Mean reversion: anchors, horizons, and reversion risk

Mean reversion asks whether a displacement is temporary

Mean reversion is the hypothesis that a measured variable tends to move back toward a reference after moving unusually far away. The variable might be a price, a return, a yield spread, or the residual between two related assets. The reference might be a rolling average, a session VWAP, or an estimated economic relationship.

The reference is the anchor. Without naming it, “price should come back” has no testable meaning. Back to yesterday’s close, a 20-day average, and a cointegrating spread are three different claims.

Mean reversion also needs a horizon. Price can revert around an intraday VWAP while remaining in a year-long uptrend. Momentum and reversion are therefore not universal opposites. They conflict only when they describe the same variable over the same interval.

Most importantly, an anchor is not automatically fair value. It is a summary of past information whose continued relevance must be tested.

Why a displacement might close

Temporary buying or selling pressure can move price farther than the available liquidity can immediately absorb. Dealer inventory, mechanical rebalancing, forced liquidation, and short-lived attention can all create an imbalance that fades once the urgent flow is complete.

Some variables also have stronger economic constraints. Related contracts may be linked through conversion, financing, or substitution; a portfolio residual may fluctuate around a stable exposure relation. In those cases the anchor has more substance than an arbitrary chart average, although transaction costs and structural change can still prevent convergence.

The competing explanation is repricing. New information may make the old reference obsolete. A reversion rule is consequently short the persistence of the displacement: it often wins small amounts when ordinary noise closes, then loses much more when the move marks a genuine regime change.

The anatomy of a reversion rule

A z-score does not solve these decisions. It simply expresses the current distance in units of an estimated standard deviation. If the average and standard deviation are unstable, the score is unstable too.

A simple example

Illustrative example. Assume a completed daily observation gives:

• rolling anchor: 100;
• estimated standard deviation of the displacement: 2; and
• current price: 95.

The normalized displacement is $(95-100)/2=-2.5$. A predeclared long reversion rule might enter at the next eligible event when the score is below −2, target the inner band at −0.5, and invalidate after five days or below −4.

Three paths show why the definition matters:

1. Price rises to 99 while the anchor stays near 100. The displacement closes as hypothesized.
2. Price remains at 95 while the rolling anchor falls to 97. The score improves, but little economic recovery occurred; the moving anchor partly chased the loss.
3. Price falls to 90 after material news. The old anchor no longer describes the state, and a rule without invalidation keeps increasing its exposure to a broken thesis.

The second case is why researchers should inspect both normalized distance and the raw path. A prettier z-score is not necessarily a profitable reversion.

Why the two sides are not mirror images

A score of −2.5 and a score of +2.5 are equally far from the anchor mathematically. They do not create equal trades economically.

For an equity index, long-run positive drift can make an upside extension persist while a short reversion position pays financing, borrow, and opportunity costs. Downside moves often arrive faster, with larger volatility and thinner liquidity, so buying the lower extension can experience a deeper overshoot before any rebound. Those are different risks: persistence asks how long a deviation lasts, while excursion asks how far it travels before closing.

Empirical findings are conditional. Some US index samples have shown quicker and larger reversal after negative monthly returns, while broad-index evidence also shows unequal waiting times for matched gains and losses. Those findings motivate side-specific tests; they do not establish a universal rule for individual stocks, futures, intraday bars, or a different sample.

The practical response is to design two sleeves rather than force one symmetric rule:

Illustrative example. Keep the anchor fixed at 100 and the estimated dispersion at 2 for one decision:

The thresholds are symmetric only so the comparison is readable. The study should still allow different timeouts, risk caps, and eligibility filters. If volatility and the anchor update after entry, preserve both the entry-time distance and the live distance; otherwise a moving denominator can make one side appear to improve without price moving toward the original reference.

What a credible result would look like

Credibility comes from a stable relationship among choices. Wider entry bands should normally create fewer, more extreme opportunities. Longer timeouts should change both convergence rate and capital usage. Costs should matter more at shorter horizons.

A result becomes difficult to trust when the anchor continuously moves toward losing trades, when most “profits” remain unrealized at the test boundary, or when one threshold produces an isolated success. The rule should also be tested around known structural changes rather than only during calm, range-bound periods.

Failure modes are part of the strategy

• Broken anchor: new information or a regime shift makes the reference irrelevant.
• Asymmetric tail: many small wins are overwhelmed by a few persistent moves.
• Scale instability: volatility expands, so a formerly extreme raw distance becomes ordinary—or the reverse.
• Overlapping observations: frequent signals can represent one prolonged event rather than independent opportunities.
• Cost sensitivity: small expected reversions vanish after spread, impact, and missed fills.
• Averaging down: adding exposure as price moves farther away can hide risk until a capital limit is reached.

Try it in Arizmic

Further reading

• Poterba and Summers, “Mean Reversion in Stock Prices: Evidence and Implications” (1988) — Finds point estimates consistent with short-horizon continuation and longer-horizon reversal across US and international markets, while emphasizing that low-powered conventional tests cannot reject a random walk.
• Kim, Nelson, and Startz, “Mean Reversion in Stock Prices? A Reappraisal of the Empirical Evidence” (1991) — Re-examines the long-horizon result using randomization and prewar/postwar splits, finding weaker evidence that is concentrated before World War II.
• Mukherji, “Are Stock Returns Still Mean-Reverting?” (2011) — Uses block-bootstrap tests through 2007 and finds that long-horizon reversion weakened in later decades and varies by company size and holding period.
• Nam, Pyun, and Avard, “Asymmetric Reverting Behavior of Short-Horizon Stock Returns: An Evidence of Stock Market Overreaction” (2001) — Finds quicker and larger reversal after negative monthly returns in value-weighted US indexes from 1926–1997; the result is specific to that sample and nonlinear model.
• Jensen, Johansen, and Simonsen, “Inverse Statistics in Economics: The Gain–Loss Asymmetry” (2003) — Measures unequal waiting times for matched gains and losses, supporting separate analysis of path direction and duration rather than establishing a profitable fade rule.
• Nagel, “Evaporating Liquidity” (2012) — Interprets short-term equity reversal returns as compensation for liquidity provision and shows that this compensation rises during market turmoil.