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This paper investigates optimal trading strategies in a financial market withmultidimensional stock returns where the drift is an unobservable multivariateOrnstein-Uhlenbeck process. Information about the drift is obtained byobserving stock returns and expert opinions. The latter provide unbiasedestimates on the current state of the drift at discrete points in time.  The optimal trading strategy of investors maximizing expected logarithmicutility of terminal wealth depends on the filter which is the conditionalexpectation of the drift given the available information. We state filteringequations to describe its dynamics for different information settings. Betweenexpert opinions this is the Kalman filter. The conditional covariance matricesof the filter follow ordinary differential equations of Riccati type. We relyon basic theory about matrix Riccati equations to investigate their properties.Firstly, we consider the asymptotic behaviour of the covariance matrices for anincreasing number of expert opinions on a finite time horizon. Secondly, westate conditions for the convergence of the covariance matrices on an infinitetime horizon with regularly arriving expert opinions.  Finally, we derive the optimal trading strategy of an investor. The optimalexpected logarithmic utility of terminal wealth, the value function, is afunctional of the conditional covariance matrices. Hence, our analysis of thecovariance matrices allows us to deduce properties of the value function.

Expert Opinions and Logarithmic Utility Maximization for Multivariate Stock Returns with Gaussian Drift