No abstract

No abstract

In this paper we consider the estimation of the weights of optimal portfolios from the Bayesian point of view under the assumption that the conditional distribution of the logarithmic returns is normal. Using the standard priors for the mean vector and the covariance matrix, we derive the posterior distributions for the weights of the global minimum variance portfolio. Moreover, we reparameterize the model to allow informative and non-informative priors directly for the weights of the global minimum variance portfolio. The posterior distributions of the portfolio weights are derived in explicit form for almost all models. The models are compared by using the coverage probabilities of credible intervals.In an empirical study we analyze the posterior densities of the weights of an international portfolio.

In this paper we discuss the distributions and independency properties of several generalizations of the Wishart distribution. First, an analog to Muirhead [R.J. Muirhead, Aspects of Multivariate Statistical Theory, Wiley, New York, 1982] Theorem 3.2.10 for the partitioned matrix A = (A i j ) i, j=1,2 is established in the case of arbitrary partitioning for singular and inverse Wishart distributions. Second, the density of A 21 A −1 11 is derived in the case of singular, non-central singular, inverse and generalized inverse Wishart distributions. The importance of the derived results is illustrated with an example from portfolio theory.

This paper proposes a multivariate shrinkage estimator for the optimal portfolio weights. The estimated classical Markowitz weights are shrunk to the deterministic target portfolio weights. Assuming log asset returns to be i.i.d. Gaussian, explicit solutions are derived for the optimal shrinkage factors. The properties of the estimated shrinkage weights are investigated both analytically and using Monte Carlo simulations. The empirical study compares the competing portfolio selection approaches. Both simulation and empirical studies show that the proposed shrinkage estimator is robust and provides significant gains to the investor compared to benchmark procedures.Portfolio selection, shrinkage estimation, multivariate shrinkage, estimation risk,