Since the development of the first asset pricing model, the capital asset pricing model (CAPM), academic research has attempted to find models that increase the explanatory power of the cross-section of stock returns. We moved from the single-factor CAPM (market beta), to the three-factor Fama-French model (adding size and value), to the Carhart four-factor model (adding momentum), to Lu Zhang’s q-factor model (beta, size, investment, profitability), to the Fama-French five-factor (adding value to the q-factor model) and six-factor models (adding back value and momentum to the q-factor model). There have also been versions that use different metrics for profitability and value, and Stambaugh and Yuan’s mispricing (anomaly)-based model.
The fact that we have seen keen competition to improve existing models should not surprise us. One reason is that, by definition, all models are flawed. If they were perfect representations of the way the world worked, we would have laws (not models), like we have in physics. Though models are flawed, that doesn’t mean they’re absent of value.
Think about it this way: Financial models aren’t cameras that provide us with a perfect picture of the way financial markets work. Instead, they are engines that advance our understanding of how markets operate and how prices are set – which is why we continue to see efforts to improve on existing models.
Matthias Hanauer contributes to the literature on asset pricing models with his March 2020 study, “A Comparison of Global Factor Models.” Hanauer compared commonly employed factor models across 50 non-U.S. developed and emerging market countries by ranking them based on their Sharpe ratios. His addition of international markets is a major contribution, as out-of-sample tests reduce the risks of sample-specific outcomes and data mining. His sample covers the period July 1990 through October 2018.
Following is a summary of his findings:
- The factor with the highest average return is momentum (WML, winners minus losers), followed by the two value factors, HML (high minus low) and HMLm (monthly updated version). The size factor, SMB (small minus big), has the smallest average return and, other than the market factor, is the only one with a t-statistic below 2 (statistically significant at the 5% confidence level. All the other factors aside from the profitability factor based on ROE (return on equity), RMWROE (robust minus weak) and the investment factor CMA have t-statistics greater than 3 (statistically significant at the 1% confidence level). The cash-based operating profitability factor (RMWCbOPtA) has the highest t-statistic, partly due to its low standard deviation, which is lowest together with the standard deviation of the operating profitability factor (RMWOPtBE).
- The CAPM is dominated by all other models, with significance at the 1% level. The CAPM explains about two thirds of the variation in returns of well-diversified portfolios but the three-factor FF model explains more than 90%. The new FF five-factor or Q models dominate the three-factor FF model, which only uses beta size and value.
- The patterns documented for markets outside the U.S. are similar to those reported for the U.S.
- The common factor models are dominated by a six-factor model (FF6) that includes cash-based profitability (as opposed to operating profitability, which includes accruals) and momentum factors as well as a value factor that is updated monthly. When substituting the operating profitability factor in the FF6 model for a cash-based profitability factor, the resulting FF6CP outperforms all models, at least at the 10% confidence level.
- The results are robust in out-of-sample tests, across subperiods, across global regions and to methodological changes.
- The results are robust to various tests across subperiods, out-of-sample tests, regions and various methodological changes.
Hanauer’s findings are consistent with those of Francisco Barillas, Raymond Kan, Cesare Robotti and Jay Shanken, authors of the 2019 working paper, “Model Comparison with Sharpe Ratios.”
Through their research, financial economists continue to advance our understanding of how financial markets work and how prices are set. The Fama-French three-factor model was a significant improvement on the single-factor CAPM. Mark Carhart advanced our understanding by adding momentum as a fourth factor. And the authors of the q-theory made further significant advancements, which in turn motivated the development of the competing FF five- and six-factor models.
The competition to find superior models is what advances our understanding not only of the markets but also about which factors to focus on when selecting the most appropriate investment vehicles and developing portfolios.
Larry Swedroe is the chief research officer for Buckingham Strategic Wealth and Buckingham Strategic Partners.
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