The Fama–French three-factor model is now the standard model used in academia for empirical research. The three factors are the market, small minus big (SMB), and high-minus-low book-to-market ratio (HML). The five-factor model extends the three-factor model by adding two factors: robust-minus-weak profitability (RMW) and low-minus-high (conservative-minus-aggressive) investment (CMA).

Like the three-factor model, the five-factor model is an empirical asset-pricing model. The authors admit that the models have “flimsy theoretical underpinnings” and that the reliability of the models can be judged only on empirical robustness. The authors expand their prior tests of the five-factor model from US data to international data.

The success of the five-factor model rests on its ability to explain the size, B/M (book-to-market ratio), profitability, and investment patterns of international returns. On the basis of the authors’ tests in this paper, they find that average stock returns for North America, Europe, and Asia Pacific increase with B/M and profitability and are negatively related to investment. The authors also find that for Japan, only the relationship between average returns and B/M is strong and the relationship between average returns and profitability or investment is weak.

One practical use of asset-pricing models is in measuring portfolio performance. The authors note that empirical asset-pricing models that stand up to robustness checks can be a tool for portfolio design. They also note that different asset-pricing models may lead to different inferences about portfolio performance. As the authors acknowledge, such tests have not been conducted on the five-factor model.

The authors test whether such factors as size, B/M, profitability, and investment can explain international stock returns. To do so, they conduct their research in several steps.

The authors first obtain international stock return and accounting data for July 1990–December 2015, primarily from Bloomberg and supplemented by Datastream and Worldscope, which are all standard databases. To increase the power of the tests, they use diversified portfolios of returns for the left-hand side of the regression. Using diversified portfolios leads to more-precise intercept terms, which are the focus of asset-pricing tests.

To create diversified portfolios, the authors combine 23 developed markets into four regions where market integration is a plausible assumption: North America, Japan, Asia Pacific, and Europe. For each region, they sort the stocks on size and combinations of the B/M, profitability, and investment factors. Following the methodology for the Fama–French three-factor model, the authors use breakpoints for B/M, profitability, and investment based on large stocks, and the size breakpoints include 90% of market capitalization in large stocks and 10% of market capitalization in small stocks to avoid undue weight on tiny stocks. For the RHS (right-hand-side) factors, the authors use portfolios constructed from 2 × 3 sorts on size and B/M, profitability, or investment.

The authors conduct a number of tests for each region and for a global portfolio. If the RHS factors capture all differences in expected returns, the intercept in the five-factor model is indistinguishable from zero for all portfolios.

Although the authors try to underplay the weakness arising from the lack of theoretical underpinnings for the five-factor model, that lack makes their findings more susceptible to data-mining criticisms. Robust empirical testing is necessary for such models to gain acceptance. Given the results of this paper, the five-factor model does not appear to have reached that stage. Moreover, even with the successful empirical testing of the three-factor model, studies have shown that the CAPM remains the preferred choice of investors and practitioners.

One issue with the study is that it is hard to separate the five factors. That is, value stocks tend to have lower rankings on profitability and invest conservatively, while growth stocks often have greater profitability and more aggressive investment programs. In some regions, a four-factor model might be as useful as the five-factor model, with more potential support for momentum or profitability than for investment. Even if a model is found that has some explanatory power for stock returns, it is not advised to use that model to calculate the cost of capital for individual firms. The five-factor model has a long way to go before it unseats the more established asset-pricing models.