Investors Like Lotteries

There’s substantial evidence from the field of behavioral finance that individual investors have a strong preference for investments that exhibit the same characteristics as lottery tickets. Two of these characteristics are high kurtosis (or fat tails) and positive skewness, meaning values to the right of (or more than) the mean are fewer but farther from it than values to the left of (or less than) the mean.

And just as is the case with lottery tickets, this preference leads investors to overinvest in the most highly skewed (right-skewed) securities. Increased demand leads to higher prices, with the consequence being that such securities will have lower subsequent average returns.

Recently, there has been a lot of research on the question of whether the higher moments of return other than volatility (specifically, the skewness of returns) helps explain equity returns. For instance, the role of idiosyncratic skewness has been put forward as an explanation for why investors actually hold under-diversified portfolios. Investors with a preference for skewness may under-diversify their portfolio to invest more in assets that have positive idiosyncratic skewness. Thus, stocks with high idiosyncratic skewness will pay a premium.

The result is that, at the firm level, expected skewness negatively affects stock returns. High idiosyncratic skewness, then, is associated with lower expected returns. Conversely, more negatively skewed equity returns (where the risk of large losses is greater) are associated with higher subsequent returns.

The bottom line is that assets with large upsides (positive skewness) are overpriced and thus have low expected returns, while assets with large downsides (negative skewness) are underpriced and thus have high expected returns.

A Study Of Investor Preferences

Benjamin Blau, T. Boone Bowles and Ryan Whitby contribute to the literature on investor preferences with their study, “Gambling Preferences, Options Markets, and Volatility,” published in the April 2016 issue of the Journal of Financial and Quantitative Analysis.

The authors’ study, which covers 3,112 stocks and the period 1997 through 2007, extends the research on investor preferences for lotteries and skewness in two ways. First, they examined whether stocks with characteristics that resemble lotteries show higher levels of call option volume. Second, and perhaps more importantly, they examined whether the preferences for lotteries exhibited through higher call option volume influences future spot price volatility.

Because of their limited downside risk and unlimited upside potential, call options seem to be an attractive security for investors with preferences for lotterylike traits, motivating the research. The authors were also motivated by prior research that has shown option trading volume contains information about future returns in the underlying stocks.

The authors approximate lottery stocks in several ways. First, they use a proxy for lottery stocks by examining positive total and positive idiosyncratic skewness in returns during the prior quarter. They used continuous estimates of skewness and indicator variables capturing stock-quarter observations with the highest total and idiosyncratic skewness during the previous quarter.

Second, they approximate lottery stocks by calculating indicator variables that capture low-priced stocks with the highest idiosyncratic volatility and the highest idiosyncratic skewness during the previous quarter. Using these approximations for lottery stocks, the authors examined the fraction of total option volume made up from call options, which they denote as the call ratio.


Following is a summary of their findings:

  • There’s a monotonically positive relationship between call ratios and the last quarter’s total skewness. Similar results are found when examining the relationship between call ratios and last-quarter’s idiosyncratic skewness.
  • There’s a significantly positive univariate (dependent on one variable) correlation between call ratios and last-quarter’s skewness. When using the indicator variable approach, they found similar results. In particular, call ratios are highest when last quarter’s skewness is highest.
  • When approximating stock lotteries using low-priced stocks with the highest idiosyncratic volatility and the highest idiosyncratic skewness, they found that call ratios are highest for these stocks.
  • There’s a robust positive relation between call ratios and the authors’ approximations for lottery stocks.

Blau, Bowles and Whitby concluded: “These results support our univariate tests and indicate that investors’ penchant for lottery stocks is also reflected in higher call ratios.”

They also concluded: “Speculative call option activity, or the portion of the call ratio that is directly related to lottery-like stock characteristics, drives the direct relation between total call ratios and next-quarter volatility. To the extent that higher call ratios in lottery-type stocks represent speculative activity in the options market, our results are consistent with theory which posits that speculative trading activity in the derivatives market can lead to increased volatility.”

What It Means For Investors

For investors, the implications are striking. The authors write: “Skewness preferences can result in an equilibrium that leads to overpriced, positively skewed stocks. Price premiums that are caused by skewness preferences will underperform stocks that are not positively skewed.”

The evidence they present also demonstrates that the availability of derivatives, such as call options, can allow investors to express their preference for skewness, which in turn can drive volatility and influence returns. This may also lead to greater levels of speculation in derivatives markets, which could produce noisy prices adversely affecting “the ability of informed investors to transmit information into prices, thus leading to greater instability of prices.”

These findings also have implications for portfolio construction. First, investors buying individual stocks should avoid those with lotterylike characteristics. Second, mutual funds can improve performance by screening out stocks with these negative traits.

This commentary originally appeared August 3 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.

© 2016, The BAM ALLIANCE

Larry Swedroe

Larry Swedroe is the Director of Research for Buckingham Strategic Wealth. He has authored or co-authored more than a dozen books and is regularly published on and Advisor Perspectives. He has made appearances on national television shows airing on NBC, CNBC, CNN and Bloomberg Personal Finance. Larry holds an MBA in finance and investment from New York University, and a bachelor's degree in finance from Baruch College in New York.

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