Swedroe: Investors Like Lotteries

August 03, 2016

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.


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