Does Probability Weighting Drive Lottery Preferences?

Abstract

We propose a test of the theory of skewness preferences. The probability weighting feature that is the basis of their theory relies on investors overweighting the probability of extreme, positive returns. The resulting investor preferences for positive skewness in return distributions will lead to excess demand, contemporaneous price premiums, and negative expected returns. We use the well-documented 52-week high bias as a method to truncate investors’ weighted probability of expected right-tail events. We find evidence supporting the theoretical framework of Barberis and Huang as the negative return premiums associated with positive skewness is driven almost entirely by stocks that are farther away from the their 52-week high. No negative premiums related to skewness are detected when stock prices are close to the 52-week high.

Keywords:

• Lotteries
• Skewness
• Anchoring
• 52-week high
• Probability weighting
• Cumulative prospect theory

Acknowledgements

We would like to thank Justin Birru, Jocelyn Evans, Jean Helwege, Haimanot Kassa, Natalia Piqueira, Matthew Wynters, and the discussants and participants at the 2017 Australasian Banking and Finance Conference, 2018 Midwest Finance Conference, 2018 FMA Europe Conference, and 2018 Financial Markets and Corporate Governance Conference.

Notes

1 Although, both Kumar (2005) and Kumar (2009) show institutional investors are skewness-averse. Autore and DeLisle (2016) find similar evidence by demonstrating institutional investors require deeper discounts to place seasoned equity offering shares with high skewness.

2 We focus on positive skewness because studies such as Bali et al. (2011), Jiang and Zhu (2017), Atilgan et al. (2019), and DeLisle, Ferguson, and Kassa (2019) show that negative skewness does not carry a discount (and thus high expected returns) as theories of skewness preferences suggest it would. In unreported results, we also find MIN, Bali et al.’s (2011) measure of negative skewness, to have no effect in the cross-section of returns.

3 We note that in columns [2] and [4], we find a positive return premium associated with Illiquidity, which is consistent with Amihud and Mendelson (1986). Further, columns [3] through [5] show that Size is negatively associated with future returns, which is consistent with findings in Banz (1981) and Fama and French (1992).

4 There is no reason to believe the skewness premium should be affected by anchoring in a linear manner. Thus, rather than forcing such a linear relation by interacting the skewness proxy with a continuous Anchor variable, we examine the how the relation is different only close to 52-week high where it would have the largest impact on an investor’s perception of the return distribution’s right tail.