Profitability and a Four-Factor Model


When constructing or evaluating a domestic equity portfolio, Index Fund Advisors has traditionally utilized the three-factor asset pricing model that Professors Eugene Fama and Ken French introduced1 in 1993.

This model states that the expected return of a broadly diversified stock portfolio in excess of a risk-free rate is a function of that portfolio’s sensitivity or exposure to three common risk factors: (1) a market factor, as measured by the excess return of a broad equity market portfolio relative to a risk-free rate; (2) a size factor, as measured by the difference between the returns of a portfolio of small stocks and the returns of a portfolio of large stocks; and (3) a value factor, as measured by the difference between the returns of a portfolio of high book-to-market (value) stocks and the returns of a portfolio of low book-to-market (growth) stocks.

The underlying premise of this model is that small cap and value stocks are riskier than large cap and growth stocks and thus carry higher expected returns.

Most notably, research by Fama2, French and Robert Novy-Marx3 shows that expected profitability—as measured by the ratio of operating profitability minus interest expense to book value—is another reliable and robust dimension of stock pricing and expected returns.

The reason for this is easily inferred from the equation that relates the current price of a stock to the discounted present value of future cash flows.

The discount rate is simply the expected return of the stock, which unfortunately, is not readily ascertainable. If the market assigns the same price to two different stocks, and one of them has higher expected future cash flows in all years, then that company must also have its cash flows discounted at a higher rate of interest -- meaning that it has a higher expected return.

Of course, the market could also assign the same expected return to both companies, which would result in a higher price for the more profitable company.

Although it may not be appropriate to refer to profitability as a risk factor, it does behave like one in that the difference in returns between high-profitability stocks and low-profitability stocks is highly volatile. One of the key findings of Novy-Marx’s research is that current profitability is a good predictor of future profitability, and future profitability is a good predictor of higher returns.

Building on their three-factor model, Fama and French have introduced a profitability factor, as measured by the difference between the returns of a portfolio of high-profitability (robust) stocks and low-profitability (weak) stocks.

For this purpose, the definition of profitability is annual revenues minus cost of goods sold, interest expense, and selling, general, and administrative expenses -- all divided by book equity.

While value (or book-to-market ratio) is a measure of how much book value an investor receives for every dollar invested, profitability is a measure of how many dollars of profit an investor receives for every dollar of book value bought.

Since these two factors are negatively correlated, it is difficult to construct a diversified portfolio that is heavily loaded with both factors. Nevertheless, a value-tilted portfolio can benefit from a consideration of profitability by gaining an increase in expected return while still maintaining broad diversification and reducing tracking error relative to the market.

The primary advantage of adding the fourth factor of profitability is that portfolios which previously appeared to have alpha -- the portion of total return remaining after accounting for exposure to the different risk factors -- significantly different from zero (either positive or negative) would now be assessed as having just one more type of beta (exposure to a dimension of returns) and essentially zero alpha.

The idea of considering profitability (or quality) as a form of beta rather than alpha is further reinforced by a working paper4 that analyzes the returns of Warren Buffett’s Berkshire Hathaway and attributes them to leverage, access to cheap capital and a consistent focus on “cheap, safe, quality stocks.”

While the four-factor model can be considered an improvement over the three-factor model, it is still far from perfect -- as shown by its failure of a statistical test that was specially designed to assess multi-factor asset pricing models.

This should not be a cause for despair. Since returns are so noisy to begin with, we cannot expect to ever find a perfect model. The model is still good enough for the empirical work of constructing portfolios or evaluating the performance of a portfolio (or a portfolio manager).

The four-factor model does address some of the known deficiencies of the three-factor model, such as an inadequate explanation of the low returns of extreme small growth stocks. The downside, of course, is the added complexity of another dimension. With the three-factor model, we can easily visualize the expected return of a portfolio relative to the market based on where it plots on a two-dimensional chart of size and value exposure. With the four-factor model, we would need a three-dimensional chart.

As an investment fiduciary, IFA will continue to keep abreast of developments in finance to ensure that our clients have the best possible investment experience that we can provide. If you have any questions on profitability, multifactor models of portfolio returns, or any other investment-related topic, please feel free to drop us a line at [email protected].


1Fama, Eugene F., and Kenneth R. French, 1993, Common risk factors in the returns on stocks and bonds, Journal of Financial Economics 33, 3–56.


2Fama, Eugene F. and French, Kenneth R., A Four-Factor Model for the Size, Value, and Profitability Patterns in Stock Returns (July 1, 2013). Fama-Miller Working Paper. Available at SSRN:

3Novy-Marx, Robert, 2012, The other side of value: The gross profitability premium, University of Rochester, May, forthcoming in the Journal of Financial Economics. (

4”Buffett’s Alpha”, by Andrea Frazzini, David Kabiller and Lasse Pedersen, August 2012's%20Alpha%20-%20Frazzini,%20Kabiller%20and%20Pedersen.pdf).