Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/244568 
Year of Publication: 
2020
Series/Report no.: 
Working Paper No. 10/2020
Publisher: 
Örebro University School of Business, Örebro
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.
Subjects: 
Tangency portfolio
high-dimensional asymptotics
hypothesis testing
JEL: 
C12
C13
G11
Document Type: 
Working Paper

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