摘要：This paper aims to analyze the efficacy of variance and measures of downside risk for of formation of investment portfolios in the Brazilian stock market. Using the methodologies of Ang (1975), Markowitz et al. (1993), Ballestero (2005), Estrada (2008) and Cumova and Nawrocki (2011), sought to find what the best method to solve the problem of asymmetric and endogenous matrix and, inspired by the work of Markowitz (1952) and Lohre, Neumann and Winterfeldt (2010), intended to be seen which risk metric is most suitable for the realization of more efficient allocation of resources in the stock market in Brazil. The sample was composed of stocks of IBrX 50, from 2000 to 2013. The results indicated that when the semivariance was used as a measure of asymmetric risk, if the investor can use more refined models for solving the problem of asymmetric semivariance-cosemivariance matrix, the model of Cumova and Nawrocki (2011) will be more effective. Furthermore, from the Brazilian data, VaR had become more effective than variance and other measures of downside risk with respect to minimizing the risk of loss. Thus, taken the assumption that the investor has asymmetric preferences regarding risk, forming portfolios of stocks in the Brazilian market is more efficient when using criteria of minimizing downside risk than the traditional mean-variance approach.
