Pairs trading on a single pair is exposing. A single convergence bet can fail due to idiosyncratic events — a takeover, a regulatory ruling, a blow-up specific to one stock. Scaling pairs trading to hundreds of simultaneous positions diversifies this risk: when many independent pairs mean-revert simultaneously, individual failures are absorbed by winners. But managing hundreds of pairs independently is impractical; what is needed is a single framework that applies to every stock at once.
The factor-residual decomposition solves this. Every stock's return is explained by shared risk factors; what remains is idiosyncratic. The idiosyncratic residual is the spread in this framework — not between two specific stocks, but between a stock and its factor-model fitted value. This is the Avellaneda-Lee approach: trade the entire universe by trading each stock's idiosyncratic residual against its factor benchmark.
Learning objectives. By the end of this note you should be able to:
- state the factor-residual decomposition and identify the systematic and idiosyncratic components;
- explain why the idiosyncratic residual is the natural "spread" in the universe-wide framework;
- describe the two sources of risk factors: PCA eigenportfolios and ETFs;
- outline the Avellaneda-Lee strategy pipeline from factor model to S-score signal;
- relate the universe-wide approach back to the pairs framework as a special case.
In this lesson
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- From pair to universe: the scaling problem
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- The factor-residual decomposition
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- Factor sources: eigenportfolios vs ETFs
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- The Avellaneda-Lee pipeline
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- Relation to pairs trading
Before you start
- APT Factor Models for Pairs Construction: The Multifactor Approach
- Market Neutrality and the Relative Value Idea
The full lesson, with worked examples and exercise solutions, is for members.
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