BAM Intelligence

Investors Love Lottery Stocks

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.

Study Results

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.”

Other Evidence

Their findings are consistent with those of prior studies. For example, Nicholas Barberis and Ming Huang, authors of the 2008 study “Stocks as Lotteries: The Implications of Probability Weighting for Security Prices,” found that:

  • Investors have a preference for securities that exhibit positive skewness, in which returns to the right of (more than) the mean are fewer but farther from it than returns to the left of (less than) the mean. Such investments provide the small chance of a huge payoff (winning the lottery). Investors find this small possibility attractive. The result is that positively skewed securities tend to be “overpriced” and, thus, subsequently earn negative average excess returns.
  • The preference for positively skewed assets explains the existence of several anomalies to the efficient market hypothesis (EMH), including the low average return on initial public offerings (IPOs), private equity and distressed stocks, despite their high risks.

Why Anomalies Can Persist

In theory, we would expect anomalies to be arbitraged away by investors who do not have this same preference for positive skewness. They should be willing to accept the risks of a large loss in exchange for the higher expected return that shorting overvalued assets can provide. However, in the real world, anomalies may persist because of limits to arbitrage.

First, many institutional investors (such as pension plans, endowments and mutual funds) are prohibited by their charters from taking short positions.

Second, the cost of borrowing a stock to short it can be expensive, and there can also be a limited supply of stocks available to borrow for the purpose of shorting. This can be especially true for small growth stocks.

Third, many investors are unwilling to accept the risks of shorting because of the potential for unlimited losses. This is prospect theory at work, where the pain of a loss is much larger than the joy of an equal-sized gain.

Fourth, short-sellers run the risk that their borrowed securities are recalled before the strategy pays off. They also run the risk that the strategy performs poorly in the short run, triggering an early liquidation.

Taken together, these factors suggest that investors may be unwilling to trade against the overpricing of skewed securities, allowing the anomaly to persist.


The evidence on the poor performance of lottery stocks is compelling. The research has found that stocks with lotterylike characteristics include IPOs, “penny stocks,” small growth stocks with high investment and low profitability, and financially distressed stocks that are either in or near bankruptcy.

Therefore, investors are best served by avoiding them. These findings also are why “passive” fund families such as Dimensional Fund Advisors (DFA) and Bridgeway Capital Management have long screened out these stocks from their portfolios. Hopefully, now that you are aware of this information, you, too, will screen them out. (In the interest of full disclosure, my firm, Buckingham Strategic Wealth, recommends DFA and Bridgeway funds in constructing client portfolios.)

This commentary originally appeared February 16 on

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The opinions expressed by featured authors are their own and may not accurately reflect those of the BAM ALLIANCE. This article is for general information only and is not intended to serve as specific financial, accounting or tax advice.

© 2018, The BAM ALLIANCE

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Larry Swedroe, Director of Research

Director of Research

Larry Swedroe is director of research for the BAM ALLIANCE.

Previously, Larry was vice chairman of Prudential Home Mortgage. Larry holds an MBA in finance and investment from NYU, and a bachelor’s degree in finance from Baruch College.

To help inform investors about the evidence-based investing approach, he was among the first authors to publish a book that explained evidence-based investing in layman’s terms — The Only Guide to a Winning Investment Strategy You’ll Ever Need. He has authored six more books:

What Wall Street Doesn’t Want You to Know (2001)
Rational Investing in Irrational Times (2002)
The Successful Investor Today (2003)
Wise Investing Made Simple (2007)
Wise Investing Made Simpler (2010)
The Quest for Alpha (2011)

He also co-authored four books: The Only Guide to a Winning Bond Strategy You’ll Ever Need (2006), The Only Guide to Alternative Investments You’ll Ever Need (2008), The Only Guide You’ll Ever Need for the Right Financial Plan (2010) and Investment Mistakes Even Smart Investors Make and How to Avoid Them (2012). Larry also writes blogs for and Index Investor Corner on

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