Portfolio optimization with multivariate elliptical stable distributions

Traditional portfolio optimization relies on the assumption that asset returns follow a normal distribution, a premise that fails to capture the heavy tails and skewness commonly observed in financial markets. This study proposes an alternative portfolio selection model based on multivariate elliptical stable distributions, which generalize the normal distribution and provide a more realistic framework for modeling extreme events. After statistically validating key assumptions we develop a model that replaces the classical covariance matrix with a shape matrix suited to stable distributions. Using data from over 300 companies in the Spanish, French, British, and German equity markets (2011–2023), we empirically evaluate the proposed model through both in-sample efficient frontiers and out-of-sample performance for different investor profiles. Results indicate that the stable model frequently outperforms the standard model, particularly in markets with pronounced non-normality (France and Germany). This evidence underscores the importance of incorporating heavy-tailed distributions in portfolio optimization for enhanced risk management and improved long-term returns.