Lottery preferences and the idiosyncratic volatility puzzle

• Date: 01 June 2019
• Published date: 01 June 2019
• DOI: http://doi.org/10.1111/eufm.12178

655Eur Financ Manag. 2019;25:655–683. wileyonlinelibrary.com/journal/eufm © 2018 John Wiley & Sons, Ltd.

DOI: 10.1111/eufm.12178

ORIGINAL ARTICLE

Lottery preferences and the idiosyncratic volatility

puzzle

Doina C. Chichernea

1

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Haimanot Kassa

2,3

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Steve L. Slezak

4

1

Reiman School of Finance, Daniels

College of Business, University of

Denver, Denver, Colorado

Email: doina.chichernea@du.edu

2

Department of Finance, Farmer School

of Business, Miami University, Oxford,

Ohio

Email: kassah@miamioh.edu

3

US Securities and Exchange

Commission, Washington, District of

Columbia

4

Department of Finance and Real Estate,

Lindner College of Business, University

of Cincinnati, Cincinnati, Ohio

Email: steve.slezak@uc.edu

Abstract

We investigate the empirical implications of investors’

heterogeneous preferences for skewness with respect to the

idiosyncratic volatility (IVOL) puzzle, that is, the negative

correlation between IVOL and mean returns. We show that

the IVOL puzzle is stronger: (1) within stocks held

primarily by agents with a preference for lottery-like

payoffs; and (2) during economic downturns, when the

demand for lottery-like payoffs is high. These results

support recent theories that suggest lottery preferences

could be a significant source of the IVOL puzzle.

KEYWORDS

economic conditions, idiosyncratic volatility, lottery preferences,

skewness

JEL CLASSIFICATION

G11,G12

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INTRODUCTION

The negative empirical relation between idiosyncratic volatility (IVOL) and subsequent stock returns

has been considered a puzzle since it was first documented by Ang, Hodrick, Xing, and Zhang (2006).

We are thankful for the helpful comments and suggestions from an anonymous referee, the editor (John Doukas), Tom

Boulton, Alexander Borisov, Kelly Brunarski, Colin Campbell, Michael Ferguson, Mark Griffiths, Hui Guo, Yvette

Harman, Tyler Henery, Bochen Li, David Manzler, Terry Nixon, Alex Petkevich, Chen Xue, Steve Wyatt, and Kim Yong.

We benefited from discussions with seminar participants at Miami University, the University of Cincinnati, the Eastern

Finance Association, the Midwest Finance Association, and the Southwestern Finance Association. We are responsible for

any errors. The Securities and Exchange Commission (SEC) disclaims responsibility for any private publication or

statement of any SEC employee or Commissioner. This paper expresses the authors’views and does not necessarily reflect

those of the Commission, the Commissioners, or other members of the staff.

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CHICHERNEA ET AL.

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The subsequent literature suggests a link between the so-called IVOL puzzle and investor preferences

for lottery-like features (i.e., skewness; see Bali, Cakici, & Whitelaw, 2011; Boyer, Mitton, & Vorkink,

2010). If so, then the IVOL puzzle should be more pronounced within the universe of stocks held by

agents who prefer lottery-like payoffs. Further, since the literature (e.g., Kumar, 2009) shows that the

demand for lottery-like characteristics varies countercyclically over time, the IVOL puzzle should also

be more pronounced during economic downturns, when the demand for lottery-like features increases.

Our paper provides evidence that supports both hypotheses.

A negative relation between positive skewness and subsequent returns is implied by heterogeneous

investors’preferences for skewness. In models in which the mean and variance are sufficient to

characterize either security returns or investors’preferences (e.g., the capital asset pricing model or

CAPM), all investors optimally hold mean–variance-efficient portfolios. If, in addition to caring about

mean and variance, some investors also derive utility from positive skewness, then these investors will,

at prices implied by mean–variance efficiency, create excess demand for securities with positive

skewness. This has two implications: (1) the prices of lottery-like assets will be bid up to clear the

market, resulting in lower subsequent returns relative to securities without lottery-like features; and

(2) since the market-clearing price is a compromise between the valuations of each type of investor,

prices are bid up in equilibrium such that mean–variance investors hold proportionally less and mean–

variance–skewness investors hold proportionally more lottery-like securities. A third implication

concerns the magnitudes of these effects. The greater the skewness benefit a security offers, the greater

the reduction in the expected return and the greater the decrease in expected return, the greater the

disparity between the proportional holdings of lottery-like securities between mean–variance and

mean–variance–skewness investors.

While it is intuitive that (at least some) investors might have a preference for positive skewness, it is

not obvious why investors would have a preference for IVOL; thus, the above argument for a negative

equilibrium relation between skewness and future returns does not apply for IVOL. However, the

literature highlights a couple of reasons why IVOL and skewness could be connected empirically. First,

it is possible that IVOL is an inherent feature of firms that have lottery-type returns. The literature

presents at least two conceptual reasons for such a connection: (1) IVOL is positively related to

corporate growth options, which induce greater skewness in returns (Andrés-Alonso, Azofra-

Palenzuela, & La Fuente-Herrero, 2006; Cao, Simin, & Zhao, 2008); and (2) a higher IVOL is related to

technological revolutions, which also induce greater skewness in returns, since a few winners emerge

and other firms fail (Jovanovic & MacDonald, 1994; Pástor & Veronesi, 2009). Second, the IVOL

measures used in the literature are typically based on models in which investors are well diversified and

hold portfolios on a mean–variance frontier (e.g., multifactor CAPM), in which there is no (negative)

risk premium for skewness. Such models will misspecify expected returns for lottery-like securities,

which will likely result in upwardly biased estimates of the true IVOL for these securities. Thus,

securities with greater skewness will have higher estimated IVOL. Finally, stocks with exceptionally

high volatility are likely to have positive skewness by default, given the limited liability nature of

equity (Conine & Tamarkin, 1981).

Regardless of the exact channel, if there is a connection between IVOL and lottery-like features,

then perhaps the IVOL puzzle is not symptomatic of a puzzle at all, but is simply a proxy for the rational

pricing of skewness instead.

1

To differentiate, it would be nice to be able to pit the alternative

1

This is also consistent with a behavioral bias. For example, Barberis and Huang (2008) argue that, under cumulative

prospect theory, investors overweight small chances of large gains (and hence have lottery preferences). Therefore, such

investors prefer (and bid up) positively skewed stocks, causing them to be overpriced and earn low subsequent returns.

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