Broken Symmetry, “Conservation Law”, and Scaling in Accumulated Stock Returns: A Modified Jones–Faddy Skew t-Distribution Perspective
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.
Fields of Study & Subjects
Complex Systems and Time Series Analysis
Financial Risk and Volatility Modeling
Statistical Mechanics and Entropy
Publication details
- Journal / source
- Foundations
- Publisher
- MDPI AG
- Volume
- 6
- Issue
- 2
- Pages
- 23–23
- Publication date
- 9 June 2026
- Language
- EN