Mean reversion is not a law of markets
Prices snap back in some markets, at some horizons, in some eras. In others they trend. Where reversion has shown up, why, and how to check before you build on it.
By Baris Demirci · · Rev00
The idea
A mean reversion rule buys after a fall, or sells after a rise, on the view that price will come back toward some recent level. It is one of the three families of entry rules, alongside trend and breakout. It is attractive because it buys weakness and tends to be right often.
The question people ask next is whether it holds everywhere. It does not. Reversion is a property of a particular market, at a particular horizon, in a particular era. Where that property is missing, the rule keeps buying weakness that gets weaker.
Reversion needs a reason
Something has to pull price back. Three mechanisms come up again and again:
- Someone is paid to absorb forced selling. When an impatient seller pushes price down, whoever takes the other side expects to be compensated as the pressure fades. Short dips of this kind tend to recover.
- An arbitrage bound. Two prices tied together by contract or by physical reality, such as one futures month and the next, or crude oil and the products refined from it.
- An economic link. Two share classes of one company, two firms in one business, two points on a yield curve.
A reversion pattern found in a backtest with no mechanism behind it is usually noise. It tends to disappear on data the rule has not seen.
Where it has shown up, and where it has not
These are patterns reported in published research and widely observed. They are not results of our own testing, and they change over time.
- Individual stocks. Reversal over days to about a week (Lehmann, 1990; Lo and MacKinlay, 1990). Over three to twelve months the tendency flips to momentum. Over three to five years it flips back to reversal (De Bondt and Thaler, 1985).
- Broad stock indices. Short-term pullback rules have looked strong on large US indices in recent decades. Before about 1990, daily index moves tended to continue rather than reverse. Same market, different era.
- Volatility indices. Among the most strongly reverting series there are. The index itself cannot be held, though, and the futures that track it carry roll costs and violent spikes.
- Spreads and pairs. They revert while the link between the two legs holds. When it breaks, through a merger, a change of regime or a crowded unwind like August 2007, the spread keeps widening.
- Currencies. Some ranging within the day, and slow reversion toward purchasing power parity measured in years. In between, trend and carry tend to dominate.
- Commodities. Outright prices tend to trend, which is why trend followers have long favoured them. Spreads held in place by physical arbitrage are a different matter.
- Crypto assets. Some reversal within the day. At daily and longer horizons, mostly trend.
Notice that the horizon matters as much as the market. One stock can revert over a week, trend over a year and revert again over five.
Costs decide more than the pattern does
Short-horizon reversion trades often. Every trade pays the spread and some slippage, and in small or thinly traded markets those costs can consume the whole effect. A reversion test without honest costs tells you very little.
The shape of the risk
Reversion rules usually produce many small winning trades and an occasional large loss. The large loss arrives when the deviation was not a deviation at all, but the start of a trend. A backtest that skips crisis periods, or charges no costs, flatters this shape badly. Know before you start what a run of those losses would look like, and decide in advance what you will do when it comes.
How to check before you build on it
Test each market, and each horizon, on its own:
- A stationarity test, such as the augmented Dickey-Fuller test, or a cointegration test for a pair. It asks whether the series drifts away or keeps coming back.
- The Hurst exponent. Below 0.5 leans toward reversion, above 0.5 toward trend. It is noisy on short samples, so treat it as a hint.
- A variance ratio at your intended holding period. A ratio below 1 suggests reversion at that horizon.
- The half-life from an Ornstein-Uhlenbeck fit, which tells you how long a typical deviation takes to shrink by half. If that is longer than you are willing to hold, the reversion may be real and still of no use to you.
Then run the full rule, with costs, on data it has never seen.
The short version
Mean reversion is not a law of markets. It is a behaviour that some markets show, at some horizons, for as long as the reason behind it lasts. Test for it every time. Never carry it from one market to another on trust.
Written for people building their own systematic portfolio management process. Nothing here is a recommendation to buy or sell anything. See the disclaimer.