Abstract
The paper presents a method for calculating a portfolio with a guaranteed return at a given confidence level. The portfolio is calculated using a sample of the returns of the assets included in the portfolio. The problem is considered in a nonparametric statistical setting, that is, the assumptions were not made on the distribution law of the return vector, and a parametric statistical setting with normal law distribution. The main elements of the method are an ellipsoid of minimum volume containing a given number of sample elements and a method for calculating it. The minimum size ellipsoid containing a sample has long been used in mathematical statistics to obtain robust estimates of the mean and covariance matrix, as well as in machine learning, so its application for an optimal portfolio looks natural.
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