Factor Investing

Factor Investing

Core Concepts

From CAPM to Multifactor Models

CAPM prices a single source of risk: E(R_i) - R_f = beta * (E(R_m) - R_f). Persistent anomalies — small caps, cheap (high book-to-market) stocks, and recent winners earning more than beta predicts — motivated adding factors. Fama-French (1993) added size and value to the market factor (3-factor model); Carhart (1997) added momentum; Fama-French (2015) added profitability and investment (5-factor model):

R_i - R_f = alpha + b_MKT*MKT + b_SMB*SMB + b_HML*HML [+ b_RMW*RMW + b_CMA*CMA] [+ b_UMD*UMD] + epsilon

The key reinterpretation: a manager's CAPM alpha may be nothing more than static factor exposure. Alpha only means skill after controlling for the factors an investor could buy cheaply. Single-factor OLS mechanics, t-statistics, and the CAPM regression itself live in the statistics-fundamentals skill; this skill generalizes to K regressors and interprets the output.

The Canonical Factors

*Approximate annualized US long-short premia over the 1963-2024 sample, Ken French data library, as of 2026. Long-run averages, not forecasts; realized decade-long stretches deviate wildly (see cyclicality below).

The rationale matters for durability: risk-based premia should persist (someone must bear the risk); behavioral premia survive only while limits to arbitrage prevent them from being competed away — and are more vulnerable to crowding.

Reading a Factor Regression

Run OLS of fund excess returns on the factor return series. Interpret:

• Loadings (b_k): exposure per unit of factor. b_HML = 0.45 means the fund behaves like it holds a 0.45-weight position in the value long-short portfolio. Judge each by its t-stat (|t| above roughly 2 for 5% significance).
• Alpha: average return unexplained by the factors — the only defensible claim to skill. A positive alpha with |t| < 2 is not evidence of skill (see statistics-fundamentals on t-statistics); most funds' alpha turns insignificant once value or momentum loadings are added.
• R-squared: fraction of return variance the factors explain. Diversified equity funds typically show R-squared of 0.90-0.99 against 3-4 factors. Use adjusted R-squared when comparing models with different factor counts — R-squared mechanically rises with every added regressor.
• Stability: run rolling windows; loadings that drift signal style drift or factor timing rather than a stable tilt.

Alpha Decomposition and Closet-Index Detection

Two complementary uses of the same regression:

1. Expected-return decomposition: E(R) = R_f + sum(b_k * lambda_k), where lambda_k are assumed factor premia. This tells you what the fund should earn from its exposures alone; realized excess return minus the factor-implied excess is the manager's implied alpha. If the implied alpha is near zero, the fund is a factor portfolio you could replicate with cheap factor ETFs.
2. Closet-index screen: a fund charging active fees while hugging its benchmark. Returns-based red flags: benchmark regression R-squared >= 0.98 and annualized tracking error <= 2%. The holdings-based analog is active share below ~60% (Cremers and Petajisto 2009). Then compute the breakeven Information Ratio: IR_breakeven = (fund fee - index fee) / tracking error. A closet indexer needs an implausibly high IR on a tiny active-risk budget just to earn back its fee gap (Information Ratio itself is covered in performance-metrics).

Smart-Beta Product Evaluation

Treat every smart-beta product as a factor portfolio (the equities skill's rule) and evaluate the implementation, not the marketing name:

• Factor purity: regress the product on the academic factors. A "value" ETF with b_HML = 0.15 and b_MKT = 1.0 is expensive beta; look for the target loading to be significant and dominant, and for unintended loadings (e.g., a value fund's negative momentum exposure) to be modest.
• Turnover: momentum needs high turnover to exist (~100%+/yr); value needs little (~15-25%/yr). Turnover far above what the factor requires is cost drag; far below means stale exposure.
• Capacity: size and momentum degrade fastest with assets (small, illiquid names; high turnover). Mega-cap value and quality scale best.
• Fees vs implementation quality: the question is never "is 0.25% cheap?" but "what loading per basis point?" A 0.15% fund delivering b_HML = 0.20 is worse value than a 0.30% fund delivering b_HML = 0.50.

Long-Short Academic Factors vs Long-Only Tilts

Published premia are measured on long-short, often leverage- and shorting-unconstrained portfolios rebalanced without costs. A long-only implementable tilt:

• captures roughly half of the paper premium (the short side, where mispricing is often larger, is unavailable; the overlap with the market portfolio dilutes the tilt);
• has loadings well below 1.0 on the academic factor (long-only value funds typically show b_HML of 0.3-0.5, not 1.0);
• pays real transaction costs and taxes the backtest ignored.

Scale expectations accordingly: a long-only value tilt with b_HML = 0.4 against a 2.5-3% premium is worth roughly 1.0-1.35%/yr before costs, not the headline long-short number.

Factor Cyclicality and the Danger of Factor Timing

Every factor endures multi-year droughts: US value underperformed growth for roughly the 2017-2020 stretch, with a relative drawdown deep enough to end careers, before rebounding sharply in 2021-2022. Momentum crashes violently in sharp reversals (2009). Because droughts are long and turning points are unforecastable, factor timing — rotating into "cheap" factors — has a poor live record and adds turnover. The defensible uses of cyclicality are (a) diversifying across factors with low mutual correlation (value and momentum are natural complements) and (b) sizing tilts so the investor can survive a decade-long drought without capitulating at the bottom.

The Factor Zoo, Crowding, and Replication

Hundreds of "significant" factors have been published — Cochrane's "factor zoo." Treat the zoo skeptically:

• Multiple testing: with hundreds of researchers mining the same data, t = 2 is far too weak; Harvey, Liu, and Zhu (2016) argue newly proposed factors should clear t > 3.
• Post-publication decay: McLean and Pontiff (2016) find anomaly returns roughly one-third lower out-of-sample and one-half lower post-publication — partly data-mining, partly investors crowding in and arbitraging the premium away.
• Crowding: popular factor trades unwind together under stress (August 2007 "quant quake"). Valuation spreads on a factor widening or compressing sharply indicate crowding in or out.
• Default to the handful of factors with decades of out-of-sample, out-of-country evidence and an economic rationale (market, value, momentum, profitability, size — in roughly that order of robustness); assume any newly marketed factor delivers materially less than its backtest.

Key Formulas

Worked Examples