Minimum dispersion portfolios with log-stable returns

Abstract

The optimization problem of a portfolio with risky assets is analyzed when the returns are modeled with log-stable processes. The objective is to optimize the asset allocation of a structured product, considering both the duration and convexity of the debt markets and the nonlinearity of the option markets through a mean-dispersion model, comparing the results with the log-gaussian distribution. We find that log-stable portfolios show a greater risk aversion than log-gaussian portfolios, given that log-stable investors improve log-gaussian performance measures; the quadratic approximation displays a behavior similar to the optimal quadratic portfolio, favoring decision making. The log-stable distributions have a limitation because they present different stability parameters, whereas the log-gaussian joint distribution has a unique stability parameter, and therefore, the assignments present differences by means of the risk components. Our contribution comes from the fact that we are modeling the debt markets and option markets, considering the participation factors of the structured product. We conclude that log-stable investors are more efficient than log-gaussian investors.