Statistical Inference for High-Dimensional Global Minimum Variance Portfolios


  • Konstantin Glombek

    Corresponding author
    1. Seminar für Wirtschafts- und Sozialstatistik, Universität zu Köln
    • Konstantin Glombek, Seminar für Wirtschafts- und Sozialstatistik, Universität zu Köln, Albertus-Magnus-Platz, 50923 Köln, Germany


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Many studies demonstrate that inference for the parameters arising in portfolio optimization often fails. The recent literature shows that this phenomenon is mainly due to a high-dimensional asset universe. Typically, such a universe refers to the asymptotics that the sample size n + 1 and the sample dimension d both go to infinity while d ∕ n → c ∈ (0,1). In this paper, we analyze the estimators for the excess returns’ mean and variance, the weights and the Sharpe ratio of the global minimum variance portfolio under these asymptotics concerning consistency and asymptotic distribution. Problems for stating hypotheses in high dimension are also discussed. The applicability of the results is demonstrated by an empirical study. Copyright © 2014 John Wiley & Sons, Ltd.