Size Factor in Multifactor Portfolios: Does the Size Factor Still Have Its Place in Multifactor Portfolios?

Abstract

The finance literature has established a size effect: stocks with small market capitalization outperform larger stocks over the long term. The size factor is included in asset-pricing models because of its explanatory power for cross-sectional differences in equity returns. However, recent studies recommend removing size from the factor menu, given its relatively weak performance. Instead of looking at the stand-alone performance, we account for cross-factor correlation to assess the impact of excluding the size factor. We consider three tests. First, we measure the impact on model fit of asset-pricing models. Second, we assess whether the size premium remains intact when accounting for implicit exposures to other factors. Third, we evaluate the impact of the size factor on the performance of optimal multifactor portfolios. Our results suggest that the size factor improves model fit, delivers a significant positive premium in the presence of other factors, and contributes positively to the performance of multifactor portfolios. Omitting the size factor has substantial cost to investors, which often exceeds that of omitting other popular factors.

TOPICS: Analysis of individual factors/risk premia, factor-based models, style investing

Key Findings

• • The size factor carries a significant premium after adjusting for implicit exposure to other factors.

• • Optimal factor portfolios allocate to the size factor even if the return assumption is extremely conservative.

• • The size factor improves diversification due to its low correlation with other factors and different exposure to macroeconomic conditions.