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

2026/04/16 by Arshia Ghasemi, Siqi Shao, R. A. Serota · 1 voice
Economics, Econometrics and Finance · #q-fin.ST

paper · pdf · doi:10.3390/foundations6020023

Abstract

We analyze historic S&P500 multi-day returns: from daily returns to those accumulated over up to ten days. Despite symmetry breaking between gains and losses in the distribution of returns, resulting in its positive mean and negative skew, realized variance (volatility squared) exhibits remarkably good linear dependence on the number of days of accumulation. Mean of the distribution also shows near perfect linear dependence as well. We analyze this phenomenon both analytically and numerically using a modified Jones-Faddy skew t-distribution.

Citations

• Broken Symmetry of Stock Returns -- a Modified Jones-Faddy Skew t-Distribution
• Asymmetry in Distributions of Accumulated Gains and Losses in Stock Returns
• 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

Cited by

• Fitting Accumulated Stock Returns with Tempered Skew t-Distribution

Discussions

• Arshia Ghasemi, Siqi Shao, R. A. Serota: Broken Symmetry, Conservation Law, and Scaling in Accumulated Stock Returns -- a Modified Jones-Faddy Skew t-Distribution Perspective https://arxiv.org/abs/260 [bsky, 0 points, 0 comments]

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