Distributional properties of portfolio weights

By Yarema Okhrin, Wolfgang Schmid. 2006

198 citations recorded by the source corpus.

In this paper, we prove several distributional properties for optimal portfolio weights. The weights are estimated by replacing the parameters with the sample counterparts. All results for finite samples are made assuming normally distributed returns. We calculate the exact covariances for the weights obtained by the expected quadratic utility. Additionally we derive the multivariate density function of the global minimum variance portfolio and the univariate density of the tangency portfolio. We obtain the conditional density for the Sharpe ratio optimal weights and show that the expectations of the Sharpe ratio optimal weights do not exist. Moreover, we determine the asymptotic distributions of the estimated weights assuming that the returns follow a multivariate stationary Gaussian process.

Subfields: Finance

View Paper: https://www.semanticscholar.org/paper/fe63d43ecdeba173a22fcfbb69f8f220f0ef11de

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Citations in the corpus

Dominating estimators for minimum-variance portfolios (2010, background): “Okhrin and Schmid (2006), Kempf and Memmel (2006) as well as Frahm (2008) all explore the properties of the traditional MVP estimator by assuming jointly normally distributed asset returns.”
Multivariate Shrinkage for Optimal Portfolio Weights (2007, background): “…w w′μ − γ 2 w′ w s.t. w′1 = 1 (12) The solution of this problem is given by the classical Markowitz weights uQ = −11 1′ −11 + Rμ γ , where R = −1 − −111′ −1 1′ −11 (13) Okhrin and Schmid (2006) derive the first two moments of the estimated optimal weights ûQ under normality assumption for log…”
EWMA Control Charts for Monitoring Optimal Portfolio Weights (2007, methodology): “They are determined by Okhrin and Schmid (2006).”
A test for the weights of the global minimum variance portfolio in an elliptical model (2008, background): “Okhrin and Schmid (2006) proved that in this case all marginal distributions of ŵM with dimension less than k follow a multivariate t-distribution.”
Optimal Shrinkage-Based Portfolio Selection in High Dimensions (2016, methodology): “The estimated weights of the optimal portfolio which maximizes the Sharpe ratio are extremely unstable as documented by Okhrin and Schmid (2006), i.”