The Role of Trading Volume in the “Volatility Puzzle”

• DOI: http://doi.org/10.1111/ajfs.12113
• Date: 01 October 2015
• Published date: 01 October 2015
• Author: Dong Wook Lee

The Role of Trading Volume in the

“Volatility Puzzle”*

Dong Wook Lee**

Korea University Business School

Received 8 May 2015; Accepted 5 August 2015

Abstract

We find that the negative average-return differential between high- and low-volatility stocks

—the so-called “volatility puzzle”—is particularly more pronounced when both groups of

stocks have large trading volume. Conversely, the return differential is completely absent

among low-turnover stocks. Such a high turnover-conditional volatility-future return relation

is long-lived and present in various segments of the market and in different time-periods—

e.g., in both small and large stocks and during low- as well as high-investor sentiment peri-

ods. While the information contents of large trading volume are likely to be multi-dimen-

sional—thereby allowing for different explanations, our results at least suggest that trading

volume is a useful empirical guide to where to (not) find the average return differential

between low- and high-volatility stocks. We also illustrate, in a setting that is neutral about

market efficiency, how trading volume interacts with volatility and affects future returns.

Keywords Volatility puzzle; Trading volume; Parameter uncertainty; Convexity

JEL Classification: G10, G11, G12

*The author is grateful for comments to Suk-Joon Byeon, Zahi Ben-David, Fousseni Chabi-

Yo, Sergey Chernenko, Anurag Gupta, Kewei Hou, Jan Jindra, Dasol Kim, Imnoo Lee, Shaoji

Lin, Anil Makhija, Peter Ritchken, Ren

e Stulz, Sam Thomas, Mike Weisbach, Ingrid Werner,

Lu Zhang, and the seminar participants at The Ohio State University and Case Western

Reserve University. This is a significantly revised version of the earlier papers tiled: “Bias in

stock price forecast and the cross-section of stock returns,” “Discount-rate uncertainty, hold-

ing period, and the cross-section of stock returns,” and “Parameter uncertainty and the

cross-section of stock returns: A new perspective on the ‘volatility puzzle’.” This paper was

supported by the National Research Foundation of Korea Grant funded by the Korean

Government (NRF-2012S1A2A1A01030725). Financial support from the Asian Institute of

Corporate Governance (AICG) at Korea University is also gratefully recognized. Dong Wook

Lee is working as a Professor of Finance in Korea University Business School. Part of this

paper was completed while Lee was visiting The Ohio State University.

**Corresponding author: Dong Wook Lee, Korea University Business School, 523 Hyundai

Motors Hall, Seoul 136-701, Korea. Tel: +82-2-3290-2820, Fax: +82-2-3290-5394, email: dong

lee@korea.ac.kr.

Asia-Pacific Journal of Financial Studies (2015) 44, 783–809 doi:10.1111/ajfs.12113

©2015 Korean Securities Association 783

1. Introduction

Prior studies have documented that stocks with greater return volatility earn a

lower return in the future than do stocks with smaller volatility (Ang et al., 2006;

Baker et al., 2011). Often known as the “volatility puzzle,” the negative average-

return differential between high- and low-volatility stock—or equivalently, the nega-

tive cross-sectional relationship between volatility and future return—has been a

robust empirical regularity that has been extensively examined.

1

In this paper, we

offer a new perspective on this issue by examining the role of trading volume in the

volatility-future return relation.

An analysis of trading volume is motivated initially by the observation that the

negative volatility-future return relation is commonly explained as a result of high-

volatility stocks being initially overvalued and subsequently experiencing a cor rec-

tion (e.g., the survey by Hou and Loh, 2012). Given that large trading volume is

typical of equity overvaluation (Scheinkman and Xiong, 2003; Hong and Stein,

2007), an investigation into trading volume appears to be a natural step toward a

better understanding of the relation. We also note, as another motivation, that a

given return predictability can be alternatively explained by investors’ rational learn-

ing about uncertain parameters (Stulz, 1987; Lewellen and Shanken, 2002; Pastor

and Veronesi, 2009; Armstrong et al., 2013) and that trading is closely related to

the learning process (Massa and Simonov, 2005; Banerjee and Kremer, 2010; Carlin

et al., 2012). Yet another motivation can be found in the observation that the nega-

tive volatility-future return relation goes beyond the very next period. As detailed

in Section 3.1, the volatility is significantly and negatively related to each of the

monthly returns over more than the next 6 months. Such a long-lived relation sug-

gests that trading volume—which itself persists over time—is worthwhile to investi-

gate.

As explained above, the information contents of trading volume are indeed mul-

ti-dimensional. Thus, trading volume can hardly be useful in offering a new expla-

nation or distinguishing among existing ones for the volatility-future return

relation. Our approach here is to use this “multi-facedness” of trading volume as a

ground for using it empirically. In other words, we view trading volume as a

“catch-all” proxy for different factors affecting the volatility-future return relation

1

The literature has grown into two strands. One focuses on the systematic volatility and

attempts to explain why higher-beta stocks earn a lower return than do stocks with a lower

beta (Hong and Sraer, 2012; Frazzini and Pedersen, 2014). The other line of research tackles

the “idiosyncratic volatility puzzle,” which is initiated by Ang et al. (2006). Hou and Loh

(2012) provide an excellent survey of this research. Stambaugh et al. (2013), Drechsler and

Drechsler (2014), and Jordan and Riley (2014) are important studies that come out after the

Hou and Loh’s survey paper. Baker et al. (2011) show that distinguishing between the sys-

tematic and the idiosyncratic volatility does not make much difference; they then recognize

the issue as the “low volatility anomaly.”

D. W. Lee

784 ©2015 Korean Securities Association