The low-beta anomaly for the capital asset pricing model (CAPM)—low-beta stocks outperform high-beta stocks—was first documented more than 50 years ago by Fischer Black, Michael Jensen, and Myron Scholes in their 1972 paper, “The Capital Asset Pricing Model: Some Empirical Tests.” In our 2016 book, “Your Complete Guide to Factor-Based Investing,” Andrew Berkin and I presented evidence demonstrating that the low-beta anomaly has been persistent and pervasive around the globe and across asset classes. However, we also showed that research demonstrated that returns to the anomaly were not only well explained by exposure to what are now the common factors of size, value, profitability, and term but also that the premium was dependent on whether low volatility was in the value or growth regime (there was a premium only in the value regime). Unfortunately for investors in low-beta strategies, their popularity has caused valuations to leave the value regime where they had historically generated alphas.

Further research into the low-beta anomaly confirmed that it has been well explained by exposure to other common factors. For example, the authors of the 2021 study “Liquidity Risk and the Beta Premium” found that the low-beta premium could be explained by another common factor found in the literature, the liquidity premium (liquidity risk decreases steadily from low- to high-CAPM beta portfolios)—CAPM beta premiums only appear in portfolios of low-liquidity stocks.

New Research

Reza Bradrania, Jose Veron, and Winston Wu, authors of the study “The Beta Anomaly and the Quality Effect in International Stock Markets,” published in the June 2023 issue of the Journal of Behavioral and Experimental Finance, investigated the beta anomaly and its relationship with another common factor, quality, in international stock markets using an extensive global database across 22 countries and three aggregate markets (Europe, Pacific, and Global). They began by noting that quality stocks are those of firms that are profitable, growing, safe, and well-managed, whereas junk stocks are those of firms that are unprofitable, stagnant, risky, and poorly managed. They noted that the research has shown that high-beta stocks are riskier and more likely to be junk stocks, while low-beta stocks are less risky and more likely to be quality stocks. It has also shown that low-beta (quality) stocks are more likely to be underpriced and high-beta stocks (junk) are more likely to be overpriced. Consequently, quality (junk) stocks have positive (negative) risk-adjusted returns, known as the “stock quality effect.” A quality-minus-junk (QMJ) factor that is long in quality stocks and short in junk stocks has earned significant risk-adjusted returns.

To test the relationship between quality and low beta, the authors examined their relationship across countries and in aggregate portfolios using portfolio and cross-sectional regression analyses. They used each stock’s sensitivity to the QMJ factor in each market as a proxy for stock quality. Their data sample covered the period from January 1990-March 2021. They constructed equally weighted portfolios to assess the beta anomaly. Following is a summary of their key findings:

• Low-beta stocks had significantly higher average returns than high-beta stocks in all three aggregate markets and 14 of the 22 country portfolios.
• High-beta (low-beta) stocks had lower (higher) quality values, consistent with prior research findings that high-beta (low-beta) stocks are more likely to be junk (quality) stocks.
• The quality factor explained the beta anomaly in international markets.
• The beta anomaly was statistically significant only among junk (low-quality) stocks—it did not exist among high-quality stocks. The performance of a zero-cost portfolio that was long in low-beta stocks and short in high-beta stocks almost doubled if constructed using only junk stocks.
• Beta predicted future stock returns only in quality stocks—the beta coefficient was small and statistically insignificant among junk stocks.
• The results were robust in portfolio and regression analyses, both before and after controls.
• CAPM, Fama-French three-factor (beta, size, and value), and Carhart four-factor (adding momentum) alphas of the zero-cost portfolio that was long low-beta stocks and short high-beta stocks became insignificant once the QMJ factor was included in the portfolio analysis. The results were robust when using the newer Fama and French five-factor model that includes investment and profitability factors to calculate alphas.

Their findings led the authors to conclude: “The beta anomaly remains economically strong and statistically significant among junk stocks, while it disappears among quality stocks.” They added: “QMJ is an important factor that should be included in asset pricing models.”

Investor Takeaways

The empirical evidence demonstrates that returns to the low-beta anomaly are well explained by exposure to other common factors, and it has only justified investment when low-beta stocks were in the value regime, after periods of strong market and small-cap stock performance, and when they excluded high-beta stocks that had low short interest.

Bradrania, Veron, and Wu’s findings provide implications for investors. They showed that low volatility strategies can be improved by limiting the strategy to low-quality stocks, as there have been no abnormal returns in low-beta, quality stocks.

It is also important to note that long-only funds that don’t focus on this anomaly can benefit from screening out the junk (“lottery”) stocks that drive the poor performance of securities in the highest quintile of beta.

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