Usually, the performance evaluation of investment funds uses traditional indices of performance, based on the normality of returns. Because it is based on the normality of returns, these traditional indexes ignore the information contained in higher order moments of the distribution. Although the classical theory of Markowitz (1952) is considered easy to use and efficient in the composition of the assets of investment portfolios, complications arise when assets have markedly non-normal distributions. Recently, several authors have proposed measures of risk-return (also known as performance measures) more consistent with the expected distribution of gains observed in practice, that is, non-normal distributions. Among them, the Omega measure, by Keating and Shadwick (2002), which takes into account not only the first moments of the distribution of asset returns (mean and variance), but the whole shape of the distribution to evaluate its risk. The main objective of this study is to compare some traditional measures of performance evaluation of investment funds in the Brazilian market, with the Omega index. This paper will verify if the performance rankings of mutual funds in Brazil, given by these measures are different. In this study, the parameters are calculated consistently through appropriate models, after the verification of the non-stationarity of the series of returns of investment funds.