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 to account the parameter uncertainty 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. In this
paper 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. Moreover, a consistent estimator of optimal portfolio weights and
their characteristics is derived under the high-dimensional settings. 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.Comment: 39 pages, 4 figures (this version: small typo in the titel corrected