G20 α-stable portfolios: Empirical evidence with Markowitz, Tobin and CAPM

Objective: This research extends Markowitz, Tobin, and CAPM optimal portafolio with α-stable processes. Methodology: The following procedures are performed on a portfolio with the G20 stock indices: 1) descriptive statistics and α-stable parameters of index returns are estimated, 2) a goodness-of-fit test is applied to validate the α- stable processes, 3) the covariation matrix is estimated to calculate the optimal portfolio assignments, and 4) the systematic risk indicators are estimated. Results: The efficient frontier is calculated without short sales and shows that α-stable portfolios present greater aversion to risk than Gaussian portfolios, and that α-stable portfolios are more efficient with respect to the return and risk ratio. Recommendations: The application of α-stable processes to model leptokurtosis, asymmetry and volatility clusters. Limitations: The α-stable multivariate analysis presents different stability parameters. Originality: G20 returns are modeled with α-stable processes and a sensitivity analysis is performed. Conclusion: α-stable analysis allows to quantify market risk more adequately than Gaussian analysis.