A test on mean-variance efficiency of the tangency portfolio in high-dimensional setting
Author:
Stanislas Muhinyuza
Journal:
Theor. Probability and Math. Statist. 103 (2020), 103-119
MSC (2020):
Primary 54C40, 14E20; Secondary 46E25, 20C20
DOI:
https://doi.org/10.1090/tpms/1136
Published electronically:
June 16, 2021
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Additional Information
Abstract: In this paper we derive the asymptotic distribution of the test of the efficiency of the tangency portfolio in high-dimensional settings, namely when both the portfolio dimension and the sample size grow to infinity. Moreover, we propose a new test based on the estimator for the slope parameter of the efficient frontier in the mean-variance space when there is a possibility in investing into the riskless asset, and derive the asymptotic distribution of that test statistic under both the null and alternative hypotheses. Additionally, we study the finite sample performance of the derived theoretical results via simulations.
References
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References
- O. Bodnar and T. Bodnar, On the unbiased estimator of the efficient frontier, International Journal of Theoretical and Applied Finance 13 (2010), no. 07, 1065–1073. MR 2738762
- T. Bodnar, A. K. Gupta, and N. Parolya, Direct shrinkage estimation of large dimensional precision matrix, Journal of Multivariate Analysis 146 (2016), 223–236. MR 3477661
- T. Bodnar, N. Hautsch, and N. Parolya, Consistent estimation of the high dimensional efficient frontier, Tech. report, 2016.
- T. Bodnar, S. Mazur, K. Podgórski, and J. Tyrcha, Tangency portfolio weights for singular covariance matrix in small and large dimensions: estimation and test theory, Journal of Statistical Planning and Inference 201 (2019), 40–57. MR 3913439
- T. Bodnar, Y. Okhrin, and N. Parolya, Optimal shrinkage-based portfolio selection in high dimensions, arXiv preprint arXiv:1611.01958 (2019).
- T. Bodnar, N. Parolya, and W. Schmid, Estimation of the global minimum variance portfolio in high dimensions, European Journal of Operational Research 266 (2018), no. 1, 371–390. MR 3737003
- T. Bodnar and M. Reiß, Exact and asymptotic tests on a factor model in low and large dimensions with applications, Journal of Multivariate Analysis 150 (2016), 125–151. MR 3534906
- T. Bodnar and W. Schmid, A test for the weights of the global minimum variance portfolio in an elliptical model, Metrika 67 (2008), no. 2, 127–143. MR 2375302
- T. Bodnar and W. Schmid, Estimation of optimal portfolio compositions for Gaussian returns, Statistics & Decisions 26 (2009), no. 3, 179–201. MR 2512267
- M. Britten-Jones, The sampling error in estimates of mean-variance efficient portfolio weights, The Journal of Finance 54 (1999), no. 2, 655–671.
- G. Frahm and U. Jaekel, Tyler’s m-estimator, random matrix theory, and generalized elliptical distributions with applications to finance, Random Matrix Theory, and Generalized Elliptical Distributions with Applications to Finance (October 21, 2008) (2008).
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- J. E. Ingersoll, Theory of financial decision making, 3 (1987).
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- R. C. Merton, An analytic derivation of the efficient portfolio frontier, Journal of Financial and Quantitative Analysis 7 (1972), no. 4, 1851–1872. MR 456374
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- R. J. Muirhead, Aspects of Multivariate Statistical Theory, Wiley, New York, 1982. MR 652932
- A. C. Rencher and W. F. Christensen, Methods of multivariate analysis, John Wiley & Sons, 2012. MR 2962097
- A. W. Van der Vaart, Asymptotic statistics, vol. 3, Cambridge University Press, 2000. MR 1652247
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Additional Information
Stanislas Muhinyuza
Affiliation:
Department of Mathematics, Stockholm University, Roslagsvägen 101, SE-10691 Stockholm, Sweden; and Department of Mathematics, College of Science and technology, University of Rwanda, P.O. Box 3900, Kigali-Rwanda
Email:
stanislas.muhinyuza@math.su.se
Keywords:
Tangency portfolio,
mean-variance portfolio,
high-dimensional settings
Received by editor(s):
September 30, 2019
Published electronically:
June 16, 2021
Additional Notes:
The author appreciates the financial support of SIDA via the project 1683030302
Article copyright:
© Copyright 2020
Taras Shevchenko National University of Kyiv