Idiosyncratic Risk, Investor Base, and Returns

• Date: 01 June 2015
• DOI: http://doi.org/10.1111/fima.12067
• Author: Michael F. Ferguson,Doina C. Chichernea,Haimanot Kassa
• Published date: 01 June 2015

Idiosyncratic Risk, Investor Base,

and Returns

Doina C. Chichernea, Michael F. Ferguson, and Haimanot Kassa∗

Using four different proxies for a firm’s investor base we demonstrate that idiosyncratic risk

premiums are larger for neglected stocks and smaller or economically insignificant for visible

stocks. Since neglected stocks have greater idiosyncratic volatility (IV), the total IV risk premium

(price ×quantity) for neglected stocks will be greater than that of visible stocks. Additionally,

we find a positive size effect and negative beta effect after controlling for IV. Overall, our results

provide strong support for Merton’s theory that market segmentation induced by incomplete

information is an important component of the influence of IV in the cross-section of returns.

The role of idiosyncratic volatility (IV) in the cross-section of returns has generated a rapidly

growing empirical literature. Standard asset pricing models, such as the Capital Asset Pricing

Model (CAPM), predict that perfectly diversified investors are able to eliminate IV. As such,

there will be no idiosyncratic risk premium in equilibrium. However, recent empirical evidence

contradicts this prediction.1A variant of the standard asset pricing model developed by Merton

(1987) demonstrates that IV can be priced in equilibrium if some investors are under-diversified

and do not hold the market portfolio.2

Merton’s (1987) basic intuition is that information about securities is costly to acquire. There-

fore, it is neither optimal nor even plausible for investors to track every security in the market.

These investors only follow a subset of the securities available in the market and construct

their investment portfolios from these known securities. Since investors hold under-diversified

portfolios, they demand compensation for securities’ IV. The market clears, but the presence of

incomplete information generates an equilibrium in which risky assets earn an additional pre-

mium (relative to the complete information case), reflecting the interaction of three separate stock

characteristics: 1) IV, 2) relative market size, and 3) breadth of the shareholder base (i.e., what

proportion of investors follow a particular stock).

Merton’s (1987) model is widely cited in two research streams that have developed indepen-

dently.The literature on “neglected stocks” focuses on the impact of investor recognition on firm

The authors thank Marc Lipson (Editor), Steve Slezak, seminar participants at the 2011 Midwest Finance Association,

and an anonymous refereefor helpful comments.

∗Doina C. Chichernea is an Assistant Professor in the Neff Department of Finance in the College of Business and

Innovation at the University of Toledoin Toledo, OH. Michael F. Ferguson is an Associate Professorin the Department of

Finance in the Carl H. Lindner College of Business at the University of Cincinnati in Cincinnati, OH. Haimanot Kassa

is an Assistant Professor in the Department of Financein the Farmer School of Business at Miami University in Oxford,

OH.

1Fu (2009), Spiegel and Wang(2005), and Malkiel and Xu (2006) f ind that idiosyncratic volatilityis positively correlated

with expected stock returns at the firm level. This contrasts with the findings of Ang et al. (2006, 2009) who note a

negative relationship betweenIV and expected returns, which they call a “puzzle.” See Section I for a detailed discussion

of this literature.

2Alternatively, Barberis and Huang (2001) develop a dynamic asset pricing model based on prospect theory in which

investors are loss averse over fluctuations in the prices of the individual stocks that they own and also obtain a positive

relation between expected returns and idiosyncratic volatility.

Financial Management •Summer 2015 •pages 267 - 293

268 Financial Management rSummer 2015

value. In contrast, Merton’s (1987) theory provides the primary nonbehavioral justification for

investigating the pricing of IV in the cross-section of returns. Surprisingly, although Merton’s

(1987) model has been used as a theoretical motivation for investigating each of these effects,

their interaction has not received much attention in the literature.3This paper examines the effect

of investor base on the correlation between IV and returns. We exploit the fact that this interaction

between the visibility of a stock (i.e., how widelyfollowed it is) and the pricing of its IV is unique

to Merton’s(1987) model, thus providing an empirically testable implication that can distinguish

Merton’s (1987) under-diversification model from alternative explanations for the pricing of IV.

If Merton’s (1987) intuition is correct, we should be able to determine that not only is IV

priced in the cross-section of returns, but also that it is priced conditionally, depending upon each

stock’s visibility. Therefore, the main questions that we address in this paper are: 1) is expected

IV indeed positively related to expected returns in the cross-section, and 2) if so, is there any

evidence that the market segmentation induced by informationally incomplete markets is strong

enough to produce the observed results? In other words, is the correlation between IV and returns

constant across stocks, or is IV priced conditionally as a function of the stock characteristics (in

particular, the completeness of investor base)?

Wef ind that expected IV is positivelycorrelated with expected stock returns. More importantly,

our results strongly reject the hypothesisthat the pricing of IV is independent of the stock’s investor

base and provide support for the idea that the pricing of IV is conditional upon a stock’s visibility.

This leads us to conclude that the market segmentation induced by costly information acquisition

is strong enough to be, at least partly,responsible for the documented role of IV in the cross-section

of returns.

Using an EGARCH-M estimate for IV, we find a positive relationship between expected IV

and expected returns. In the interest of robustness, we construct four proxies for investor base

that categorize stocks in terms of their degree of visibility (an inverse measure of information

acquisition costs): breadth of institutional ownership, number of analysts following a stock,

number of shareholders, and advertising expenses. Although these proxies are produced from

different sources and cover different samples (both in terms of time periods and stocks covered),

we find that the results for each of the four proxies paint a consistent picture. As anticipated,

neglected stocks are, in general, smaller and less liquid, and have higher returns and higher IV

relative to more visible stocks. Double sorts and Fama-MacBeth (1973) regressions conditioned

on the magnitude of the investor base indicate that: 1) IV is positively related to returns in the

cross-section, and 2) the IV premium is decreasing in the visibility of the stock. Specifically,

we find that the IV premium is larger for neglected stocks, and smaller or even economically

insignificant for the most visible stocks. For neglected stocks, long-short portfolios sorted on IV

generate a significant risk-adjusted return between 2.57% and 6.10% per month depending upon

the investor base proxy. However, for visible stocks, such a strategy does not generate statistically

and economically significant returns. Moreover, after controlling for IV, we find that larger stocks

are characterized by larger returns. This final point lends support to the hypothesis advanced by

Merton (1987) that the well-documented size effect is actually a manifestation of an omitted

variable problem.

3An important exception is Bodnaruk and Ostberg (2009). They use a comprehensive database of Swedish individual

investor shareholdings to construct measures of the shareholder base and build a proxy for the shadowcost of incomplete

information as described by Merton (1987). They report that expected returns are negatively related to the shareholder

base after controlling IV. In addition, Lehavy and Sloan (2008) investigate the relation between investor recognition and

stock returns and touch on the fact that this relation is stronger for stocks with greater idiosyncratic volatility.