Tests for the Weights of the Global Minimum Variance Portfolio in a High-Dimensional Setting (original) (raw)
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Abstract
In this paper, we construct two tests for the weights of the global minimum variance portfolio (GMVP) in a high-dimensional setting, namely, when the number of assets ppp depends on the sample size nnn such that fracpnrightarrowcin(0,1)\frac{p}{n}\rightarrow c \in (0,1)fracpnrightarrowcin(0,1) as nnn tends to infinity. In the case of a singular covariance matrix with rank equal to qqq we assume that q/nrightarrowtildecin(0,1)q/n\rightarrow \tilde{c}\in (0, 1)q/nrightarrowtildecin(0,1) as nrightarrowinftyn\rightarrow \inftynrightarrowinfty. The considered tests are based on the sample estimator and on the shrinkage estimator of the GMVP weights. We derive the asymptotic distributions of the test statistics under the null and alternative hypotheses. Moreover, we provide a simulation study where the power functions and the receiver operating characteristic curves of the proposed tests are compared with other existing approaches. We observe that the test based on the shrinkage estimator performs well even for values of ccc close to one.
Publication:
IEEE Transactions on Signal Processing
Pub Date:
September 2019
DOI:
arXiv:
Bibcode:
Keywords:
- Finance;
- portfolio analysis;
- global minimum variance portfolio;
- statistical test;
- shrinkage estimator;
- random matrix theory;
- singular covariance matrix;
- Quantitative Finance - Statistical Finance;
- Mathematics - Statistics Theory
E-Print:
16 pages, 10 figures (final version, accepted for publication in IEEE Transactions of Signal Processing)