Factor Investing: Quantitative Risk Premia
Factor investing moves beyond the Capital Asset Pricing Model (CAPM) by identifying persistent drivers of return that explain the cross-section of equity returns. It treats asset classes as bundles of underlying risk factors.
1. Beyond CAPM: The Multi-Factor Framework
The classic CAPM assumes returns are driven solely by market beta (\beta):
E[R_i] = R_f + \beta_i(E[R_m] - R_f)
Factor investing utilizes the Arbitrage Pricing Theory (APT) framework, positing that returns are a linear function of multiple factors:
E[R_i] = R_f + \sum \beta_{i,j} \lambda_j
Where\beta_{i,j}is the exposure (loading) to factorj, and\lambda_jis the risk premium for that factor.## 2. The Fama-French 5-Factor Model
The foundational model for factor analysis is the Fama-French 5-Factor Model, which expands the original 3-factor model to include profitability and investment:
R_{it} - R_{ft} = \alpha_i + \beta_{i1}(R_{mt} - R_{ft}) + \beta_{i2}SMB_t + \beta_{i3}HML_t + \beta_{i4}RMW_t + \beta_{i5}CMA_t + \epsilon_{it}
- Market (R_m - R_f): Equity risk premium.* SMB (Small Minus Big): The Size premium. Small-cap stocks tend to outperform large-cap stocks over long horizons.
- HML (High Minus Low): The Value premium. Stocks with high book-to-market ratios (Value) outperform those with low ratios (Growth).
- RMW (Robust Minus Weak): Profitability factor. Firms with high operating profitability perform better.
- CMA (Conservative Minus Aggressive): Investment factor. Firms that invest conservatively outperform those with aggressive investment growth.
3. Key Factor Premiums and Math
3.1 Value (HML)
Value is a "cheapness" factor. It exploits behavioral biases (overreaction) and risk premia (distress risk).
- Proxies: P/B, P/E, EV/EBITDA, Cash Flow/Price.
- The Math: Portfolio is constructed by longing high B/M stocks and shorting low B/M stocks.
3.2 Momentum (WML)
The tendency for assets that have performed well in the recent past (3–12 months) to continue performing well.
- Calculation: 12-1 Momentum (Returns from month -12 to -2, excluding the most recent month to avoid short-term reversal).
- Persistence: Attributed to underreaction to news and herding behavior.
3.3 Quality and Volatility
- Quality: Focuses on low debt, stable earnings growth, and high margins.
- Low Volatility: The "Low Vol Anomaly"—low beta/low volatility stocks often provide higher risk-adjusted returns than high-risk stocks, contradicting basic CAPM.
4. Implementation: Smart Beta and Multi-Factor
Experts don't just "buy value"; they optimize for Factor Interaction.
- Top-Down: Weighting individual factor indices.
- Bottom-Up (Preferred): Scoring each security across multiple factors simultaneously to find stocks that provide "Value + Quality" exposure, reducing the risk of "Value Traps."
4.1 Rebalancing and Turnover
Factor premiums are not static. High-turnover factors like Momentum require careful transaction cost modeling.
Net\ Return = \sum (w_i \cdot r_i) - \text{Trading Costs} - \text{Market Impact}
5. Summary of Factor Premiums
| Factor | Description | Theoretical Driver |
|---|
| Value | Cheap relative to fundamentals | Distress risk / Behavioral overreaction |
| Size | Small market capitalization | Liquidity risk / Information asymmetry |
| Momentum | Trend persistence | Herding / Underreaction to news |
| Quality | Strong balance sheets/earnings | Barrier to entry / Management quality |
| Low Vol | Lower idiosyncratic risk | Leverage constraints / Lottery preference |
Factor investing requires a disciplined, rules-based approach to capture these premia while managing the significant periods of underperformance (cyclicality) inherent in any single factor.