Should the size factor be fired from multi-factor models?

Smart-beta providers point to its weak returns, but new research questions the logic behind its exclusion

Should the size factor be fired from multi-factor models?

While funds that focus on small-cap stocks remain fairly popular, smart-beta providers are quick to argue that it performs poorly relative to other factors. Other critics also argue that the size factor lacks robustness, while some even point out that historical studies suggesting outperformance from size may not be based on clean data.

But a new paper from Scientific Beta argues that in spite of the evidence against it, the size factor should not be discarded outright, particularly in the case of multi-factor portfolios.

“[A] common recommendation in the asset management industry is to remove Size from the factor menu, given its relatively weak post-publication performance,” the paper said. “Instead  of  looking  at  the  stand-alone  performance,  we  account  for  cross-factor  correlation  to  assess  the  impact  of  excluding  the  Size  factor.”

In one analysis, the authors of the paper examined how well multi-factor asset pricing models are able to explain patterns of returns across different portfolios when the size factor is excluded. “When omitting a useful factor, model misfit should increase,” they explained. “When omitting a useless factor, model misfit should remain stable or even decrease.”

The researchers found that eliminating the size factor from a model negatively impacts its ability to explain average excess returns; the original 60% proportion of unexplained returns increases to above 80%. Omitting momentum or high profitability factors erodes the model’s performance to a slightly lesser degree; excluding value produced no meaningful impact, while omitting low risk and low investment factors yielded slight improvements.

Another analysis involved measuring the size premium after adjusting for implicit exposures to other factors. The researchers noted the well-known negative exposure to quality factors, such as high profitability and low investment, that come with small-cap stocks. “What we are interested in is whether average returns not explained by other factors are still positive,” they said.

Analysing US market data spanning more than 55 years, the researchers found that all factors they observed, including the size premium, have significantly positive returns over the long term. But while size had the lowest premium, they noted that the high profitability premium was hardly better, adding just two basis points more than size; ultimately, the logic of excluding one factor would require that only the best-performing factor be left in the menu.

Correcting for residual exposures, they added, results in only two of the six factors (momentum and low risk) having a premium that is higher than that for size. Premiums from value, low risk, and low investment factors were also markedly reduced after researchers accounted for their exposures to other factors, suggesting that the returns they products are partly explained by their exposure to those factors.

“[I]f one is considering excluding a  factor, Size does not stand out as an obvious candidate,” they said.


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