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Portfolio optimization relies in three main elements: the utility function, the use of multivariate dependence measure between assets and the returns of the assets. The first problem is well known in finance since one can use several different types of portfolio utility functions depending on her objective function and constraints. The two remaining problems are relevant topics of research: the measure and forecast of the dependence between assets and the forecast of the returns of assets. In this paper, we present a new method with artificial intelligence to estimate the variance and covariance matrices of financial time series data accounting for small sample size, large number of assets and presences of outliers. We compare results using different approaches, e.g., Minimum covariance determinant (MCD), Minimum Volume Ellipsoid (MVE), Minimum Regularized Covariance Determinant (MRCD) and Orthogonalized Gnanadesikan-Kettenring (OGK). The proposed approach is robust under several financial stylized facts and presents good performance with respect to the cumulative returns in the US markets (NASDAQ Stock Exchange) for 95 assets during 2015 to the beginning of 2019. These study contributes to fill in the literature gap in covariance estimation for small sample size, large number of assets and presences of outliers and contributes to investors to making better portfolio management.

Artificial intelligence in portfolio formation and forecast: Using different variance-covariance matrices