Market Excess Returns, Variance and the Third Cumulant

Abstract

In this paper, we develop an equilibrium asset pricing model for market excess returns, variance and the third cumulant by using a jump‐diffusion process with stochastic variance and jump intensity in Cox et al. (1985) production economy. Empirical evidence with the S&P 500 index and options from January, 1996 to December, 2005 strongly supports our model prediction that the lower the third cumulant, the higher the market excess returns. Consistent with existing literature, the theoretical mean–variance relation is supported only by regressions on risk‐neutral variance. We further demonstrate empirically that the third cumulant explains significantly the variance risk premium.

Risk‐neutral moments and return predictability: International evidence

“…On the other hand, because these ETFs are tracking on highly diversified MSCI indices, which normally have the mean‐reversion expectation to these indices, stock traders prefer to go long for the assets in a period when these out‐of‐money put options are believed to be overpriced, as the risk‐return trade‐off and skew preference theory mentioned in Conrad et al (2013). In addition, Zhang et al (2020) develop an equilibrium asset pricing model and theoretically proved that the variance and the third‐order cumulant can positively and negatively predict market excess returns, respectively, by inputting parameters from Santa‐Clara and Yan (2010) paper. The eighth to 10th columns show the results of slope coefficients of of ETFs.…”

Implied volatility smirk in the Australian dollar market

“…We follow Li et al . (2019) in testing the predictive power of the factors, their first difference and the third and fourth cumulants (as in Ruan and Zhang, 2018 and Zhang et al ., 2018).…”

How do US options traders “smirk” on China? Evidence from FXI options

“…Ideally, we would always use VWLS to emphasize information from more liquid contracts, but we also want to fit the market IVs well when trading is concentrated in a small number of contracts. Following Zhang et al (2019) and Ruan and Zhang (2018), we are also interested in the predictive power of the risk-neutral third and fourth cumulants and that of their first differences. In line with Ang et al (2006), Chang, Christoffersen, et al (2013), Chatrath et al (2016), and Xing et al (2010), we expect that those moments, and therefore the quantified IV factors, contain information on the future returns of the underlying FXI ETF.…”

“…Therefore, they are expected to have predictability of the future excess returns of the underlying FXI ETF, as is the case in other equity option markets (Ang, Hodrick, Xing, & Zhang, 2006;Chang, Christoffersen, & Jacobs, 2013;Chatrath, Miao, Ramchander, & Wang, 2016;Xing, Zhang, & Zhao, 2010). We test the predictability of FXI monthly excess returns using the factors and the risk-neutral third and fourth cumulants (Zhang, Chang & Zhao, 2019;Ruan & Zhang, 2018), as well as their first differences (Ang et al, 2006) for the in-sample and out-of-sample univariate regressions. We find that the first differences of the third cumulants can predict the future FXI monthly excess returns significantly in both in-sample and out-of-sample tests.…”