Why people choose negative expected return assets  – an empirical examination of a utility theoretic explanation

Abstract

Using a theoretical extension of the Friedman and Savage (1948) utility function developed in Bhattacharyya (2003), we predict that for assets with negative expected returns, such as state lottery games, expected return will be a declining and convex function of skewness. That is, lottery players trade-off expected return for skewness. Using two samples of lottery game data, we find that our theoretical conclusions are supported by the empirical results. The findings obtained here not only contribute to the literature on why individuals may participate in unfair gambles, the framework could be extended to an analysis of the stock market where higher returns cannot be solely explained by risk (variance).

Acknowledgements

The authors would like to thank Melissa Kearney for providing the data used is this article.

Notes

¹ Casinos typically return 85 cents or more of every dollar wagered back to players in the form of winnings. For larger casinos in a competitive area, payout rates are likely closer to 95 cents for every dollar wagered. Minimum casino payout percentages are set by state law. Racetracks keep roughly $0.17 to $0.20 of every dollar wagered, with the remaining funds allocated to the prize pools.

² Source: National Association of State and Provincial Lotteries (www.naspl.org). Commercial and Native American casinos generated roughly $44 billion in revenue and pari-mutuel wagering revenues totalled $3.8 billion in 2003 (see www.americangaming.org).

³ Golec and Tamarkin (1998) and Walls and Busche (2003) explore the ‘long shot bias’ in horse racing, where high-probability, low-variance bets provide high average returns (and are underbet), and low-probability, high-variance bets provide lower average returns (and are overbet). Sobel and Raines (2003) and Coleman (2004) evaluate the long shot bias within risk/return models.

⁴ On-line games are those games that require the player to fill out a play slip and watch the drawing on TV. Instant, or ‘scratch-off’games, are not included. See Kearney (2005) for a detailed description of the data. Our sample of lottery games has 14 592 observations [we omitted missing observations from Kearney's (2005) 15 564 total observations].

⁵ It is unclear whether state demographic and economic characteristics, such as income, racial composition, employment, etc., would have an effect on the expect return of lottery games. Thus, we include state dummy variables to capture any unobserved difference across states that may influence lottery sales.

⁶ See Brannas and Nordman (2003).