Mean reversion may be the most cited and least specified idea in finance. Galton’s original 1886 work was precise: reversion is relative before absolute — a variable measured against its sample average; convergence exists in balance with divergence; and the behaviour expresses itself across domains, not just in one dataset. For 130 years the idea sat in the open, un-extended.
The paper builds the missing framework and states its requirements plainly: any proxy expressing Galtonian reversion should be simple, relative and universal. On a stock-market case, that becomes relative ranking against the group, a relative average as the attractor, and both forces — convergence and divergence — priced as first-class citizens. Reversion’s famous “failures” stop being anomalies; they are the divergence half of the balance.
The mechanics
| Galton, 1886 | Framework translation |
|---|---|
| Relative before absolute | Rank components against the group — never against a price level |
| Relation to the sample average | The relative average is the attractor the system oscillates around |
| Convergence balanced by divergence | Both forces are priced; a failed reversion is divergence, not an anomaly |
| Cross-domain expression | One proxy — simple, relative, universal — works beyond markets |
Extremes carry odds
Reversion is not a promise; it is a probability gradient. The further a component sits from its group mean, the better the odds of the journey back — and percentile bands are what make that gradient usable. A stock at the 95th percentile of relative performance is not “due” to fall; it simply carries measurably different odds than one at the 60th.
Bands convert forecasting into bookkeeping. No price targets, no narratives — just positions located relative to their band, each carrying historical transition odds. That is the kind of information a probabilistic engine can compound: small, persistent edges applied across a whole universe, rebalance after rebalance.
What it means for portfolios
This is the oldest pillar under the 3N™ engine — the paper that turns a nineteenth-century observation into a construction rule. Weighting by where a constituent sits relative to the group, with divergence expected rather than explained away, is what allows a benchmark to hold reversion candidates the cap-weighted rule quietly discards. If you read one paper in this series first, read this one.
- Galtonian reversion is relative: measured against the group’s average, never a price level.
- Convergence and divergence are one balance — reversion’s “failures” are the other half of the law.
- A valid reversion proxy is simple, relative, universal — the specification 3N™ builds on.
Pal, M. (2015). Mean Reversion Framework. SSRN 2607963.
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