IDIOSYNCRATIC RISK PREMIA AND MOMENTUM

• Author: Steve L. Slezak,Doina C. Chichernea
• Date: 01 September 2013
• Published date: 01 September 2013
• DOI: http://doi.org/10.1111/j.1475-6803.2013.12016.x

IDIOSYNCRATIC RISK PREMIA AND MOMENTUM

Doina C. Chichernea

University of Toledo

Steve L. Slezak

University of Cincinnati

Abstract

Theory predicts that in the presence of incomplete information, underdiversified

investors will demand idiosyncratic risk premia (IRP) as compensation for idiosyncratic

volatility (IV). We estimate IV and IRP at the individual stock level and document the

extent to which momentum profits can be explained by cross‐sectional variation in IRP.

We show that a large portion of momentum profits can be explained by cross‐sectional

variation in IRP and that, as predicted by theory, variations in both momentum profits and

IRP are related to the ratio of firm size to investor base. However, significant momentum

profits in low‐IV securities cannot be explained by cross‐sectional variation in IRP.

JEL Classification: G12, G14

I. Introduction

The existence of significantly positive excess returns from momentum strategies is well

established in the literature. However, there remain questions about the source of these

excess returns. Whether these profits are symptomatic of mispricing (as originally

proposed by Jegadeesh and Titman 1993) or variation in risk premia (Conrad and

Kaul 1998; Chordia and Shivakumar 2002) is still an open debate. Motivated by the limits

to arbitrage argument (Shleifer and Vishny 1997), recent studies examine the degree to

which momentum profits are concentrated in securities with high idiosyncratic volatility

(IV). Pontiff (2006) argues that IV as a holding cost constitutes one of the main barriers to

arbitrage: the greater the IV of a mispriced security, the less likely it is that risk‐averse

arbitrageurs are willing to trade aggressively enough to correct the mispricing. In the case

of momentum, if IV is high for securities in the winner and loser portfolios, then whatever

mispricing caused them to be placed in those portfolios is likely to persist.

Consistent with this mispricing/limits‐to‐arbitrage hypothesis, many empirical

studies (e.g., Hung and Glascock 2010; Arena, Haggard, and Yan 2008; Li et al. 2008;

McLean 2010) show that indeed the securities that comprise the winner or loser portfolios

typically have higher IV than those in the other deciles. Additionally, the securities in the

We wish to thank the following people for their extremely useful comments: Gregory W. Brown, Jennifer

Conrad, Tarun Chordia, Michael Ferguson, Hui Guo, Brian Hatch, Steven L. Jones (associate editor), Yong Kim,

David Manzler, Nadia Vozlyublennaia (reviewer), and Diana Wei. Any errors of omission or commission are ours

alone.

The Journal of Financial Research Vol. XXXVI, No. 3 Pages 389–412 Fall 2013

389

© 2013 The Southern Finance Association and the Southwestern Finance Association

loser portfolio appear to have significantly higher IV on average than those in the winner

portfolio. Although limits‐to‐arbitrage implies that there should be higher IV in the

extreme momentum portfolios, it also implies that conditioning on IV should generate

higher momentum profits. This hypothesis is investigated by McLean (2010), who shows

that, in fact, momentum profits are equally strong across IV quintiles and independent of

whether the momentum portfolios are equally weighted or weighted by IV. The author

concludes that if mispricing is the root of momentum, then it must be that high transaction

costs (rather than IV) sustain this mispricing.

1

We examine an alternative null hypothesis that is consistent with the results

documented by McLean (2010) but does not rely on a mispricing/limits‐to‐arbitrage

argument. Specifically, motivated by theoretical asset‐pricing models that show the

existence of equilibrium risk premia for IV (hereafter referred to as idiosyncratic risk

premia [IRP]), we examine the extent to which cross‐sectional variation in IRP

contributes to momentum profits. Although the traditional view in asset pricing maintains

that IV should be diversified away and should not affect mean returns in equilibrium,

theoretical work (Levy 1978; Mayers 1976; Merton 1987; Malkiel and Xu 2006) shows

that in the presence of barriers to full diversification, each security will have an IRP that

compensates investors for the contribution of that security’s IV to the risk in their

portfolios.

2

The existence of such positive IRP is the null hypothesis that is maintained in

our empirical investigation.

The theory (i.e., Merton 1987) highlights that the IRP for a specific security need

not be increasing in that security’s IV; the rationale for positive IRP (i.e., incomplete

market integration across all investors) is the very reason there is no single price per unit of

IV. Rather, the theory implies that, per unit of IV, IRP will be increasing in the ratio of firm

size over investor base. Holding constant firm size, the more widely held a security is, the

less each investor holds on average and, as a result, the less it generates in terms of risk to

their portfolios. This results in a smaller premium per unit of IV being required to

compensate investors in equilibrium. Similarly, holding the investor base constant, the

larger the firm size, the greater the amount of IV that must be held by investors on average,

resulting in a higher premium per unit of IV.

The fact that IRP are not necessarily increasing in IV is important for two reasons.

First, even though the securities in the loser portfolio have higher IV on average than those

in the winner portfolio, winners can have higher IRP than losers as long as their price per

unit of IV is sufficiently high.

3

If so, the relation between IV and momentum profits

1

This follows Lesmond, Schill, and Zhou (2004), who find that momentum strategies require high transaction

costs.

2

Empirical evidence shows that most investors are in fact not fully diversified: Barber and Odean (2000) report

that for their sample of customers of a retail broker, the mean (median) household holds only 4.3 (2.61) stocks;

Benartzi (2001) and Goetzmann and Kumar (2008) also provide evidence that the equity portfolios of individual

investors are underdiversified.

3

In fact, the literature provides mixed evidence concerning the role of IV in the cross‐section of returns, with

some studies showing higher IV associated with higher mean returns, and other studies showing the opposite (see

Malkiel and Xu 2006; Fu 2009 vs. Ang et al. 2006, 2009). These mixed results are consistent with the IRP of a

security not simply increasing in the level of that security’s IV; rather, a positive (negative) relation in the cross‐

section might simply mean that higher levels of IV are associated with higher (lower) IRP on average. Such an

average result does not foreclose the possibility that some securities have high (low) IRP and low (high) IV.

390 The Journal of Financial Research