Statistical inference for the tangency portfolio in high dimension. Issue 3 (4th May 2021)

• Record Type: Journal Article
• Authors: Karlsson, Sune; Mazur, Stepan; Muhinyuza, Stanislas
• Is Part Of: Statistics. Volume 55:Issue 3(2021)
• Page Start: 532
• Page End: 560
• Publication Date: 2021-05-04
• Subjects: Tangency portfolio -- high-dimensional asymptotics -- hypothesis testing; 62H10 -- 62H12 -- 91G10; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2021.1951730
• Languages: English
• ISSNs: 0233-1888

Abstract

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 analyse the TP weights in portfolios containing stocks from the S&P 500 index.