Applications of robust statistics in the portfolio theory

The appropriate selection of portfolio components and determining their weights have a significant influence on the later performance of the investor. The classical method of calculating the weights of individual components in mean variance portfolios is based on sample mean and sample covariance matrix, which are optimal when the data come from multivariate normal distribution. In practice, the distribution of stock returns is not a normal distribution and frequently (albeit to a small extent) is contaminated by outliers; therefore, theoretically, a better approach to determine optimal weights in a portfolio would be to apply robust estimation methods. The main contribution of this paper is to present the possibilities of applying robust statistics methods in the Markowitz portfolio theory. This article contains an overview of the most important robust estimators applied in the portfolio theory. All the methods have been grouped according to the method of determining the outliers and to the accepted disorder models. Moreover, it presents the relevant achievements to date and the results of empirical research in this field. It also shows the potential problems resulting from the practical application of the robust estimation in the rolling horizon.