Average skewness in global equity markets

• Published date: 01 June 2023
• Author: Yigit Atilgan,K. Ozgur Demirtas,A. Doruk Gunaydin,Imra Kirli
• Date: 01 June 2023
• DOI: http://doi.org/10.1111/irfi.12395

ORIGINAL ARTICLE

Average skewness in global equity markets

Yigit Atilgan | K. Ozgur Demirtas | A. Doruk Gunaydin | Imra Kirli

Sabanci Business School, Sabanci University,

Istanbul, Turkey

Correspondence

A. Doruk Gunaydin, Sabanci Business School,

Sabanci University, Orhanli Tuzla 34956,

Istanbul, Turkey.

Email: doruk.gunaydin@sabanciuniv.edu

Funding information

BAGEP Award of the Science Academy;

TÜBA-GEB_

IP Award of Turkish Academy of

Sciences

Abstract

This paper examines the predictive power of average

skewness, defined as the average of monthly skewness

values across stocks, documented by the prior literature

for US market returns in an international setting. First, we

confirm the validity of the results in the original study and

show that the intertemporal relation between average

skewness and aggregate returns becomes weaker in an

alternative sample period. Second, when we repeat the

analysis in 22 developed non-US markets, we find that

average skewness has no robust predictive power for

future market returns. The loss of forecasting power in

the international sample does not depend on the method

used to calculate average skewness or the regression

specification and is supported by additional out-of-sample

tests and subsample analysis.

KEYWORDS

average skewness, equity returns, international finance, market

skewness, time-series predictability, volatility

JEL CLASSIFICATION

G11, G12, G15

1|INTRODUCTION

The role of skewness in asset pricing is a vibrant topic of discussion. Early studies such as Arditti (1967,1971), Scott

and Horvath (1980), and Kimball (1990) suggest that investors demand higher (lower) returns from investments

whose return distributions are negatively (positively) skewed. This preference for skewness can impact security

prices. Most of this early work focuses only on coskewness which is the component of an asset's skewness which

can be explained by aggregate skewness. The assumption behind this focus is that fully diversified investors will take

Received: 3 September 2021 Revised: 22 August 2022 Accepted: 10 September 2022

DOI: 10.1111/irfi.12395

© 2022 International Review of Finance Ltd.

International Review of Finance. 2023;23:245–271. wileyonlinelibrary.com/journal/irfi 245

skewness into account in their investment decisions only as far as it poses a systematic risk and idiosyncratic skew-

ness will be diversified away. Kraus and Litzenberger (1976) incorporate preference for skewness into the standard

CAPM framework and studies such as Harvey and Siddique (2000) and Dittmar (2002) provide empirical evidence

for the role of coskewness in equity pricing.

On the other hand, subsequent work has also documented the ability of various measures of idiosyncratic skew-

ness to explain the cross-section of equity returns whether interpreted as ameasure of downside risk or lottery pref-

erence (e.g., Amaya et al., 2015; Bali et al., 2011; Bali & Murray, 2013; Boyer et al., 2010; Boyer & Vorkink, 2014;

Conrad et al., 2013; Conrad et al., 2014; Kumar, 2009). The common theme that runs through these studies is that

investors under-diversify their portfolios due to their preference for individual stock skewness (Mitton &

Vorkink, 2007).

1

Several theoretical studies present models that hinge on alternative utility functions and/or behav-

ioral biases and provide a justification for this type of under-diversification (e.g., Barberis & Huang, 2008; Bordalo

et al., 2012; Brunnermeier et al., 2007; Brunnermeier & Parker, 2005).

Jondeau et al. (2019) carry these ideas from the cross-section to the time-series of aggregate returns. They pre-

sent a model which suggests that if investors have a preference for both systematic and individual stock skewness,

idiosyncratic moments do not vanish in the expression for expected market returns due to under-diversification. In

other words, the stochastic discount factor should also incorporate idiosyncratic higher-order moment risk. This

framework suggests a role for average skewness across stocks to predict aggregate returns and the authors test this

hypothesis in the US data. Monthly skewness values for individual equities are calculated as the third moment of the

distribution of demeaned and standardized daily excess stock returns. Next, these monthly skewness values are aver-

aged using either market capitalization or equal weights and two measures of average skewness are calculated. The

authors also construct two analogous measures of average variance by averaging monthly variance values across

stocks. Moreover, market variance and market skewness are calculated using daily excess market returns. Results

from univariate regressions indicate that both value- and equal-weighted skewness are powerful predictors of future

market return. Multivariate regressions that control for lagged market return, market variance and market skewness

show that average skewness has incremental forecasting power and captures independent information about future

aggregate returns. The results are robust after measuring average skewness and average variance in alternative ways,

controlling for various macroeconomic and financial variables, utilizing different specifications and performing out-

of-sample tests.

This paper investigates the predictive power of average skewness for future market returns in 23 developed

countries including the United States. Most empirical regularities in financial economics are first documented in the

US data and international tests of such regularities are subsequently conducted to validate the initial findings in an

out-of-sample setting. Given the existence of significant predictive patterns in US data, a cross-country investigation

of the relation between average skewness and future market returns is warranted to understand whether such pat-

terns extend to non-US markets. If we find that average skewness has widespread forecasting power outside the

United States, this would lend additional support to the theoretical conjectures and empirical findings of Jondeau

et al. (2019) and serve as a credible robustness test. However, if average skewness plays a predictive role for aggre-

gate returns in only a small fraction of non-US markets, this raises the possibility that the US-based findings are not

easily generalizable in terms of investor behavior and asset pricing. Our empirical results are in line with the latter

rather than the former scenario.

Our sample period begins in January 1990 and ends in September 2019. To make sure that our empirical imple-

mentation is accurate, we first replicate the methodology of Jondeau et al. (2019) who present their findings for two

samples. Their full sample covers the period between 1963 and 2016 and a subsample extends from 1990 to 2016.

We validate our variable construction procedure by comparing the summary statistics and correlation structures for

our US data and the data used by Jondeau et al. (2019) during the overlapping sample period between 1990 and

2016. We also validate the significantly negative relation between average skewness and future aggregate returns

during this period in our data. However, when we estimate the predictive regressions using our extended sample

that ends in 2019, the intertemporal relation becomes weaker.

246 ATILGAN ET AL.