Decomposition✓ Mathematical
◆ The PatternDecompose returns into systematic factor exposures
CAPM uses a single factor (market beta). The Fama-French three-factor model adds size and value. Modern models include momentum, quality, and low-volatility.
ri = αi + β1F1 + β2F2 + … + εi
Factor tilts explain most of long-only active returns. Pure alpha — returns unexplained by any factor — is exceedingly rare.
// Factor decomposition — beta exposures
| Factor | Premium Source |
|---|---|
| Market (β) | Equity risk premium |
| Size (SMB) | Small-firm illiquidity |
| Value (HML) | Distress / behavioral |
| Momentum | Under-reaction |
Pattern bridge: Regression and betas are explored in The Toolkit — Regression.