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

Battle Count: 69

The paper provides a more realistic parametric model for the distribution of stock returns, capturing negative skew, positive mean, and asymmetric power-law tails. This is directly relevant to risk management (VaR/CVaR estimation), tail risk assessment, and understanding the statistical properties that underpin trading strategies. However, it is primarily a descriptive/statistical modeling paper rather than a trading strategy paper. The asymmetric tail modeling is valuable for position sizing, stop-loss calibration, and portfolio stress testing.

The analytical framework involves special functions (Gamma, Beta, incomplete Beta), Bayesian parameter fitting of 4-5 parameter distributions, and numerical evaluation of medians and confidence intervals. The PDF/CDF expressions are well-defined but require careful numerical implementation. The Bayesian fitting procedure is not fully detailed. Overall moderate complexity for someone familiar with statistical distributions and Bayesian methods.

S&P500 data is publicly available from Yahoo Finance. Fitting parameters are fully reported in Tables 1 and 2. Analytical expressions for PDF, CDF, mean, variance, mode, and skewness are provided. However, no code or GitHub repository is provided, and the Bayesian fitting procedure details (priors, MCMC settings) are not fully specified. Data is stated as 'available upon request.'