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Market Excess Returns, Variance and the Third Cumulant

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  • Jin E. Zhang
  • Eric C. Chang
  • Huimin Zhao

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.

Suggested Citation

  • Jin E. Zhang & Eric C. Chang & Huimin Zhao, 2020. "Market Excess Returns, Variance and the Third Cumulant," International Review of Finance, International Review of Finance Ltd., vol. 20(3), pages 605-637, September.
    • Handle: RePEc:bla:irvfin:v:20:y:2020:i:3:p:605-637
    DOI: 10.1111/irfi.12234
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    References listed on IDEAS

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    Cited by:

    1. Xiaolan Jia & Xinfeng Ruan & Jin E. Zhang, 2021. "The implied volatility smirk of commodity options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(1), pages 72-104, January.
    2. Junyu Zhang & Xinfeng Ruan & Jin E. Zhang, 2023. "Risk‐neutral moments and return predictability: International evidence," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 42(5), pages 1086-1111, August.

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