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

2025/12/29 by Siqi Shao, Arshia Ghasemi, Hamed Farahani +1 · 1 voice · 2 citations
Economics, Econometrics and Finance · #q-fin.ST #econ.TH

paper · pdf · doi:10.3390/economies14030084

arxiv published 2025/12/29 · arxiv updated 2026/02/16

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.

Citations

• Asymmetry in Distributions of Accumulated Gains and Losses in Stock Returns
• Entropy corrected geometric Brownian motion
• Distributions of Historic Market Data - Stock Returns
• A Model for Stock Returns and Volatility
• Dragon-kings: mechanisms, statistical methods and empirical evidence
• Robust Statistical Tests of Dragon-Kings beyond Power Law Distributions
• Black swans or dragon kings? A simple test for deviations from the power law
• Universal Behavior of Extreme Price Movements in Stock Markets
• Probability distribution of returns in the Heston model with stochastic volatility
• Random diffusion and leverage effect in financial markets
• Large Stock Market Price Drawdowns Are Outliers

Cited by

• Fitting Accumulated Stock Returns with Tempered Skew t-Distribution
• Broken Symmetry, Conservation Law, and Scaling in Accumulated Stock Returns -- a Modified Jones-Faddy Skew t-Distribution Perspective

Discussions

• Siqi Shao, Arshia Ghasemi, Hamed Farahani, R. A. Serota: Broken Symmetry of Stock Returns -- a Modified Jones-Faddy Skew t-Distribution https://arxiv.org/abs/2512.23640 https://arxiv.org/pdf/2512.2364 [bsky, 0 points, 0 comments]

Related

• Broken Symmetry, Conservation Law, and Scaling in Accumulated Stock Returns -- a Modified Jones-Faddy Skew t-Distribution Perspective
• Fitting Accumulated Stock Returns with Tempered Skew t-Distribution
• Asymmetry in Distributions of Accumulated Gains and Losses in Stock Returns
• The Process of price formation and the skewness of asset returns
• Realized Stochastic Volatility Model with Skew-t Distributions for Improved Volatility and Quantile Forecasting