  The Black-Litterman model combines investors' personal views with historical
data and gives optimal portfolio weights. In this paper we will introduce the
original Black-Litterman model (section 1), we will modify the model such that
it fits in a Bayesian framework by considering the investors' personal views to
be a direct prior on the means of the returns and by adding a typical Inverse
Wishart prior on the covariance matrix of the returns (section 2). Lastly, we
will use Leonard and Hsu's (1992) idea of adding a prior on the logarithm of
the covariance matrix (section 3). Sensitivity simulations for the level of
confidence that the investor has in their own personal views were performed and
performance of the models was assessed on a test data set consisting of returns
over the month of January 2018.
