Mean reversion

The bet that a price, or a combination of prices, has a level it returns to. One of the two camps chan-algorithmic-trading divides trading strategies into, and the one it spends four of eight chapters on.

The unit is often not a single instrument but a portfolio constructed to be mean-reverting even when its components aren’t: an ETF pair or triplet, an ETF against its component stocks, a currency pair, a futures calendar or intermarket spread. Two assets that both wander can hold a stable relationship, and the strategy trades the relationship.

The question is whether the series actually reverts

What separates this from a hunch is that the property is testable before any strategy is built. chan-algorithmic-trading names two families:

Is one series stationary? The augmented Dickey-Fuller (ADF) test, the Hurst exponent, the variance ratio test, and the half-life of reversion — the last being the practically useful one, since it says not only whether the series reverts but how long a trade must be held.

Do several series cointegrate? The cointegrated ADF test and the Johansen test, which ask whether a linear combination of instruments is stationary even though each leg is not. This is what justifies constructing the portfolio above rather than trading one symbol.

Chan’s stated aim is intuition over recipe — “what they are really testing and the simple mathematical equations behind them” — and he flags a preprocessing choice the tests are sensitive to: whether to use raw prices, log prices or ratios.

Trading it

Three approaches named, in increasing sophistication: a linear rule (position proportional to deviation), Bollinger bands (enter at a threshold in standard deviations), and a Kalman filter, which Chan singles out as useful “in multiple ways and in multiple strategies” — the natural fit, since a hedge ratio between two cointegrated legs is a hidden state that drifts.

He also flags two operational hazards specific to this camp: the pros and cons of scaling in (adding to a losing position, which is what mean reversion tells you to do and what risk management tells you not to), and the danger of data errors, which hit spread strategies hardest because a bad print on one leg looks exactly like the opportunity the strategy is hunting.

Why it stops working

Mean-reverting strategies decay for reasons the tests can’t see. chan-algorithmic-trading attributes recent difficulty to dark pools and high-frequency trading competing the edge away, and gives the case of a “hitherto very profitable ETF pair” unhinged by a fundamental change — where understanding the fundamentals both explains the break and suggests the repaired version. That is market-regime-analysis arriving from the strategy side: the statistical relationship was real and then the world changed underneath it.

The other camp: momentum

The sibling bet — that a move continues — gets two chapters (interday and intraday) to mean reversion’s four, and the excerpt this wiki holds cuts off mid-sentence on its main theme, so the corpus has the label and little else. What is named: statistical tests for time-series momentum, as the mirror of the stationarity tests above. ../machine-learning-wiki’s time-series-forecasting holds the general-purpose version of the same problem, and the algorithmic-trading taxonomy lists momentum alongside arbitrage, pairs/statistical arbitrage and market making. A momentum source is the obvious next gap in this corner.

Related

chan-algorithmic-trading · algorithmic-trading · backtesting · market-regime-analysis · market-making · synthesis