Heterogeneous Beliefs and Risk-Neutral Skewness

Abstract

This study tests whether belief differences affect the cross-sectional variation of riskneutral skewness using data on firm-level stock options traded on the Chicago Board Options Exchange from 2003 to 2006. We find that stocks with greater belief differences have more negative skews, even after controlling for systematic risk and other firm-level variables known to affect skewness. Factor analysis identifies latent variables linked to risk and belief differences. The belief factor explains more variation in the risk-neutral skewness than the risk-based factor. Our results suggest that belief differences may be one of the unexplained firm-specific components affecting skewness.

The relationship between the option-implied volatility smile, stock returns and heterogeneous beliefs

“…The finding that firmlevel idiosyncratic slope predicts future stock returns is consistent with earlier studies which find that the implied volatility smile is related to firm-level belief difference variables (Friesen et al, 2012).While our empirical results are independent of the interpretation one ascribes to them, we note that belief differences need not be interpreted as "irrational", nor do they necessarily lead to any sort of "over-reaction".…”

“…Bakshi, Kapadia, and Madan (2003) suggest that belief differences can affect risk-neutral skewness and option implied volatility, while Buraschi and Jiltsov (2006) develop a model to show that heterogeneous beliefs among investors can affect option prices and explain the option implied volatility smile. Empirical work by Friesen, Zhang, and Zorn (2012) confirms that the volatility smile and risk-neutral skewness reflect investor belief differences.…”

Is the Information on the Higher Moments of Underlying Returns Correctly Reflected in Option Prices?

“…Harvey and Siddique (2000) and Mitton and Vorkink (2007) develop an asset pricing model that incorporates the effect of coskewness of a security with the market portfolio and idiosyncratic skewness, respectively, and Dittmar (2002) incorporates kurtosis in addition to skewness into his asset pricing model. Xu (2007) and Friesen et al (2012) support the importance of skewness in asset pricing by showing that heterogeneous beliefs or variables related to belief differences are strongly related to skewness. Das and Sundaram (1999) show the relation between option prices and higher moments of their underlying assets.…”

“…That is, there are many anomalies showing that expected returns on individual assets are not solely determined by the covariance of their returns with the market portfolio. The possibility that skewness is priced in asset returns as a risk factor is shown in the empirical studies of Das and Sundaram (1999), Buraschi and Jiltsov (2006), Xu (2007) and Friesen, Zhang, and Zorn (2012). Considering that Kraus and Litzenberger (1976) proposed an asset pricing model incorporating skewness of returns in 1976, asset pricing models with higher moments have a long history, but researchers have been focusing on them recently in earnest.…”

Large-Scale Empirical Tests of the Markov Tree Model

“…Using 350,000 distinct option quotes (both calls and puts), this study examines the differences between implied risk neutral distributions for index and individual equity options. The effect of variables such as the price-to-earnings ratio and market capitalization on the skewness of implied risk neutral distributions has been studied using four years of end-of-week option data for 856 unique firms [36]-this data set comprises 67,910 distinct option quotes.…”