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Statistical Arbitrage / The Factor-Residual Model and the S-Score

Overview

The pairs-trading framework of Topic 2 treats each pair in isolation. In practice, a stat-arb desk runs hundreds of simultaneous positions, and the central question shifts: how do you build a single, unified framework for identifying and sizing convergence bets across the entire stock universe, rather than one pair at a time?
The Avellaneda-Lee (2010) factor-residual model answers this by decomposing every stock's return into a component explained by a small number of statistical risk factors (PCA eigenportfolios or ETFs) and a residual idiosyncratic return. The residual is modelled as an Ornstein-Uhlenbeck process. The normalised OU deviation — the S-score — is a single comparable signal across the full cross-section: trade any stock whose S-score exceeds a threshold, sized by the OU equilibrium standard deviation.

By the end of this topic you should be able to:

  • decompose a universe of stock returns into PCA eigenportfolios and interpret the leading eigenvectors as market, sector, and style factors;
  • regress a stock's return onto the eigenportfolio returns and extract the idiosyncratic residual;
  • model the idiosyncratic residual as an OU process and calibrate κ\kappa, mm, and σ\sigma from the AR(1) regression on discretised residuals;
  • compute the S-score and apply the Avellaneda-Lee trading thresholds;
  • explain why the factor-residual model is an extension of the pairs approach to the full universe.

In this lesson

  1. Contents
  2. The big picture

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