Fama-French Three Factor Model vs. Markowitz Portfolio Theory

Introduction to the Fama-French Three Factor Model

Eugene Fama and Kenneth French designed the Fama-French Three Factor Model to describe stock returns. The model uses three variables and extends the Capital Asset Pricing Model (CAPM) by adding two additional factors:

r = RF + β3(Km − Rf) + bs · SMB + bv · HML + ε

Where r is the portfolio's rate of return, RF is the risk-free return rate, and KM is the return of the whole stock market.

Over 90% of diversified portfolio returns are explained by the Fama-French Three Factor Model. It measures investment returns using an academic and mathematical approach. Consequently, "small cap" stocks and stocks with a high book-to-market ratio tend to provide greater returns than the general market. For Fama and French, high returns are a reward for high risk — meaning that if returns increase with price, stocks with a high price ratio should be more risky (Fama, 2005).

The market index weights stocks on the basis of market capitalization, making it valuation-blind and size-biased. Momentum is another factor explained by this reasoning. Momentum reflects the direction in which money flows. To take advantage of market efficiency, one may adjust an index with a momentum weighting after its initial construction.

The Fama-French model is used to explain the performance of portfolios via linear regression. The two additional factors provide two extra axes, so the regression effectively operates in four dimensions.

Portfolio theory deals with the value and risk of portfolios, in contrast to the FF model, which focuses on stock returns. It is often called Modern Portfolio Theory (MPT) or Markowitz Portfolio Theory.

Markowitz Modern Portfolio Theory

In contrast to the FF model, MPT holds that the volatility of a portfolio is less than the weighted average of the volatilities of its individual securities. It does not deal with individual securities in isolation; rather, its results concern the construction of efficient portfolios.

Despite offering a description of portfolio risk and return, Markowitz Portfolio Theory is not universally accepted. The theory analyzes how risks can be reduced and how wealth can be invested across assets, whereas the FF model focuses on stock returns. The FF model accepts higher risk in pursuit of higher returns, while MPT reduces risk through diversification.

Modern Portfolio Theory assumes that volatility defines risk. It states that investors are risk-averse — that is, they accept more risk only in exchange for higher payoffs, and prefer lower returns if it means a less volatile investment.

MPT attempts to maximize return for a given level of portfolio risk, or to minimize risk for a targeted level of expected return. It defines risk as the standard deviation of return, models a portfolio as a weighted combination of assets so that the portfolio's return is the weighted combination of each asset's returns, and models each asset's return as a normally distributed function (Markowitz, 1999).

MPT makes various assumptions about markets and investors. While these are not entirely accurate, each represents a reasonable approximation. The correlation, risk, and return measures used in MPT are based on expected values — mathematical statements about the future. It is also important to note that diversification decreases non-systematic risk while increasing systematic risk exposure relatively.

The factors SMB and HML mimic risk factors associated with book-to-market ratio and firm size. SMB (Small Minus Big) is the average return of a long position in portfolios containing small-cap stocks minus a short position in portfolios containing large-cap stocks. HML (High Minus Low) is the average return of a long position in portfolios with value stocks minus a short position in portfolios with growth stocks.

There are many different kinds of factor-based analysis (FBA), but the best-known and most powerful is the three-factor model of Fama and French.

Advantages and Disadvantages of the FF Model

Research has found that the Fama-French model lacks a formal financial theory to support the effect of its new variables on return rates. The SMB and HML variables were identified empirically — through analysis of observed relationships between those variables and return rates — rather than derived from theory. Moreover, the risk factors in the stock market may include additional variables beyond size and value effects.

Additionally, CAPM has an advantage in being a more general and straightforward method. The Fama-French model is comparatively more complex in its application (Kosowski, Timmermann, Wermers, and White, 2006).

Factor analysis combines two or more variables into a single factor. Factors are typically selected by grouping related items, which simplifies the analytical framework.

Factor analysis reveals how interrelated variables are connected to one another, making it easier to identify patterns in complex datasets.

Factor analysis is only as reliable as the data it uses. When researchers rely on less valid or less reliable measures — such as self-reports — this introduces problems into the analysis.

Factor analysis interpretation is based on the use of heuristics — convenient solutions that are not absolutely certain. Because multiple interpretations of the same data are possible, factor analysis cannot definitively identify causality (Kosowski, Timmermann, Wermers, and White, 2006).