 20 periods and 2 deviations are defaults, not universal optimal settings. A tag gives relative location, not an automatic reversal order. RSI is price-derived too: conventional 30/70 levels do not supply a win probability. Our distance statistic is z=(price−mean)/standard deviation. State the window, current-bar inclusion and divisor; a −2 reading describes distance rather than a rebound deadline.

ADX is a price-derived regime filter one may test. A low value does not prove a future range or grant a trade; a high value is not a universal prohibition. Define its calculation and threshold, then compare otherwise identical rules with and without it on a later evaluation period. Several price indicators are not automatically independent evidence.

Why the strategy catches a falling knife in a trend

A price can continue along an outer band; the creator explicitly distinguishes tags from signals. This possibility undermines an unconditional return claim. Adding positions after a loss changes exposure, not the mathematical likelihood of reversion. Whether a level, residual or updated average has useful reversion properties remains a separate empirical question.

Even with exactly the same prior window, changing ddof can change the signal. For the four prices above, standard deviation is √(8/4)≈1.4142 pips at ddof 0, but √(8/3)≈1.6330 at ddof 1. The current −4-pip distance gives z≈−2.8284 or −2.4495 respectively. A fictional z≤−2.5 test passes only with ddof 0. This threshold is selected to show the convention difference, not claimed as a better trading parameter.

Record what happens at zero standard deviation as well as at ordinary values. If all window prices coincide, z would require 0/0 and is undefined; do not silently report zero or an entry. A method that handles this boundary differently is a different specification, even without a price move.

Bollinger’s rules reject automatic statistical assumptions from the bands. A two-deviation envelope does not establish a 95% chance of return, and adding RSI plus a rejection candle does not turn the band tag into proof of a profitable trade.

What entry and exit discipline looks like

Write down a complete test rule: measured series, source prices, signal window, entry time, execution, exit and cost assumptions. A support or resistance filter can be compared under the same protocol, but it is not required by mean reversion’s definition. Preserve all eligible signals, including those that never reach the reference.

Choose explicitly whether the target is frozen at the signal’s reference or updated with later data. Also define loss exits, holding-time limit and cancellation conditions. A 1.5 × ATR distance is one optional parameter, not a usual mandatory stop. Ordinary stop execution may be worse than the chosen trigger; calculate risk and costs from the actual price model.

A missed time limit means the stated objective was not met within that limit; it does not prove a new trend has begun. Evaluate the amount and frequency of net wins and losses together. Neither win rate alone nor a chosen manual-exit deadline establishes survival or positive expectancy.

A hypothetical example, step by step

Continue the fictional Bid sequence with three more 1.0996 closes. Four-close means including the current bar at t0,t1,t2,t3 are 1.09990,1.09975,1.09970,1.09960; price-minus-mean is −3,−1.5,−1,0 pips. The moving mean reaches the unchanged price. The frozen old 1.1000 target is never reached in this sequence. At t3 all four prices coincide and z is undefined.

Assume a hypothetical 10,000-EUR buy at the first quote after t0, Ask 1.0997, and a sale after the t3 signal, Bid 1.0996. With USD 0.40 total commission, a USD account and no financing or other fees, net P&L=(1.0996−1.0997)×10,000−0.40=−USD 1.40. Spread is already in these fills and is not deducted twice. Reaching the updated average thus coincides with a net loss. A separate hypothetical fill at Bid 1.1000 would give +USD 2.60, but that price is absent from the unchanged-price sequence.

Who this strategy fits, and who it does not

Mean-reversion rules require testing with specified entries, exits and costs. ESMA's 2018 CFD intervention announcement cited historical loss-account ranges across jurisdictions; they are not a current loss percentage for a particular style. Risk management and discipline cannot guarantee profitability.

What to do tomorrow

1. Define the reversion object and units: price, deviation from a reference or a weighted multi-series spread. Correlation alone does not choose the coefficient or establish stability.
2. Record window length, source price side, ddof, current-bar inclusion and zero-deviation handling. Check the implementation on identical data before evaluating trade outcomes.
3. State whether the target is frozen or updated, and define entry, loss/time exits, volume and transaction costs before the test. A chart target is not an actual fill.
4. Separate parameter selection from later evaluation and record every eligible signal. Demo checks implementation; several dozen cases or a 1% budget do not establish profitability or readiness for live money.
5. Specify what a missed objective or holding-time limit does to the position. Treat any averaging rule as a separate exposure change and test its full net-result distribution.