There are several anomalies that modern financial theory has to deal with. Perhaps the most well-known anomaly for both the CAPM and the Fama-French three-factor models is the existence of momentum in all asset classes.
Another one that has become prominent in the literature is what’s sometimes referred to as the “low-risk” or “low-volatility” anomaly—an inverse relationship has been found between future stock returns and beta (a measure of the volatility, or systematic risk, of a security or a portfolio in comparison to the market as a whole). Specifically, high-beta stocks have the lowest returns, but, after that, returns in the other quintiles are comparable. However, risk falls monotonically so that Sharpe ratios increase monotonically.
The historical evidence shows that low-beta portfolios meaningfully outperform high-beta portfolios in both U.S. and international markets. This runs counter to economic theory, which predicts that higher expected risk is compensated with higher expected return.
Investors Won’t Give Up On Lottery Stocks
Turan Bali, Stephen Brown, Scott Murray and Yi Tang contribute to the literature on the low-beta anomaly with their study “A Lottery-Demand-Based Explanation of the Beta Anomaly,” which appears in the December 2017 issue of the Journal of Financial and Quantitative Analysis. They proposed that demand for lotterylike stocks plays an important role in explaining the beta anomaly.
They explain: “Lottery investors generate demand for stocks with high probabilities of large short-term up moves in the stock price. Such up moves are partially generated by a stock’s sensitivity to the overall market—market beta. A disproportionately high (low) amount of lottery demand-based price pressure is therefore exerted on high-beta (low-beta) stocks, pushing the prices of such stocks up (down) and therefore decreasing (increasing) future returns.”
The authors’ proxy for lottery demand is a measure called MAX, the average of the ﬁve highest daily returns of the given stock in the given month.
In their analysis, Bali, Brown, Murray and Tang controlled for other variables known to predict the cross section of future stock returns. They grouped these variables into three categories of company characteristics (such as market capitalization, book-to-market ratio, momentum, stock illiquidity and idiosyncratic volatility), measures of risk (such as skewness and downside beta) and measures of stock sensitivity to aggregate funding liquidity factors. Their data sample covers the period July 1963 through November 2012.
Following is a summary of their findings:
- The -1.15% average monthly return of the high-MAX-minus-low-MAX portfolio is both economically large and highly statistically signiﬁcant with a t-statistic of -4.41. And with the exception of the ﬁrst-decile portfolio, the excess returns of the decile portfolios decrease monotonically across MAX deciles. Note the lowest-MAX stocks are first decile and the highest-MAX stocks are tenth decile.
- Lottery-demand price pressure is predominantly on high-beta stocks—lottery demand and beta are positively correlated. However, there is important time variation in this relationship.
- In months when lottery-demand price pressure is not disproportionately exerted on high-beta stocks, the returns associated with the beta anomaly are very low or nonexistent.
- When lottery-demand price pressure falls largely on high-beta stocks, the beta anomaly is very strong and is explained by the lottery-demand factor.
- The returns associated with the beta anomaly are no longer apparent after controlling for lottery demand. After controlling for MAX, there is a positive and statistically signiﬁcant relationship between beta and expected stock returns (the expected risk/return relationship).
- The lottery demand phenomenon is attributable to individual, not institutional, investors. The beta anomaly is very strong among stocks with low institutional ownership and nonexistent among stocks with high institutional ownership.
Bali, Brown, Murray and Tang concluded that the results of their analysis “indicate that lottery demand is a strong driver of the beta anomaly, since the eﬀect is no longer detected when controlling for MAX. The anomaly persists when controlling for all other ﬁrm characteristics, risk measures, and funding liquidity sensitivities.”