Analysis of risk metrics in share portfolio optimization

Abstract

ABSTRACT Markowitz and Sharpe’s studies formed the basis of the so-called Modern Portfolio Theory. Over the years, their papers were reviewed and alternative measures for portfolios optimization were presented. In view of this fact, there is a need to evaluate what are the differences between these measures. According to Roman and Mitra, this problem constitutes a new phase of studies, called Post-Modern Portfolio Theory. The purpose of this article is to compare the optimization models using risk measures such as standard deviation (SD), lower partial moment (LPM) and conditional value at risk (CVaR) to study their different forms of allocations in portfolios comprised of stocks traded on the BM&FBovespa. The article is divided into two stages: the first begun with the selection of risk measures and the definition of the analysis period; in the second stage, there was the division of assets according to the shape of the probability distribution of returns, with a group of stocks with returns normally distributed and another group of stocks with returns without normal distribution. As for risk measures, tests showed similar characteristics between models; as for the returns, the models that minimized LPM and CVaR showed superior results compared to the SD. Such results are relevant because they oppose the studies according to which there are no significant differences between the models.