Skewness and index futures return

• Published date: 01 November 2020
• Author: Xuewu Wang,Qunzi Zhang,Zhipeng Yan,Eric Jondeau
• Date: 01 November 2020
• DOI: http://doi.org/10.1002/fut.22112

J Futures Markets. 2020;40:1648–1664.wileyonlinelibrary.com/journal/fut1648

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© 2020 Wiley Periodicals, Inc.

Received: 14 February 2020

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Accepted: 26 February 2020

DOI: 10.1002/fut.22112

RESEARCH ARTICLE

Skewness and index futures return

Eric Jondeau

1

|Xuewu Wang

2

|Zhipeng Yan

3

|Qunzi Zhang

4

1

Faculty of Business and Economics

(HEC Lausanne), Swiss Finance Institute,

University of Lausanne, Lausanne,

Switzerland

2

School of Business, Quinnipiac

University, Hamden, Connecticut

3

Martin Tuchman School of Management,

New Jersey Institute of Technology,

Newark, New York

4

School of Economics, Shandong

University, Jinan, China

Correspondence

Qunzi Zhang, School of Economics,

Shandong University, 250100 Jinan,

China.

Email: qunzi.zhang@sdu.edu.cn

Funding information

Shandong Province Social Science Fund,

Grant/Award Number: 19CJRJ19

Abstract

In this paper, we show that the individual skewness, defined as the average of

monthly skewness across firms, performs very well at predicting the return of

S&P 500 index futures. This result holds after controlling for the liquidity risk

or for the current business cycle conditions. We also find that individual

skewness performs very well at predicting index futures returns out‐of‐sample.

KEYWORDS

average skewness, index futures return, return predictability

JEL CLASSIFICATION

G11; G12; G13; G17

1|INTRODUCTION

For decades, a substantial literature has explored the dynamics between the U.S. equity index market and the index

futures market. The common finding is that the futures market is an important determinant of the equity index market.

And there is scant evidence that the equity market performs well at predicting the index futures market. Additionally,

predicting the index futures market based on equity market remains a challenging task. However, theoretically the

equity market should provide valuable forecasting indicators as the price of an index futures contract is supposed to

reflect the expected value of the underlying equity market index.

In this paper, we fill this gap by providing a new finding that the cross‐firm average skewness in the equity market

plays a prominent role in predicting the S&P 500 index futures market return. Specifically, we find that average skewness

significantly predicts the index futures return, that is a one‐standard‐deviation increase in monthly average skewness

predicts a 0.59% decrease in the monthly index futures return. Additionally, we find this significant negative relation

between average stock skewness and index futures return holds over subsample periods. It also holds after controlling for

the usual variables known to predict market returns suchas market illiquidity measures and business conditions. We also

find that average skewness outperforms other economic variables proposed by Goyal and Welch (2008)inpredictingthe

index futures returns.

Additionally, we evaluate the out‐of‐sample performance of the average skewness as a predictor for the index

futures return. For this purpose, we perform out‐of‐sample 1‐month ahead forecasts with several predictors, including

the equity index return, the average variance, the average skewness, and economic variables proposed by Goyal and

Welch (2008). We find evidence that the predictive power of the average skewness dominates that of the other

predictors. Additionally, we show that an investor forms her strategy based on timing average skewness does not only

make positive investment profit but also enjoys significant economic gains. All these results confirm that the average

(individual) skewness is an important predictor of subsequent index futures returns.

In fact, the potential relation between individualskewness and the future asset returns has been investigated in a long‐

standing literature. Several theories have been proposed to explain why high (individual or idiosyncratic) skewness

determines expected returns. First, the role of idiosyncratic skewness has also been put forward to explain why investors

actually hold underdiversified portfolios (Conine & Tamarkin, 1981;Kumar,2009;Mitton&Vorkink,2007; Simkowitz &

Beedles, 1978). That is, investors with preference for skewness may hold underdiversified portfolios to benefit from the

upside potential of positively skewed assets. Mitton and Vorkink (2007) argue that investors with preference for skewness

underdiversify their portfolio to invest more in assets with positive idiosyncratic skewness. At the equilibrium, stocks

with high idiosyncratic skewness will pay a premium. This finding contrasts to the traditional view that individual or

idiosyncratic skewness risk should not be priced since it can be diversified away.

Second, investors' beliefs and preferences on skewness influence future asset returns. Brunnermeier, Gollier, and

Parker (2007) show that investors choose to have distorted beliefs about the probabilities of future states to maximize

their expected utility. They will tend to underdiversify their portfolio by investing in positively skewed assets. In the

context of cumulative prospect theory (Kahneman & Tversky, 1979), Barberis and Huang (2008) construct a model in

which investors wrongly measure probability weights. This results in an overpricing of positively skewed securities,

which earn a negative average excess return at the equilibrium (see also Bali, Cakici, & Whitelaw, 2011; Kumar, 2009).

Bordalo, Gennaioli, and Shleifer (2013) develop a theory in which investors overweight the salient payoffs relative to

their objective probabilities. In this approach, assets with large upside (positive skewness) are overpriced, whereas

assets with large downsides (negative skewness) are underpriced.

Third, the potential growth of firms is also related to skewness which in turn affects firm's stock return. Trigeorgis

and Lambertides (2014) and Del Viva, Kasanen, and Trigeorgis (2017) argue that growth options are significant

determinants of idiosyncratic skewness. This relation is due to the convexity of the payoff of real options. As investors

are willing to pay a premium to benefit from the upside potential of the real option, firms with growth options are

generally associated with a negative return premium.

1

However, to date, the literature on the relation between the average skewness and the subsequent equity index return

is very scarce and provides mixed results. Using S&P index options to estimate skewness, Chang, Zhang, and Zhao (2011)

find a negative and weakly significant effect of the physical market skewness on the future monthly return for the period

1996–2005. Garcia, Mantilla‐Garcia, and Martellini (2014) investigate the ability of cross‐sectional var iance and a robust

measure of skewness, based on the quantiles of the cross‐section distribution of monthly returns, to predict the future

market return based on CRSP data between 1963 and 2006. The empirical estimate that they find for the skewness

parameter is insignificant when predicting the monthly value‐weighted market return. In contrast, Stöckl and Kaiser

(2016)findthatcross‐sectional skewness adds to the predictive power of cross‐sectional volatility in the short run.

A recent study by Jondeau, Zhang, and Zhu (2019) find a significant negative relation between average skewness

and future stock market returns. More negatively skewed returns are associated with subsequent higher returns. So far,

no paper has investigated the ability of the average (individual) skewness to predict the subsequent index futures

return. We do this by extending the work of Goyal and Santa‐Clara (2003), Bali, Cakici, Yan, and Zhang (2005), and

Jondeau et al. (2019). We use the same data and methodology and perform a similar robustness analysis. We note that

our measure is different from the ones from Jondeau et al. (2019). Their monthly individual firm's skewness is

calculated with demeaned individual return, where the mean is the average of individual firm return within each

month; however, we use the average of equity market index return within each month as the mean to demean the

individual firm return. In this way, we eliminate the effect from the equity market return and focus on the idiosyncratic

skewness risk from the current equity market. In the end, we find that average skewness calculated based on this

procedure is an effective predictor for index futures returns.

The rest of this paper is organized as follows. Section 2conducts literature review. Section 3describes the data and

the construction of the variables used in the paper. Section 4presents empirical evidence that the average skewness

negatively predicts subsequent market return. We show that this result is robust to several alterations of the baseline

specification. In Section 5, we evaluate the out‐of‐sample performance of the average skewness as a predictor of the

index futures market return. We also find that average skewness generates superior economic performance compared to

alternative predictors. Section 6concludes.

1

Cao, Simin, and Zhao (2008) and Grullon, Lyandres, and Zhdanov (2012) provide evidence that real options are important drivers of idiosyncratic

volatility and may explain the positive relation between stock return and volatility documented by Duffee (1995).

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