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Broken Symmetry of Stock Returns -- a Modified Jones-Faddy Skew t-Distribution

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  • Siqi Shao
  • Arshia Ghasemi
  • Hamed Farahani
  • R. A. Serota

Abstract

We argue that negative skew and positive mean of the distribution of stock returns are largely due to the broken symmetry of stochastic volatility governing gains and losses. Starting with stochastic differential equations for stock returns and for stochastic volatility we argue that the distribution of stock returns can be effectively split in two -- for gains and losses -- assuming difference in parameters of their respective stochastic volatilities. A modified Jones-Faddy skew t-distribution utilized here allows to reflect this in a single organic distribution which tends to meaningfully capture this asymmetry. We illustrate its application on distribution of daily S&P500 returns, including analysis of its tails.

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  • Siqi Shao & Arshia Ghasemi & Hamed Farahani & R. A. Serota, 2025. "Broken Symmetry of Stock Returns -- a Modified Jones-Faddy Skew t-Distribution," Papers 2512.23640, arXiv.org, revised Feb 2026.
    • Handle: RePEc:arx:papers:2512.23640
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    References listed on IDEAS

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