Statistical arbitrage (stat arb) is a class of quantitative strategies that exploit temporary mispricings between related securities, expecting them to converge back to their historical relationship. The simplest form is pairs trading: find two stocks that historically move together (Coca-Cola and PepsiCo, for example), and when the spread between them widens beyond normal, go long the underperformer and short the outperformer. When the spread contracts back to normal, you profit from both sides. This is 'market neutral' because you're hedged against broad market moves — if the entire market crashes, your long and short positions offset each other.

The mathematical foundation of stat arb is cointegration, not correlation — a crucial distinction. Correlation measures whether two series move in the same direction. Cointegration measures whether two series maintain a stable long-run relationship, meaning their spread is mean-reverting. Two stocks can be highly correlated but not cointegrated (they trend together but the gap between them can wander). Cointegration means the spread will return to its mean — that's what makes the trade work. Testing for cointegration uses the Augmented Dickey-Fuller test or the Engle-Granger two-step method. The half-life of mean reversion (how long it takes the spread to revert halfway) determines whether the trade is practical — if the half-life is 200 days, your capital is tied up too long.

Modern stat arb operates at a scale far beyond simple pairs. Institutional stat arb portfolios might trade hundreds or thousands of stocks simultaneously, using principal component analysis (PCA) to identify the common factors driving returns and then trading the residuals — the idiosyncratic movements that should revert. This is sometimes called 'factor-neutral' stat arb because it hedges out not just market risk but all major systematic factors (size, value, momentum). The positions are typically held for 1-10 days with small per-trade profits and leverage of 4-8x to amplify the returns to meaningful levels.

The risks in stat arb are real and have caused some of the most dramatic blowups in hedge fund history. In August 2007, the 'quant quake' saw stat arb strategies across dozens of funds simultaneously unwind, causing massive losses across the industry as correlated positions were liquidated. The fundamental risk is regime change — historical relationships that seemed stable can break permanently due to regulatory changes, industry disruption, or structural market shifts. Crowding is another risk: when too many firms run similar stat arb strategies, the same positions are held by everyone, and when one fund liquidates, the cascade hits all of them. Stat arb remains profitable for the best quant firms, but it requires sophisticated risk management, continuous model updates, and deep infrastructure.