Size and Style Biases in Popular Stock Market Indices

July 10, 2024

By Peter Mladina, Executive Director of Portfolio Research, Wealth Management
Andrew Gauthier, Senior Investment Research Analyst, Wealth Management
David Moore, CFA, CAIA, Director of Manager Research, Wealth Management

Fama and French (1993) showed that market, size and value factors explain the return and risk of diversified equity portfolios. Despite the discovery of additional factors in subsequent years, Mladina and Germani (2022)¹ showed empirically that these three factors are the genuine systematic risk factors in real-world equity portfolios.

The S&P 500, Dow Jones Industrial Average and NASDAQ Composite are the three most commonly cited U.S. stock market indices in the financial media. We demonstrate each is simply a unique mix of the three factors, with varying sensitivities to market risk, small vs. large size biases, and value vs. growth style tilts. Exhibit 1 provides the results of regressions of each index’s returns since inception through March 2024 on U.S. market, size and value factors.

The alphas for each index are statistically insignificant (t-stat < 1.96), meaning there are no unexplained return premiums (i.e., no true, non-random alphas). And the high adjusted R² indicates the risk (variance) of each index is well-explained by its unique exposure to the three systematic risk factors. The factor betas (exposures) tell us the S&P 500 has a large-cap bias (-0.19 size beta) with no meaningful style tilt (0.02 value beta). The Dow Jones Industrial Average also has a large-cap bias (-0.22 size beta) but with a moderate value tilt (0.15 value beta). The NASDAQ Composite has higher sensitivity to market risk (1.11 market beta), along with a moderate small-cap bias (0.18 size beta) and material growth tilt (-0.31 value beta). When interpreting the reported returns of these popular indices, investors should be aware that they are explained by simple differences in the underlying factor mix.

To make these results more intuitive, we construct factor return benchmarks for each index from their respective mixes of factor betas. Exhibit 2 compares the annualized return and risk (standard deviation) of each index to those of its factor benchmark.

The returns of the three indices are nearly identical to the returns of their respective factor benchmarks. The small observed return differences in Exhibit 2 are random because the alphas are random in Exhibit 1. The standard deviations of the three indices are also nearly identical to those of their respective factor benchmarks (though the risk of the Dow is a bit higher than its benchmark because it is less diversified). Factor exposures almost entirely explain the return and risk of these popular stock market indices over the long run.

The factor betas for each index have been remarkably consistent over any lookback period of the past 20 years, which is noteworthy given the rise of the so-called “Magnificent 7” stocks during the last decade. The “Magnificent 7” now comprise nearly one-third of the market value of the S&P 500, leading some to consider use of the S&P 500 Equal-Weighted index in an attempt to capture broader breadth of the U.S. equity market than the capitalization-weighted S&P 500. Exhibit 3 shows the results of our regression of S&P 500 Equal-Weighted index returns on U.S. market, size and value factors since index inception through March 2024.

Again we find that the alpha is statistically random, so there is no unexplained return premium. And the high adjusted R² indicates risk is well-explained by its underlying factor mix. The equal-weighted index has a more neutral size bias (0.07 size beta) than the standard S&P 500 (-0.19 size beta), but perhaps, surprisingly, it has a meaningful value tilt (0.29 value beta). In other words, there is nothing unique or different about the S&P 500 Equal-Weighted index; it is just another permutation of factors.

In fact we can closely replicate the return and risk of the S&P 500 Equal-Weighted index with a blend of the S&P 500 and Russell 2000 Value (small cap value) indices. For example, over the trailing 10 year period ending March 2024, the S&P Equal-Weighted index returned 10.9% (annualized) with 16.6% standard deviation, while a 70/30 blend of the S&P 500 and Russell 2000 Value returned 11.3% with 16.1% standard deviation — the return and risk are nearly identical.³ However, the S&P 500 Equal-Weighted index requires far more turnover to rebalance, generally resulting in higher transaction costs and taxes for taxable investors.

International versions of the three factors also explain the return and risk of international stocks. The MSCI EAFE is perhaps the most popular international equity index. Exhibit 4 shows the regression results of the MSCI EAFE against international market, size and value factors from the 1990 inception of the international factors through March 2024.

The alpha is random and the mix of factor betas well explains the return and risk of international stocks. The MSCI EAFE index has a large-cap bias (-0.19 size beta) and neutral style orientation (0.02 value beta) when factors are constructed from international stocks only.

Global investors seek the diversification benefit of owning both U.S. and international equities. Therefore, it is worth evaluating size and style biases of U.S. vs. international indices when factors are constructed from global (i.e., U.S. plus international) stocks. Exhibit 5 provides the factor betas for the S&P 500 and MSCI EAFE over the last 10 years (ending March 2024) using global factors.

The S&P 500 has a mega-cap bias (-0.31 size beta) and modest growth tilt (-0.12 value beta), while the MSCI EAFE has a neutral size bias (0.03 size beta) and modest value tilt (0.16 value beta). An investor seeking broad diversification can eliminate latent size and style biases by owning global equity instead of having a heavy U.S. bias.

Systematic risk factors almost entirely explain the returns of widely referenced stock indices, as well as the returns of diversified mutual funds, exchange-traded funds and separately managed accounts. Investors should be aware of these exposures in their portfolios, as they are the fundamental drivers of equity return and risk.