Tests for the Weights of the Global Minimum Variance Portfolio in a HighDimensional Setting
31/10/2017 Tuesday 31st October 2017, 11:00 (Room P3.10, Mathematics Building)
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Wolfgang Schmid, European University, Frankfurt (Oder), Germany
In this talk tests for the weights of the global minimum variance portfolio (GMVP) in a highdimensional setting are presented, namely when the number of assets $p$ depends on the sample size $n$ such that $p/n \to c$ in $(0,1)$, as $n$ tends to infinity. The introduced tests are based on the sample estimator and on a shrinkage estimator of the GMVP weights (cf. Bodnar et al. 2017). The asymptotic distributions of both test statistics under the null and alternative hypotheses are derived. Moreover, we provide a simulation study where the performance of the proposed tests is compared with each other and with an approach of Glombeck (2014). A good performance of the test based on the shrinkage estimator is observed even for values of $c$ close to $1$. (joint work with Taras Bodnar, Solomiia Dmytriv and Nestor Parolya) References: Bodnar, T. and Schmid, W. (2008). A test for the weights of the global minimum variance portfolio in an elliptical model, Metrika, 67, 127143.
 Bodnar, T., Parolya, N. and Schmid, W. (2017). Estimation of the minimum variance portfolio in high dimensions, European Journal of Operational Research, in press.
 Glombeck, K. (2014). Statistical inference for highdimensional global minimum variance portfolios, Scandinavian Journal of Statistics, 41, 845865.
 Okhrin, Y. and Schmid, W. (2006). Distributional properties of portfolio weights, Journal of Econometrics, 134, 235256.
 Okhrin, Y. and Schmid, W. (2008). Estimation of optimal portfolio weights, International Journal of Theoretical and Applied Finance, 11, 249276.
