High Idiosyncratic Volatility and Low Returns: A Prospect Theory Explanation

• Author: Ajay Bhootra,Jungshik Hur
• Published date: 01 June 2015
• Date: 01 June 2015
• DOI: http://doi.org/10.1111/fima.12057

High Idiosyncratic Volatility and Low

Returns: A Prospect Theory Explanation

Ajay Bhootra and Jungshik Hur∗

The well-documented negative relationship between idiosyncratic volatility and stock returns

is puzzling if investors are risk-averse. However, under prospect theory, while investors are risk-

averse in the domain of gains, theyexhibit risk-seeking behavior in the domain of losses. Consistent

with risk-seeking investors’ preference for high-volatility stocks in the loss domain, we find that

the negative relationship between idiosyncratic volatility and stock returns is concentrated in

stocks with unrealized capital losses, but is nonexistent in stocks with unrealized capital gains.

This finding is robust to control forshort-term return reversals and maximum daily return, among

other variables.

According to the standard asset pricing theory, only the systematic risk of securities should

be priced and there should be no compensation for diversifiable idiosyncratic risk. However,

according to Merton’s(1987) investor recognition hypothesis, if investors invest only in securities

with familiar risk-return characteristics and, consequently, hold underdiversified portfolios, id-

iosyncratic risk should be priced in equilibrium. In direct contrast to the implications of Merton’s

(1987) hypothesis, Ang et al. (2006) document a puzzling negative cross-sectional relationship

between stocks’ idiosyncratic volatility and their returns in the following month.

Merton’s (1987) implication of a positive volatility-return relationship with suboptimal di-

versification assumes risk-averse investors with a concave utility of wealth function within the

standard expected utility framework. However, Kahneman and Tversky’s (1979) prospect theory

(PT) model of decision making under uncertainty postulates an S-shaped utility function that is

concave in the domain of gains, but convex in the domain of losses. The S-shaped utility function

is consistent with risk-aversion over positive prospects, but risk-seeking behavior over negative

prospects.

We posit that investors’ divergent attitude toward risk over positive and negative prospects is

the key to understanding Ang et al.’s (2006) idiosyncratic volatility anomaly. Specifically, the

risk-seeking behavior of investors in the domain of losses suggests a preference for stocks with

high idiosyncratic volatility. In conjunction with mental accounting (MA) (Thaler, 1980), such

a tendency would result in lower returns to high idiosyncratic volatility stocks with unrealized

capital losses if the relevant mental accounts are the paper gains and losses associated with

individual stocks.

We thank Marc Lipson (Editor) and an anonymous referee for many suggestions that led to significant improvements.

We are grateful to Bing Han, David Hirshleifer, Greg Kadlec, Vijay Singal,and seminar participants at the 2011 FMA

annual meetings and the 2013 California Corporate Finance Conference at Loyola Marymount University for helpful

suggestions. We thank Ken French and Jeff Wurgler for providing the Fama-French factors and the sentiment index,

respectively,on their websites.

∗Ajay Bhootra is an Assistant Professorof Finance in the Mihaylo College of Business and Economics at California State

University in Fullerton, CA. Jungshik Hur is an Assistant Professor of Finance in the Department of Economics and

Finance at Louisiana TechUniversity in Ruston, LA.

Financial Management •Summer 2015 •pages 295 - 322

296 Financial Management rSummer 2015

Note that in the framework of Grinblatt and Han (2005), the demand distortions induced by the

presence of PT/MA investors result in overvaluation (undervaluation) of stocks with unrealized

capital losses (gains).1Weargue that the investors’ affinity for high idiosyncratic volatility stocks

within the loss domain would lead to greater overpricing among these stocks. Therefore, the

PT/MA frameworkprovides a rationale for the existence of a negative volatility-return relationship

among stocks with unrealized capital losses (and not among stocks with unrealized capital gains).

Based on the foregoing discussion, we hypothesize that the negative relationship between

idiosyncratic volatility and subsequent stock returns is concentrated in stocks with unrealized

capital losses. In order to empirically test this hypothesis, we construct a capital gains over-

hang measure similar to Grinblatt and Han (2005), employing a proxy for the market’s aggre-

gate cost basis in a stock as the relevant reference point to determine unrealized gains and

losses.

Comparing the value-weighted and equally weighted returns of five idiosyncratic volatil-

ity portfolios separately within the subgroups of stocks segregated based on unrealized cap-

ital losses (CL) and unrealized capital gains (CG), we find that for the subgroup of stocks

with the largest unrealized losses, the difference in monthly value-weighted (equally weighted)

raw returns of high and low idiosyncratic volatility portfolios is −1.57% (−1.55%) with a

t-statistic of −5.52 (−7.19). The corresponding alphas from the capital asset pricing model

(CAPM) (Sharpe, 1964; Lintner, 1965; Mossin, 1966) and Fama and French (1993) models

are even larger in magnitude and are also statistically significant. In particular, the returns

to the largest idiosyncratic volatility portfolio within the CL subgroup are consistently neg-

ative. On the other hand, for the subgroup of stocks with the largest unrealized gains, the

monthly value-weighted (equally weighted) raw return spread between high and low idiosyn-

cratic volatility portfolios is 0.35% (0.42%) with a t-statistic of 1.42 (1.86). The correspond-

ing alphas are also positive, but statistically insignificant. We obtain similar results when us-

ing the same idiosyncratic volatility cutoffs for the CL and CG subgroups, suggesting that

this result is not driven by the presence of extreme idiosyncratic volatility stocks in the CL

subgroup.2

We perform several tests to ensure the robustness of the above results. Recent evidence in

Huang et al. (2010) suggests that the idiosyncratic volatility puzzle is attributable to the short-term

reversals in returns documented in Jegadeesh (1990), Lehmann (1990), and Lo and MacKinlay

(1990).3These authors find that in the cross-sectional regressions of stock returns on idiosyncratic

volatility that control for the previous month’s return, the coefficient on idiosyncratic volatility

is no longer statistically significant.

In contrast to the evidence in Huang et al. (2010), we find that when stocks priced below

$5 are excluded from the sample, we still obtain a negative relationship between idiosyncratic

volatility and stock returns in CL stocks for both value-weighted and equally weighted portfolio

returns, as well as in Fama-MacBeth (1973) firm-level cross-sectional regressions that control

1The demand distortions occur because the S-shaped value function from the prospect theory, together with mental

accounting, leads to the disposition effect: the tendency of investors to sell their winning stocks too quicklyand hold on

to their losing stocks too long (Shefrin and Statman, 1985).

2It is noteworthy that in Ang et al. (2006, table VIII, Panel B, p. 291), the Fama-French (1993) alpha associated with

high minus low (HML) idiosyncratic volatility portfolio is −2.25% for the loser stocks, but only −0.48% for the winner

stocks, where winners and losers are identified based on the past 12-month returns. In accordance with Grinblatt and Han

(2005), our focus is on unrealized gains and losses rather than on past returns.

3Fu (2009) also documents a similar role of return reversals in the negative volatility-return relationship.