Fama french

What Is Fama French?

The Fama French model is a prominent asset pricing model that expands upon traditional financial theories by identifying additional factors that explain asset returns beyond overall market risk. It represents a significant contribution to portfolio theory and asset pricing. Introduced by Nobel laureate Eugene Fama and his colleague Kenneth French, the model posits that certain characteristics of companies—specifically, their size and value—systematically influence their stock returns. The Fama French model helps investors and analysts understand why some stocks historically tend to outperform others, offering a more nuanced view than single-factor models.

History and Origin

The Fama French model emerged from the empirical observations of Eugene Fama and Kenneth French in the early 1990s. Their seminal work in 1992, "The Cross-Section of Expected Stock Returns," challenged the prevailing Capital Asset Pricing Model (CAPM) by demonstrating that market beta alone could not fully explain the variations in stock returns. Fama and French identified two additional factors that historically appeared to drive returns: firm size and book-to-market equity ratio (a proxy for value).

T⁵⁸heir research provided a framework for why certain types of stocks, namely small-cap stocks and value stocks, have historically generated higher average returns than the broader stock market. Eugene Fama's foundational work in asset pricing, which included the development of the Fama French model, contributed to him sharing the Nobel Memorial Prize in Economic Sciences in 2013.

#⁵⁵, ⁵⁶, ⁵⁷# Key Takeaways

• The Fama French model expands on traditional asset pricing by including factors beyond market risk.
• ⁵⁴ The original three-factor model incorporates market risk, company size (SMB), and value (HML) to explain stock returns.
• ⁵³ Small-cap stocks and value stocks have historically tended to outperform large-cap and growth stocks, respectively, as highlighted by the model.
• ⁵² The model is widely used in quantitative analysis for portfolio construction, performance attribution, and evaluating investment strategies.
• ⁵⁰, ⁵¹ Later extensions, such as the five-factor model, added profitability and investment factors for a more comprehensive explanation of returns.

Formula and Calculation

The most widely known version, the Fama French three-factor model, extends the CAPM by adding two extra factors: size (Small Minus Big, SMB) and value (High Minus Low, HML). The model's formula for the expected return of an asset is:

$R_i - R_f = \alpha_i + \beta_M (R_M - R_f) + \beta_{SMB} SMB + \beta_{HML} HML + \epsilon_i$

Where:

• ( R_i ): The expected return of stock or portfolio i.
• ( R_f ): The risk-free rate of return (e.g., the yield on short-term government bonds).
• ( R_M ): The expected return of the overall market portfolio.
• ( R_M - R_f ): The market risk premium, representing the excess return of the market over the risk-free rate.
• ( \alpha_i ): The alpha (or intercept), representing the asset's excess return not explained by the model's factors. In a perfectly efficient market, this would ideally be zero.
• ( \beta_M ): The sensitivity of the asset's return to the market risk premium, similar to the beta in CAPM.
• ( SMB ): The Small Minus Big factor, representing the historical excess return of small-cap stocks over large-cap stocks. It captures the size premium.
• ⁴⁸, ⁴⁹ ( \beta_{SMB} ): The sensitivity of the asset's return to the size factor.
• ( HML ): The High Minus Low factor, representing the historical excess return of value stocks (high book-to-market ratio) over growth stocks (low book-to-market ratio). It captures the value premium.
• ⁴⁶, ⁴⁷ ( \beta_{HML} ): The sensitivity of the asset's return to the value factor.
• ( \epsilon_i ): The error term, representing the unexplained portion of the asset's return.

The SMB and HML factors are constructed from portfolios of stocks categorized by size and book-to-market ratios. These factors, along with the market risk premium, are typically obtained from historical data provided by academic sources like Kenneth French's data library.

#⁴⁵# Interpreting the Fama French Model

Interpreting the Fama French model involves understanding the coefficients ((\beta)) assigned to each factor. These coefficients indicate a portfolio's or security's sensitivity to market, size, and value premiums.

• Market Beta ((\beta_M)): This coefficient is similar to the beta in the CAPM and measures the sensitivity to overall market movements. A higher (\beta_M) suggests the asset's returns are more volatile than the market.
• SMB Beta ((\beta_{SMB})): A positive (\beta_{SMB}) indicates that the asset's returns tend to be higher when small-cap stocks outperform large-cap stocks. Conversely, a negative (\beta_{SMB}) implies a tendency to move with larger companies. Investors interested in exposure to smaller firms might seek assets with a higher positive (\beta_{SMB}).
• HML Beta ((\beta_{HML})): A positive (\beta_{HML}) suggests that the asset's returns are positively correlated with the performance of value stocks relative to growth stocks. A negative (\beta_{HML}) would mean the asset tends to perform better when growth stocks outperform. Investors pursuing value investing strategies would generally look for assets with a higher positive (\beta_{HML}).

The Fama French model's strength lies in its ability to explain a significant portion of the variation in diversified portfolio returns—often exceeding 90% in empirical studies, compared to around 70% for the CAPM. The ⁴⁴remaining unexplained portion, or alpha, can then be attributed to unique, security-specific factors or the skill of a portfolio manager.

Hypothetical Example

Imagine an investor, Sarah, wants to evaluate a mutual fund's performance over the past year. Instead of just comparing it to a broad market index, she uses the Fama French three-factor model.

Assume the following annualized data for the past year:

• Risk-free rate ((R_f)) = 2%
• Market return ((R_M)) = 10%
• SMB factor (Small Minus Big) = 4% (meaning small caps outperformed large caps by 4%)
• HML factor (High Minus Low) = 3% (meaning value stocks outperformed growth stocks by 3%)
• The mutual fund's actual return ((R_i)) = 15%

Sarah runs a regression analysis of the mutual fund's historical excess returns against the historical market excess returns, SMB, and HML factors to determine its sensitivities ((\beta) coefficients). Let's say her analysis yields the following sensitivities for the fund:

• Market Beta ((\beta_M)) = 1.1
• SMB Beta ((\beta_{SMB})) = 0.5
• HML Beta ((\beta_{HML})) = 0.8

Now, Sarah can calculate the expected return of the fund according to the Fama French model:

1. Calculate Market Risk Premium: ( R_M - R_f = 10% - 2% = 8% )
2. Calculate Expected Excess Return:
   ( \beta_M (R_M - R_f) = 1.1 \times 8% = 8.8% )
   ( \beta_{SMB} SMB = 0.5 \times 4% = 2.0% )
   ( \beta_{HML} HML = 0.8 \times 3% = 2.4% )
3. Sum the factor contributions: ( 8.8% + 2.0% + 2.4% = 13.2% )
4. Add back the risk-free rate to get the expected total return: ( 13.2% + 2% = 15.2% )

According to the Fama French model, the expected return for a portfolio with these characteristics, given the observed market, size, and value premiums, would be 15.2%. Since the fund's actual return was 15%, the fund slightly underperformed its Fama French model-derived expected return by 0.2% ((15% - 15.2% = -0.2%)), implying a small negative alpha. This suggests that while the fund captured expected returns from market, size, and value exposures, it did not generate significant additional returns beyond what these risk factors would predict.

Practical Applications

The Fama French model has several practical applications in investment management and financial analysis:

• Portfolio Construction: Investors can use the Fama French model to intentionally tilt their portfolios towards certain factors. For instance, if an investor believes in the continued outperformance of small-cap or value stocks, they can construct a portfolio with higher positive exposures to the SMB and HML factors. This informs a targeted investment strategy aimed at capturing these specific premiums.
• ⁴², ⁴³Performance Attribution: The model allows analysts to break down a portfolio's returns into components attributable to market exposure, size exposure, and value exposure. This helps in understanding what truly drove a portfolio's performance and whether a manager's returns were due to skill (true alpha) or merely exposure to these recognized factors. Dime⁴¹nsional Fund Advisors, for example, is known for its investment approach rooted in Fama and French's research, focusing on systematic exposure to these factors.
• ⁴⁰Investment Product Design: Many exchange-traded funds (ETFs) and mutual funds are designed as "factor-tilted" or "smart beta" products that aim to capture the premiums identified by the Fama French model and its extensions. These products provide investors with systematic ways to access specific factor exposures like value or size.
• Cost of Equity Estimation: Companies can use the Fama French model to estimate their cost of equity, providing a more refined figure than the CAPM by acknowledging the impact of size and value characteristics on expected returns.
• Academic Research: The model remains a cornerstone of academic finance, serving as a baseline for new research into asset pricing anomalies and the development of more complex multi-factor models.

Limitations and Criticisms

Despite its widespread acceptance and empirical success, the Fama French model, particularly the three-factor version, has faced several limitations and criticisms:

• Missing Factors: One of the most significant criticisms is that the three-factor model does not capture all relevant aspects of stock returns. Critics argued it failed to fully explain phenomena like the momentum anomaly (the tendency for stocks that have performed well recently to continue performing well, and vice versa). This³⁸, ³⁹ led Fama and French themselves to expand the model. In 2014, they introduced a five-factor model by adding two new factors: profitability (Robust Minus Weak, RMW) and investment (Conservative Minus Aggressive, CMA). This five-factor model aims to provide a more comprehensive explanation of average stock returns.
• ³⁶, ³⁷Empirical vs. Theoretical Basis: Some critics argue that the model is largely empirical—identifying factors that historically worked—rather than being fully grounded in strong economic theory for why these factors should be persistent sources of risk premium. While Fa³⁴, ³⁵ma and French explain these factors through rational risk-based arguments (e.g., small and value firms might be riskier), behavioral finance proponents suggest that these premiums could also arise from investor biases or market inefficiencies.
• Fa³², ³³ctor Definitions and Robustness: The construction of the SMB and HML factors relies on specific sorting methodologies (e.g., market capitalization, book-to-market ratio). The exact definitions and robustness of these factors have been debated, especially regarding their performance in different markets or over varying time periods.
• Ti³¹me-Varying Premiums: The premiums associated with size and value factors are not constant over time and can vary significantly, sometimes leading to periods of underperformance for factor-tilted portfolios.
• La³⁰ck of Universality: While effective in developed markets, the model's explanatory power can vary when applied to emerging markets, sometimes showing that the size factor performs less effectively.

Even th²⁹e expanded five-factor model still faces critiques, particularly for its exclusion of the momentum factor and for certain robustness issues with the new profitability and investment factors.

Fama²⁷, ²⁸ French vs. Capital Asset Pricing Model (CAPM)

The Fama French model and the Capital Asset Pricing Model (CAPM) are both fundamental concepts in asset pricing, but they differ significantly in their approach to explaining asset returns.

The primary difference lies in the number of risk factors considered. While CAPM assumes that a single market beta is sufficient to explain asset returns, the Fama French model asserts that company size and value characteristics also systematically influence returns. Empirical studies often show that the Fama French model provides a better fit for observed stock returns compared to CAPM, with higher R-squared values indicating greater explanatory power.

FAQs

⁹, ¹⁰, ¹¹

What are the main factors in the Fama French model?

The original Fama French three-factor model includes three main risk factors: the market risk premium (the excess return of the market over the risk-free rate), the size factor (Small Minus Big, SMB), and the value factor (High Minus Low, HML). The expanded five-factor model adds profitability (Robust Minus Weak, RMW) and investment (Conservative Minus Aggressive, CMA) factors.

Why ⁷, ⁸was the Fama French model developed?

The Fama French model was developed to address the shortcomings of the Capital Asset Pricing Model (CAPM), which empirically failed to explain certain patterns in stock returns, particularly the higher average returns observed in small-cap stocks and value stocks. It sought to provide a more comprehensive explanation of how expected returns are determined.

How ⁶is the Fama French model used in practice?

In practice, the Fama French model is used by financial professionals for several purposes. It helps in evaluating the performance of investment portfolios and managers by identifying how much of their returns are attributable to exposure to the market, size, and value factors versus true alpha. It also guides the construction of "factor-tilted" portfolios, where investors intentionally emphasize small-cap or value stocks in their investment strategy to potentially capture associated premiums.

Is t⁴, ⁵he Fama French model still relevant today?

Yes, the Fama French model remains highly relevant in modern finance. While it has evolved with new factors (like the five-factor model) and faces ongoing academic debate, its core insight—that market, size, and value are significant drivers of stock returns—is widely accepted and applied. It forms the basis for much of today's quantitative investing and factor-based investing approaches.

Does the², ³ Fama French model predict future returns?

The Fama French model is primarily an explanatory model, meaning it helps to understand what has historically driven returns. While it identifies factors that have been associated with higher average returns over long periods, it does not guarantee future performance or provide precise short-term return predictions. It's used to decompose and attribute past returns and inform long-term portfolio construction based on historical factor premiums.¹