Broken Symmetry of Stock Returns—A Modified Jones–Faddy Skew t-Distribution
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 and analyze its tails.
Fields of Study & Subjects
Complex Systems and Time Series Analysis
Financial Risk and Volatility Modeling
Financial Markets and Investment Strategies
Publication details
- Journal / source
- Economies
- Publisher
- MDPI AG
- Volume
- 14
- Issue
- 3
- Pages
- 84–84
- Publication date
- 9 March 2026
- Language
- EN