A robust strategy for building a financial portfolio

The mean-variance portfolio constitutes the milestone of the modern portfolio theory. The mean-variance model relies on two fundamental assumptions. First, a rational investor maximizes, over a single period, the expected return of an asset for a given level of risk, which is measured by the variance of stock returns themselves. Second, the random returns are normally distributed. In reality, it is well-known that the time series of returns have heavier tails and a higher peak than in a normal distribution. In this paper, we propose the application of statistical weighted depth functions as an alternative non-parametric tool. The aim is to build a robust mean-variance model within the standard portfolio selection framework. Real data are used to investigate the performances of the proposed approach.