Title: Sampling distributions of optimal portfolio weights and characteristics in low and large dimensions
Authors: Erik Thorsen - Stockholm University (Sweden) [presenting]
Taras Bodnar - Stockholm University (Sweden)
Nestor Parolya - Leibniz University Hannover (Germany)
Holger Dette - Ruhr-Universitaet Bochum (Germany)
Abstract: Optimal portfolio selection problems are determined by the (unknown) parameters of the data generating process. If an investor want to realise the position suggested by the optimal portfolios he/she needs to estimate the unknown parameters and account for the parameter uncertainty introduced into the decision process. Most often, the parameters of interest are the population mean vector and the population covariance matrix of the asset return distribution. We characterise the exact sampling distribution of the estimated optimal portfolio weights and their characteristics by deriving their sampling distribution which is present in terms of a stochastic representation. This approach possesses several advantages, like (i) it determines the sampling distribution of the estimated optimal portfolio weights by expressions which could be used to draw samples from this distribution efficiently; (ii) the application of the derived stochastic representation provides an easy way to obtain the asymptotic approximation of the sampling distribution. The later property is used to show that the high-dimensional asymptotic distribution of optimal portfolio weights is a multivariate normal and to determine its parameters. Via an extensive simulation study, we investigate the finite-sample performance of the derived asymptotic approximation and study its robustness to the violation of the model assumptions used in the derivation of the theoretical results.