Arbeitspapier
Statistical Inference for the Tangency Portfolio in High Dimension
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.
- Language
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Englisch
- Bibliographic citation
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Series: Working Paper ; No. 10/2020
- Classification
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Wirtschaft
Hypothesis Testing: General
Estimation: General
Portfolio Choice; Investment Decisions
- Subject
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Tangency portfolio
high-dimensional asymptotics
hypothesis testing
- Event
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Geistige Schöpfung
- (who)
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Karlsson, Sune
Mazur, Stepan
Muhinyuza, Stanislas
- Event
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Veröffentlichung
- (who)
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Örebro University School of Business
- (where)
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Örebro
- (when)
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2020
- Handle
- Last update
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10.03.2025, 11:44 AM CET
Data provider
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Object type
- Arbeitspapier
Associated
- Karlsson, Sune
- Mazur, Stepan
- Muhinyuza, Stanislas
- Örebro University School of Business
Time of origin
- 2020
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