Statistical Inferences for Realized Portfolio Weights

Statistical inferences for weights of the global minimum variance portfolio (GMVP) are of both theoretical and practical relevance for mean-variance portfolio selection. Daily realized GMVP weights depend only on realized covariance matrix computed from intraday highfrequency returns. In this paper we deduce both finite sample and asymptotic distributional properties of the realized GMVP weights. Then we develop statistical tests for the GMVP proportions and elaborate sequential monitoring procedures for on-line decisions whether a given portfolio composition deviates from the current GMVP significantly. Our theoretical results are illustrated both in Monte Carlo simulations and in an empirical application