Mean Reversion and Statistical Arbitrage › Summary

This chapter developed the theory and practice of mean reversion and statistical arbitrage, from the fundamental economic mechanisms that create mean reversion to the practical implementation of trading strategies that exploit it.

Key concepts covered include:

• Mean reversion fundamentals: The Ornstein-Uhlenbeck process provides a mathematical framework for mean-reverting dynamics, with the mean reversion speed $\kappa$ determining how quickly deviations correct.

• Testing for mean reversion: The Augmented Dickey-Fuller test distinguishes mean-reverting series from random walks, essential for validating trading strategies.

• Cointegration: Two non-stationary series are cointegrated if a linear combination is stationary. The Engle-Granger and Johansen procedures test for cointegration and estimate hedge ratios.

• Pairs trading: The classic mean reversion strategy trades the spread between cointegrated securities using z-score signals, going long when the spread is unusually low and short when unusually high.

• Statistical arbitrage portfolios: Factor-neutral construction using PCA isolates idiosyncratic returns while hedging common factor exposures, which allows diversification across many small mean reversion bets.

• Regime risk: Relationships can permanently break, causing mean reversion strategies to accumulate losses. Stop losses, position limits, and correlation monitoring help manage this risk.

• Practical challenges: Transaction costs, execution risk, model instability, and capacity constraints limit strategy profitability.

The next chapter examines trend following and momentum strategies, which take the opposite view from mean reversion. Rather than betting against price movements, momentum strategies bet that recent trends will continue, exploiting a different market inefficiency entirely.