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Title: Inference for tangency portfolio weights for small sample and singular covariance matrix Authors:  Taras Bodnar - Stockholm University (Sweden)
Stepan Mazur - Orebro University (Sweden)
Krzysztof Podgorski - Lund University (Sweden)
Joanna Tyrcha - Stockholm University (Sweden) [presenting]
Abstract: Estimation of covariance matrix between portfolio assets plays a very important role in risk management. The inverse of an estimate is used to estimate the optimal portfolio weights. The sample covariance matrix is typically used for this purpose under the assumption of a non-singular true (population) covariance matrix. However, the problem of potential multicollinearity and strong correlations of asset returns results in clear limitations in taking such an approach due to potential singularity or near singularity of the population covariance. Further, realistic financial applications are often characterized by a smaller number of observations (sample size) than the number of assets in the portfolio. A stochastic representation of the tangency portfolio weights estimator as well as the linear hypothesis test for the portfolio weights is presented under singular conditions caused both by the number of data points being lower than the number of assets and by the singularity of population covariance matrix. The asymptotic distribution of the estimated portfolio weights is also established under a high-dimensional asymptotic regime. The motivation for the considered singularities in real data and practical relevance of theoretical results are presented. The theoretical results are applied to real stock returns in an illustrative example.