Statistical Inference for the Tangency Portfolio in High Dimension

Sune Karlsson (), Stepan Mazur and Stanislas Muhinyuza ()
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Stanislas Muhinyuza: Department of Mathematics, Stockholm University, Postal: Department of Mathematics, Stockholm University, SE - 106 91 Stockholm, Sweden

No 2020:10, Working Papers from Örebro University, School of Business

Abstract: In this paper, we study the distributional properties of the tangency portfolio (TP) weights assuming a normal distribution of the logarithmic returns. We derive a stochastic representation of the TP weights that fully describes their distribution. Under a high-dimensional asymptotic regime, i.e. the dimension of the portfolio, k, and the sample size, n, approach infinity such that k/n → c ∈ (0, 1), we deliver the asymptotic distribution of the TP weights. Moreover, we consider tests about the elements of the TP and derive the asymptotic distribution of the test statistic under the null and alternative hypotheses. In a simulation study, we compare the asymptotic distribution of the TP weights with the exact finite sample density. We also compare the high-dimensional asymptotic test with an exact small sample test. We document a good performance of the asymptotic approximations except for small sample sizes combined with c close to one. In an empirical study, we analyze the TP weights in portfolios containing stocks from the S&P 500 index.

Keywords: Tangency portfolio; high-dimensional asymptotics; hypothesis testing (search for similar items in EconPapers)
JEL-codes: C12 C13 G11 (search for similar items in EconPapers)
Pages: 34 pages
Date: 2020-10-09
New Economics Papers: this item is included in nep-ecm and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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