Is stock return predictability of option‐implied skewness affected by the market state?

• Author: Tong Suk Kim,Heewoo Park
• Published date: 01 September 2018
• Date: 01 September 2018
• DOI: http://doi.org/10.1002/fut.21921

1024 © 2018 Wiley Periodicals, Inc. wileyonlinelibrary.com/journal/fut J Futures Markets. 2018;38:1024–1042.

Received: 17 October 2017

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Accepted: 17 March 2018

DOI: 10.1002/fut.21921

RESEARCH ARTICLE

Is stock return predictability of option-implied skewness

affected by the market state?

Tong Suk Kim

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Heewoo Park

College of Business, Korea Advanced

Institute of Science and Technology

(KAIST), Seoul, Republic of Korea

Correspondence

Heewoo Park, College of Business, Korea

Advanced Institute of Science and

Technology (KAIST), 85 Hoegi-ro,

Dongdaemun-gu, Seoul, Republic of Korea.

Email: laax@kaist.ac.kr

We use (Bakshi, Kapadia, and Madan, 2003, Review of Financial Studies 16:

101–143) methodology to measure the option-implied ex ante skewness of the risk-

neutral returns distribution for underlying stocks.We find a negative relation between

option-implied skewness and subsequent stock returns, even after controlling for a

myriad of firm-characteristic variables. Specifically, the cross-sectional stock return

predictability of option-implied skewness is only significant during periods of low

market return and high investor sentiment. Furthermore, we find that the predictive

power of skewnesscan be attributed to market state rather than sentiment.Our findings

suggest that investors should consider high option-implied skewness stocks as they

would lottery-like stocks.

KEYWORDS

cross-sectional return predictability, option-implied skewness, skewness preference

JEL CLASSIFICATION

G11, G12, G14

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INTRODUCTION

Over half a century of finance literature has focused on investigating whether investors consider return skewness when they

invest. Arditti (1967) and Scott and Horvath (1980) show that under general assumptions, investors prefer a positive skewness in

returns distribution. Because skewness is largely affected by the outliers of returns, measuring skewness is not a simple task.

Researchers have examined several methodologies to compute skewness, including co-skewness, idiosyncratic skewness, and an

ex ante version of skewness.

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Recent research has attempted to measure ex ante skewness to investigate the pricing implications of skewness. Boyer,

Mitton, and Vorkink (2009) construct a cross-sectional model of expected idiosyncratic skewness and show that stocks with high

expected idiosyncratic skewness have lower subsequent returns. However, because expected idiosyncratic skewness requires

5 years of data to measure, capturing short-term changes in expected skewness is difficult.

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Using option data, it is possible to

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Harvey and Siddique (2000) and Dittmar (2002) provide empirical results that stock returns’co-skewness with the market portfolio return is priced.

Mitton and Vorkink (2007) and Barberis and Huang (2008) establish their models and show that stocks with high idiosyncratic skewness exhibit lower

expected returns.

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Boyer et al. (2009) denote that expected skewness premium has time-series variation, but they do not find which factors affect the skewness premium.

We refer short-term to one month in this article.

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KIM AND PARK

compute ex ante skewness without requiring a long history of data.

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Option-implied risk-neutral skewness may even capture

short-term changes in the stock return predictability of skewness.

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To our knowledge, researchers have not examined the time-

varying return-predictive power of option-implied skewness. According to our findings, we can further understand the

characteristics of option-implied skewness.

In this paper, we examine whether the stock return predictive power of option-implied skewness varies with market state and

investor sentiment. Option-implied skewness has a negative relation between subsequent stock returns. First, we find that the

return predictive power of skewness remains even after controlling for firm-characteristic variables that are known to forecast

stock returns such as idiosyncratic volatility, return reversal, momentum, market capitalization, book-to-market ratio, market

beta, and the illiquidity measure. In addition, return predictability of skewness is only significant during downturn market

periods and high investor sentiment states. Kumar (2009) and Fong and Toh (2014) also find that investors’demand for lottery-

like stocks increases during economic downturns or high investor sentiment periods. Thus, we conclude that investors regard

high option-implied skewness stocks as they do lottery-like stocks. Our analysis suggests that option-implied skewness also has

economic meanings beyond just that of a theoretically calculated measure.

We begin our analysis with daily option data to compute option-implied skewness. There are some advantages using

option-implied skewness to see short-term changes in stock return predictability. First, use of option prices reduces the

need for long time-series stock data to estimate the skewness of a returns distribution. In particular, option-implied

skewness readily captures changes in the return predictive power of skewness during periods of change in the expectation

of investors’skewness preferences. Second, option prices are a market-based estimate of investors’expectations. Bates

(1991), Rubinstein (1994), and Jackwerth and Rubinstein (1996) find that option prices contain information regarding

market participants. Thus, under the assumption that no-arbitrage rules hold between the options and the stocks market,

option prices contain information identical to stock prices.

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Third, options contain ex ante expectations of the stock

returns distribution. The predictive power of option data on stock returns is caused by informed traders who choose the

option market to trade first, and then trade in the stock markets (e.g., Chowdhry & Nanda [1991] and Easley, O'hara, &

Srinivas [1998]).

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We examine whether the return predictability of skewness depends on the market state or not. Kumar (2009) shows that

excess buy–sell imbalance (EBSI) for high skewness stocks is high when the market return is low. In other words, investors

especially prefer high skewness stocks during bad market states because investors have a similar preference for high skewness

stocks and state lotteries.

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We separately investigate the return predictability of skewness during downturn markets and upturn

markets. Our results confirm that the return predictability of skewness is only significant during downturn markets.

The return predictability of skewness also depends on the sentiment of market participants. We proxy investor sentiment

index for the University of Michigan consumer sentiment index (MCSI) following Lemmon and Portniaguina (2006). Fisher and

Statman (2003) find a positive correlation between investor sentiment and consumer sentiment. We find that high skewness

stocks exhibit significantly lower subsequent returns during high investor sentiment periods (i.e., levels of the MCSI above the

median value). When investor sentiment is high, investors are more optimistic about the future payoffs of high skewness stocks

and so future returns on such stocks become low. Fong and Toh (2014) also argue that lottery-like stocks exhibit low subsequent

returns only during high investor sentiment periods.

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In addition, we compare the effect of market returns and the MCSI to the return predictive power of skewness. We examine

the return predictability of skewness in four sample periods that are divided by a two-way classification of market state and

investor sentiment. We find that the return predictability of skewness is mostly affected by market return rather than investor

sentiment. Then we analyze the time-series relations between them. Prior literature finds that consumer sentiment is related to

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Bakshi and Madan (2000) and Bakshi et al. (2003) show that risk-neutral skewness of stock returns can be calculated by using a set of daily option prices

with different strike prices on that stock. Using Bakshi et al. (2003) risk-neutral skewness, Dennis and Mayhew (2002) and Conrad et al. (2013) examine

cross-sectional stock return predictability of skewness.

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We calculate option implied skewness using the methodology of Bakshi et al. (2003).

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Ofek and Richardson (2003) and Battalio and Schultz (2006) say that option prices and the prices of underlying stocks did not diverge during the Internet

bubble when eliminating options of stale price quotes. In section 2.1, we employ filters to avoid misleading prices of options.

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Bali and Hovakimian (2009), Cremers and Weinbaum (2010), and Xing, Zhang, and Zhao (2010) also use a cross section of options data to show that

option prices include predictive information about stock returns.

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Lottery studies explain that people find the tiny probability of a large payoff more attractive during bad economic conditions. Mikesell (1994) empirically

shows that people are attracted more toward state lotteries during economic downturns.

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They define the lottery-like stocks as high MAX stocks. MAX is defined as maximum daily returns (MAX) over the past month.