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Risk Factors, Fama-French 4 Factor Model

Risk Factors, Fama-French 4 Factor Model

The Fama-French factor model is rooted in the idea that risk factors, such as fundamental macroeconomic factors, can outperform the market.  When such factors or anomalies persist, markets lack perfect efficiency, and investment opportunities exist outside of the market portfolio.


The Capital Asset Pricing Model is a financial model, which calculates expected returns as a function of the risk-free rate, market risk, and market returns.  Central to this model is the idea that returns are solely dictated by systematic risk.  That is, if all market participants hold similar beliefs about expected returns and the dispersion of returns, then only increases or decreases in market risk will change portfolio returns.

While the idea behind the CAPM seems generally okay, I have some issues with it.  Deep down, the CAPM relies on a static beta, which is a correlation measure between stocks and the market.  Unfortunately, historical measures of individual stocks’ market correlation are fluid, so the robustness of the model is suspect.  Furthermore, market participants hold a variety of risk tolerances, time horizons, and investment constraints.  This assortment of characteristics differs from the CAPM’s primary tenet.

Fama-French 3 Factor Model

In 1993, Fama and French challenged the CAPM idea that market risk was the only determinant of returns.  Instead, Fama and French argued that risk factors, such as style and size of companies, could be used to enhance portfolio returns for a given level of risk.  Style, which can be measured as a company’s book-to-market ratio, historically favors value stocks (low book-to-market) over growth stocks (high book-to-market).  For example, over many years, a group of cash cow, well known companies will have better stock returns than trendy start-up companies with high expectations.  Size, which is measured by market capitalization, historically favors smaller companies over large companies.  For example, over many years, smaller, niche player companies will have better stock returns than larger, established companies.

Fama and French took the CAPM market factor and added style and size to create the Fama-French 3 Factor Model.  Here, the style factor is calculated as high value stocks minus low value stocks, and the size factor is calculated as small stocks minus big stocks.  In other words, the style factor buys value stocks while shorting growth stocks, and the size factor buys small cap stocks while shorting large cap stocks.

Using data from Ken French’s website, one can replicate empirical data behind the conclusion.  Since 1927, the Fama-French 3 Factor Model (blue line) has outperformed the market portfolio (red bars).  Look at the gap between the blue line and red bars.

In the graph, three particular time periods show noteworthy outperformance.  In 1943-45, both style and size contributed significant outsized gains.  From 1963-68, style (value) outperformed for a few years, then size (small stocks) outperformed in the later years.  Lastly, small cap stocks dominated large cap stocks from 1975-83 while value stocks beat growth stocks from 1981-84.  Among these three time periods, no attribute singlehandedly dominated.  The risk factors are successful in combination and over a series of years.

Value seems to persist because of investor behaviors.  Investors tend to over-extrapolate past growth rates into the future and bid up prices to the point of excessive optimism; this optimism does not always materialize, and prices retreat.  Thus, returns of growth stocks tend to be less than returns of value stocks.  This anomaly persists because a multi-year time horizon is generally necessary to capture the value opportunity.  Since fund managers are evaluated on monthly, quarterly, and annual bases, the euphoric competition for short term excessive returns creates a structural opportunity for value investing.

Style persists because of the amount of information needed to be processed.  Thousands of small, publicly traded stocks exist, and finding winners among the group requires a herculean effort.  Here too, fund managers play a role by tending to guard their reputation.  If a fund manager does poorly by investing in well known companies like Apple, Exxon Mobil, and Wal-Mart, his misfortune may be excused as just a market downturn.  Yet, if the manager unsuccessfully invests in smaller companies that few people have heard of, he will be considered aloof for investing in such losers.  Thus, feasibility and reputation risk are likely to favor the style attribute going forward.

Fama-French 4 Factor Model

Also in 1993, Jegadeesh and Titman found that adding a fourth factor, momentum, to the market-style-size model also enhanced portfolio returns for a given level of risk.  Momentum is calculated by investing in firms that have increased in price while selling firms that previously decreased in price (winners minus losers).  Today, the four factors of market, style, size, and momentum, constitute the Fama-French 4 Factor Model.