The history of asset pricing models is one of evolution. As anomalies are discovered, our knowledge advances and new models are developed.

Building on the work of Harry Markowitz, the trio of John Lintner, William Sharpe and Jack Treynor are generally given most of the credit for introducing the first formal asset pricing model, the capital asset pricing model (CAPM). It was developed in the early 1960s, and provided the first precise definition of risk and how it drives expected returns.

The CAPM looks at risk and return through a “one-factor” lens—the risk and return of a portfolio are determined only by its exposure to market beta. This beta is the measure of the equity-type risk of a stock, mutual fund or portfolio relative to the risk of the overall market. The CAPM was the financial world’s operating model for about 30 years.

With the publication of the 1992 paper “The Cross-Section of Expected Stock Returns” by Eugene Fama and Kenneth French, the CAPM was replaced by the Fama-French three-factor model, which added the size and value factors.

Mark Carhart, in his 1997 study, “On Persistence in Mutual Fund Performance,” was the first to use momentum, together with the Fama-French factors, to explain mutual fund returns, and the Carhart four-factor model became the new standard.

**Five Factors**

Then, Fama and French, in a new paper, “A Five-Factor Asset Pricing Model,” which appeared in the April 2015 issue of the Journal of Financial Economics, explored a five-factor asset pricing model.

Their objective was to determine whether two new factors—profitability (RMW, or robust-minus-weak profitability) and investment (CMA, or conservative-minus-aggressive investment)—first proposed by Kewei Hou, Chen Xue and Lu Zhang and later published in the 2015 study “Digesting Anomalies: An Investment Approach,” added explanatory power.

In other words, if Fama and French knew in 1992 (when they constructed their original three-factor model) what they know today, which would they have chosen?

Following is a summary of their findings:

- While a five-factor model doesn’t fully explain the cross section of returns (there are still anomalies), it provides a good description of average returns.
- The model’s main problem is its failure to explain the low average returns on small stocks that invest a lot despite low profitability. The Fama-French three-factor model, it turns out, has the same problem explaining the poor performance of small growth stocks.
- A four-factor model that excludes the value factor (HML, or high minus low) captures average returns as well as any other four-factor model they considered. A five-factor model including HML doesn’t improve the description of average returns over that of four-factor models, because the average HML return is captured by HML’s exposure to other factors. Thus, in the five-factor model, HML is redundant for explaining average returns.

Fama and French did note that “while the five-factor model doesn’t improve the description of average returns of the four-factor model that drops HML, the five-factor model may be a better choice in applications.

For example, though captured by exposures to other factors, there is a large value premium in average returns that is often targeted by money managers.” Thus, they write, “in evaluating how investment performance relates to known premiums, we probably want to know the tilts of the portfolios toward each of the factors.” They added: “For explaining average returns, nothing is lost in using a redundant factor.”

Importantly, Fama and French furthermore found that their five-factor model performs well. They write: “Unexplained average returns for individual portfolios are almost all close to zero.”

One of the authors’ more interesting discoveries is that “the lethal combination for microcaps is low profitability and high investment; low profitability alone doesn’t appear to be a problem.”

However, Fama and French found this problem doesn’t hold for large stocks with low profitability and high investment (note that passive portfolios may benefit from this knowledge by simply screening out stocks with these characteristics).