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Statistical inferen...
Statistical inference for the tangency portfolio in high dimension
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- Karlsson, Sune, Professor, 1960- (author)
- Örebro universitet,Handelshögskolan vid Örebro Universitet,Department of Statistics,Örebro University School of Business, Sweden
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- Mazur, Stepan, 1988- (author)
- Örebro universitet,Handelshögskolan vid Örebro Universitet,Department of Statistics,Örebro University School of Business, Sweden
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- Muhinyuza, Stanislas (author)
- Stockholms universitet,Matematiska institutionen,University of Rwanda, Rwanda
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(creator_code:org_t)
- 2021-07-21
- 2021
- English.
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In: Statistics. - : Taylor & Francis. - 0233-1888 .- 1029-4910. ; 55:3, s. 532-560
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Abstract
Subject headings
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- 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 is an element of (0, 1), we deliver the asymptotic distribution of the TP weights. Moreover, weconsider 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. Wealso 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.
Subject headings
- NATURVETENSKAP -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Probability Theory and Statistics (hsv//eng)
- SAMHÄLLSVETENSKAP -- Ekonomi och näringsliv -- Nationalekonomi (hsv//swe)
- SOCIAL SCIENCES -- Economics and Business -- Economics (hsv//eng)
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Keyword
- Tangency portfolio
- high-dimensional asymptotics
- hypothesis testing
- Matematik
Publication and Content Type
- ref (subject category)
- art (subject category)
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