Factor Finance Model

The Fama-French factor model, a cornerstone of modern finance, extends the Capital Asset Pricing Model (CAPM) by incorporating factors beyond market risk to explain asset returns. While CAPM posits that only market risk (beta) drives expected returns, the Fama-French model argues that size and value premia also play significant roles.

The most widely recognized version is the three-factor model, introduced in 1993 by Eugene Fama and Kenneth French. It adds two factors to the market beta: Size (SMB) and Value (HML).

SMB (Small Minus Big) reflects the historical tendency for small-cap stocks to outperform large-cap stocks. It is calculated by subtracting the returns of large-cap portfolios from the returns of small-cap portfolios. This factor captures the 'size effect,' suggesting that smaller companies are inherently riskier or have unique growth opportunities not captured by market beta alone.

HML (High Minus Low) captures the 'value effect,' where value stocks (those with high book-to-market ratios) have historically outperformed growth stocks (those with low book-to-market ratios). HML is calculated by subtracting the returns of growth stock portfolios from the returns of value stock portfolios. Value stocks are often considered undervalued by the market, possibly due to financial distress or unpopularity, and thus offer a higher potential return as compensation for this perceived risk.

The Fama-French three-factor model is expressed as follows:

E(Ri) = Rf + βiMkt * (E(Rm) - Rf) + βiSMB * SMB + βiHML * HML

Where:

• E(Ri) is the expected return of asset i
• Rf is the risk-free rate
• βiMkt is the beta of asset i with respect to the market portfolio
• E(Rm) is the expected return of the market portfolio
• βiSMB is the beta of asset i with respect to the SMB factor
• SMB is the return of the SMB factor
• βiHML is the beta of asset i with respect to the HML factor
• HML is the return of the HML factor

The coefficients βiSMB and βiHML represent the asset's sensitivity to the size and value factors, respectively. A higher βiSMB suggests that the asset's return is more sensitive to changes in the performance of small-cap stocks relative to large-cap stocks. Similarly, a higher βiHML indicates a greater sensitivity to the performance of value stocks relative to growth stocks.

Later, a five-factor model was proposed, adding Profitability (RMW) and Investment (CMA) to the existing three. RMW (Robust Minus Weak) captures the tendency for more profitable firms to outperform less profitable firms. CMA (Conservative Minus Aggressive) reflects the tendency for firms with conservative investment strategies to outperform those with aggressive investment strategies. These additions further enhance the model's explanatory power, particularly in accounting for the profitability and investment patterns of firms.

Factor models are used in various applications, including portfolio construction, performance evaluation, and risk management. They help investors understand the sources of returns and construct portfolios that are aligned with their risk preferences. While these models are powerful tools, they are not without limitations. They rely on historical data, which may not be predictive of future performance. Furthermore, the underlying factors themselves may be subject to interpretation and debate.