The size factor is one of the equity risk factors. offered a premium over the long termRecently, however, some researchers have questioned its usefulness based on comparing its performance to other well-known factors. for example, Ron Alquist, Ronen Israel, Tobias Moskowitz Even if Noah Beck, Jason Hsu, Vitali Karesnik, Helge Kostka We argue that there is neither strong empirical evidence nor strong theoretical support for a persistent size premium.
However, there are reasons why most investors should question the validity of these conclusions.
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statistical analysis by Joel L. Horowitz, Tim Loughran, NE Savin It shows that the stand-alone outperformance of small-cap stocks over large-cap stocks is weak and may even disappear once exposure to market factors is taken into account. In particular, increasing the set of independent variables with lagging market returns in addition to contemporaneous market returns leads to marginal magnitude premiums.
Although of little statistical interest, this result has little practical significance for investors. In fact, lagging market “factors” are artificial components that investors cannot keep in their portfolios, so they have only hypothetical statistical applications. So it makes no economic sense to measure alpha for such non-investment components.
A more important question for us is whether the scale factor adds value to an investor’s portfolio.
Factor performance should be evaluated from a portfolio perspective
The easiest way to determine whether a factor adds value to a portfolio is to compare the Sharpe ratios of portfolios with and without the factor. The higher the Sharpe ratio, the higher the overall portfolio risk-adjusted return. A single factor premium cannot answer this question. This is because it does not take into account the factor’s risk profile, i.e. the correlation between the factor under consideration and other factors in the portfolio.
Furthermore, measuring exposure to a market factor alone does not give a complete picture of how that factor affects a portfolio, as it ignores correlations with other factors. Adding the lagging value of the market factor to the regression does not solve this problem. We also assume that the investor’s choice is limited to holding only the market or holding the market and size.
Proper analysis of the size factor requires assessing its utility within a set of economically relevant factors. Examining size factors in conjunction with economically meaningless or redundant factors provides little statistical or economic insight. Therefore, exposure to all these other factors must be integrated into the analysis to determine whether size increases portfolio value and improves the Sharpe ratio.
of previously published work Beta Investment Strategy Journal, Scientific Beta researchers Mikheil Esakia, Felix Goltz, Ben Luyten, and Marcel Sibbe conducted several tests to determine whether the size factor actually improves the Sharpe ratio for multifactor investors. Did. The results shown in the chart below show that it is clear that Consistent with findings from other researchersThe graph, which has been widely used, shows the investor’s sharpe ratio maximizing factor weights for choosing between market, size, value, momentum, low-risk, high-return, and low-investment factors. rice field. both in academic and practical research.
This is a simple way of assessing the impact of factors on a portfolio’s risk/return characteristics. Any deviation from these weights will reduce the sharpe ratio. The size factor gave him over 9% weight in the portfolio. This is greater than value (2.9%) and closer to momentum (11.4%) and low risk (11.7%).
Weights for mean-variance-optimal portfolios, July 1963 to December 2018
![Graph showing weights for mean-variance-optimal portfolios, July 1963 to December 2018](https://i2.wp.com/blogs.cfainstitute.org/investor/files/2023/02/Weights-in-Mean-Variance-Optimal-Portfolio.png?resize=640%2C287)
In the same study, the researchers also reported that the stand-alone size factor produced the lowest returns among the factors on the menu during the analysis period. Momentum and low risk had average stand-alone premiums about three times higher. However, the weights of the optimal portfolio momentum and low risk factors are no greater than the weights of the size factor.
What explains these results? Ultimately, optimal factor weighting does not depend solely on returns. It also relies on the risk profile, particularly the volatility of the factors and the correlation between each factor and non-market factors. Taking into account these risk characteristics is particularly useful as they can be measured with considerable reliability. Expected returns are notoriously difficult to estimate..
The positive weighting of the size factor in the optimal portfolio indicates that including exposure to size improves the risk/return profile of multi-factor portfolios. In particular, the size factor contributes to the Sharpe ratio because it has a particularly low correlation with other traditional factors, making it an effective portfolio diversifier. In fact, its diversification effect is so strong that even with little premium, the size factor is a worthy addition to a multifactor portfolio.
The size factor may not give you great returns, but it’s a worthy addition to your portfolio.
Taking into account the portfolio’s exposure to factors other than market factors, adding a size factor clearly improves the risk/return profile of the portfolio. Size is a powerful diversifier over other traditional factors and as a result adds value to multi-factor portfolios. An analysis that ignores momentum, profitability, and exposure to other factors is of little use to investors.
Finally, there is the size effect. Claiming otherwise contradicts various academic asset pricing models that show that the size factor adds explanatory power to the cross-section of returns. By including non-market factors, these models provide investors with meaningful conclusions and confirm the important contribution of size factors to portfolio diversification and risk management.
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All posts are the opinion of the author. As such, they should not be construed as investment advice, and the opinions expressed do not necessarily reflect those of CFA Institute or the author’s employer.
Image credit: ©Getty Images /Liudmila Chernetska
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