A Five-factor Asset Pricing Model

In 1993 Eugene Fama and Kenneth French came up with a new model in order to improve the capital asset pricing model (CAPM), which was the three-factor model which compare to CAPM included two additional factors, size, and value. Even though the three-factor model was a great upturn, it was not capable of explaining some anomalies nor the cross-sectional variation in expected returns particularly related to profitability and investment.

This paper is about the introduction of 2 new factors by the Fama and French in the older model. The one factor is about the profitability and the other for the investment. The incentive was Novy-Marx et al (2013) and similar papers which had spotted that it could be further improved.The first part of this work is about the methodology that Fama and French used and how they came up with the five-factor model. At the second part of my work, I will oppose and discuss if this new model is useful to practitioners and the application of this model in comparison with his older brother.metrology data from many research show that stock returns are related to the book-to-market equity ratio as well as to profitability and investment.

As a starting point, the authors use the dividend discount model to explain why these variables are related to average returns. With a bit of manipulation based on the dividend discount model, the authors are able to extract two additional factors, profitability, and investment, to add to their three-factor model. They define profitability as operating profit minus interest expense divided by book equity, and they measure investment as the change in total assets divided by total assets. The authors test how the five-factor model performs in 2 basic steps. In their work FF (2014) they compare if the new model is performing better than the old one when it is used to explain average returns related to prominent anomalies not targeted by the model. Farma and French also tried to explain if model failures are related to shared characteristics of problem portfolios. They run empirical tests to check if the five-factor model and relative ones can explain average returns on portfolios formed to produce large spreads in Size, B/M, profitability, and investment. Their starting point in that was to examine the Size, B/M(Book to Market), profitability, and investment patterns in average returns. In order to examine which factors construction are important in tests of asset pricing models, Fama and French used 3 sets of factors.

The first set is the classic three-factor model of FF (1993) and defining the profitability and investment factors as a value factor in this model. The second is the four-factor model and the last one was the five-factor model. The study of the authors, covers 606 months of data, from July 1963 to December 2013, which includes an additional 21 years of new data from when their archetypal three-factor model was published in 1993. Using NYSE market-cap breakpoints, at the end of each June, stocks are allocated to various size groups. The other factors (i.e., value, operating profit, etc.) are segregated within their respective categories and ranked from low to high. The authors calculate the excess monthly returns of the factor portfolios over the one-month Treasury bill rate. Finally, they measure the standard deviations, t-statistics, correlations, regression intercepts, coefficients, and slopes of the portfolios they construct to analyze the data.

Discussion and analysis

The main objective of this paper 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. There are three main findings in this work. Firstly the five-factor model does not fully explain the cross-section of returns but it describes fair enough the average returns. Secondly, the main flow of this model is the inability to explain the low average returns on small stocks that invest a lot despite low profitability. Lastly, a four-factor model that excludes the value factor (HTML, or high minus low) captures average returns as well as any other four-factor model they considered. Having under consideration HTML in the five-factor model does not improve average returns over that of four-factor models, because the average HTML return is captured by HML’s exposure to other factors. Thus, in the five-factor model, HTML is redundant for explaining average returns. Today the five-factor model may be becoming the new workhorse asset pricing model in finance. Furthering its case, Fama and French have now provided an out-of-sample test of their model with the study "International Tests of a Five-Factor Asset Pricing Model," which was published in the March 2017 issue of the Journal of Financial Economics.

Fama and French concluded: "In short, all ?ve factors are important for describing NA average returns for 1990-2015." In other regions, not all factors are important. However, they note: "We would not be surprised to ?nd that factors that are redundant for describing average returns in one period are important in another."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 HTML, 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 are 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).

All asset pricing models, by definition, are flawed or wrong. If such models were perfectly correct, they would be laws (such as the laws we have in physics). But that doesn’t mean asset pricing models don’t provide value. As Fama and French note in their conclusion: "Complete success is almost certainly impossible, but less-than-perfect models can provide useful descriptions of expected returns."When using regional pricing models, the international evidence provides out-of-sample support for the Fama-French five-factor model being the new workhorse in evaluating portfolio performance.