2. Mean reversion and pairs trading: betting that the price comes back

Theory 6: A survey of real strategies

The family of strategies in the previous module bet that the recent move continues. The family in this one bets on exactly the opposite. And neither of them is wrong.

If momentum bets that the move continues, here the bet is that price, after straying too far from some reference point, tends to come back toward it.

This is mean reversion, and its most conceptually elegant application is pairs trading.

The premise: everything returns to its place

The premise of mean reversion is that many assets, or many relationships between assets, oscillate around a 'normal' or equilibrium level. And that extreme deviations from that level tend, over time, to correct.

There is the symmetry with the previous module. Momentum works best in sustained trends. Mean reversion works best in sideways or range-bound markets, precisely the scenario in which momentum suffers most.

The z-score: measuring how far it has strayed

A common way to operationalize this idea is the z-score, which measures how many standard deviations the current price has moved away from its recent mean.

• A z-score of +2 indicates that price is unusually high relative to its recent typical behavior. It suggests, without guaranteeing, a higher probability of a downward correction.
• A z-score of -2 suggests the opposite.

The more extreme the z-score, the stronger the potential reversion signal. But also the greater the risk of something uncomfortable. It may be that this time the asset is genuinely breaking out of its usual range for a real fundamental reason, and not through a simple temporary overreaction by the market.

That is the central risk of any mean reversion strategy. And the reason such strategies are almost always combined with some filter that rules out trading reversion during strong, clearly established trends.

Pairs trading: trading the distance, not the price

Pairs trading takes this idea a step further. It applies it not to the absolute price of a single asset, but to the relative relationship between two historically correlated assets. Two companies in the same sector, for example, whose businesses are exposed to very similar economic factors.

Instead of betting on the direction of either asset separately, the strategy trades the spread between them.

Suppose that spread moves unusually far from its historical behavior: one of the two stocks rises far more than the other, with no clear fundamental reason to justify it. The strategy responds with two simultaneous positions:

• Long the relatively lagging asset.
• Short the relatively advanced one.

The bet is that the spread converges back toward its historical relationship, regardless of whether the market as a whole rises or falls over that period.

That feature is called market neutrality. It is one of the reasons pairs trading appeals to managers seeking returns uncorrelated with the broad index. That is a diversification objective connecting directly with what we saw in the level devoted to risk and correlation.

Correlation is not enough: you need cointegration

The central statistical requirement of pairs trading is cointegration.

It is not enough for two assets to be correlated in the sense we saw earlier, that is, to move in the same direction frequently. The spread between them must also be stationary: it must oscillate stably around a constant mean over time, rather than drifting without limit in one direction or the other.

Two assets can be highly correlated without being cointegrated. Both rise over time, but the distance between them keeps growing.

Trading that pair as if it were mean-reverting, without first checking cointegration, is one of the most common ways for an apparently promising pairs trade to end up losing money steadily. The spread never comes back to the level the strategy assumed was 'normal'.

The risk the two of them share

Both pure mean reversion and pairs trading share a common structural risk: that this time the historical relationship breaks permanently because of a real fundamental change.

One company in the pair suffers a scandal. It changes its business model. Or it simply goes bankrupt.

At that point, 'betting that it comes back' stops being a statistically reasonable bet. It becomes holding a losing position against a genuine and durable trend: exactly the mistake that the trend following of the previous module is designed to avoid.