The Size Premium in Multifactor PortfoliosMikheil Esakia, Felix Goltz, Ben Luyten, and Marcel Sibbe, authors of the study “Size Factor in Multifactor Portfolios: Does the Size Factor Still Have Its Place in Multifactor Portfolios?” published in the Winter 2019 issue of The Journal of Index Investing, sought to answer the question of whether the inclusion of the size premium in multifactor portfolios improves the portfolio’s efficiency. They began by noting:
Thus, their study sought to determine the cost or benefit of removing the size factor from a menu of factors investors can use in building portfolios. The seven factors they evaluated were: the market (beta), size, value, momentum, low risk, high profitability, and low investment. These factors have been widely used in both academic and practitioner research. They first tested how measures of model fit deteriorate when each of those factors is omitted—enabling them to compare the relevance of each factor in explaining expected returns across equity portfolios. They then examined the long-term factor premia when controlling for different factors—enabling them to determine if the factor was subsumed (made redundant) by other factors. And finally, they examined the ex-post mean-variance efficient (MVE) portfolio and the weights it allocates to each of the seven factors—enabling them to determine whether a factor has contributed positively to the risk-return profile in the presence of other factors. Their data covers the period of July 1963 through 2018. Following is a summary of their findings:
The size factor may be extremely useful to investors if it explains differences in returns that remain unexplained by other factors. From an investment perspective, this would suggest that considering a size tilt along with other tilts would provide benefits to investors in terms of risk and return.
- The reduction in the explanatory power of their seven-factor model is highest when the size factor is excluded. Omitting the size factor reduces the model’s ability to explain average excess returns by an absolute 22 percent.
- Omitting the momentum or high-profitability factors also leads to deterioration in the model performance, but the magnitude is slightly lower than that of size.
- There is no meaningful impact from excluding the value factor (consistent with prior research finding that the value factor becomes redundant in the presence of the investment and profitability factors) and slight improvements when low risk and low investment factors are omitted.
International EvidenceAs a test of pervasiveness, Esakia, Goltz, Luyten, and Sibbe ran the same tests in developed and emerging markets. They concluded:
“Consistent to our findings in US data, accounting for cross-factor interactions on top of the market factor increases the size premium. The multifactor alpha is higher than the CAPM alpha in both developed and emerging markets.”
Having found that the size factor carries a premium unexplained by other commonly used equity factors, we should expect that investors can improve their risk/return profile by including the size factor in their portfolio because it carries a premium not captured by other factors. They tested this in an ex-post MVE U.S. portfolio that maximizes the Sharpe ratio over the full sample. The following chart shows the results. As you can see, despite the size factor having the lowest return among the factors in the menu, the size factor plays a far greater role than the value factor and similar roles to the momentum and low-risk factors. Their tests also revealed that “the exclusion of the size factor would lead to about a 3% reduction in Sharpe ratio.” They also found that “one should have an expected zero return for the size factor to consider excluding it.” They noted this demonstrates that “some factors can stomach a sizable reduction in their premium.” In another test related to macroeconomic conditions, they found that:
“Our main finding that the size premium is not lower than that of other factors, once we properly account for multiple exposures, holds across developed and emerging markets.”
In general, they found that,
“size turns out to be the only factor that tends to perform well when the dividend yield is unexpectedly rising. Hence, we predict that size has an important role for investors who wish to reduce their exposure to interest rate shocks or dividend yield shocks.”
“the analysis of macroeconomic risk and multi-asset class portfolios confirms that the size factor offers substantial diversification benefits. Omitting size would be costly for an investor who is exposed not only to the equity factors but also to other sources of risk, such as interest rates and other macroeconomic risks.”
SummaryEsakia, Goltz, Luyten, and Sibbe’s results demonstrate the importance of not considering just the standalone factor premium but also its volatility and its correlation to the other factors in the portfolio. Their test results provide no evidence suggesting that one should exclude the size factor when constructing multifactor portfolios. Their findings are consistent with those of prior research, which I presented in detail in my Advisor Perspectives article of October 16, 2019, “The Size Premium is Alive and Well.” Following is a summary of that piece:
- The size premium has been “polluted” by the very poor performance of small growth stocks, especially those with high investment and low profitability.
- Once you control for other factors (quality, profitability and low volatility), the size premium is persistent and pervasive around the globe and is no longer concentrated in the tiniest stocks. For example, small quality stocks outperform large quality stocks, and small junk stocks outperform large junk stocks, but the standard size effect suffers from a size-quality composition effect. In other words, controlling for quality restores the size premium.