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Statistical inference for the tangency portfolio in high dimension
Örebro University School of Business, Sweden.
Örebro University School of Business, Sweden.
Stockholm University, Sweden;University of Rwanda, Rwanda.
2021 (English)In: Statistics (Berlin), ISSN 0233-1888, E-ISSN 1029-4910, Vol. 55, no 3, p. 532-560Article in journal (Refereed) Published
Abstract [en]

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 (Formula presented.), 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.

Place, publisher, year, edition, pages
Taylor & Francis, 2021. Vol. 55, no 3, p. 532-560
National Category
Probability Theory and Statistics
Research subject
Mathematics, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-124647DOI: 10.1080/02331888.2021.1951730ISI: 000675362300001Scopus ID: 2-s2.0-85110941947OAI: oai:DiVA.org:lnu-124647DiVA, id: diva2:1797770
Funder
Sida - Swedish International Development Cooperation Agency, UR-Sweden Programme for Research, Higher EducationAvailable from: 2023-09-15 Created: 2023-09-15 Last updated: 2023-10-17Bibliographically approved

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Muhinyuza, Stanislas

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