On Portfolio Selection: Improved Covariance Matrix Estimation for Swedish Asset Returns

Mean-Variance (MV) theory for portfolio selection is based on assumptions involving parameters that have to be estimated using historical data. Depending on the method of estimation, the estimates will suffer from estimation error and/or specification error, both of which will effect the portfolio optimization in such a way that the resulting optimal portfolio is not the true optimal portfolio. It is therefore of interest to make the estimates as good as possible, in order to avoid as much as possible the effects of this uncertainty. In this paper we focus on the estimation of the covariance matrix for stock returns on the Swedish market. This is one of the two input parameters of MV optimization, the other being the expected return vector. We do this using Bayesian shrinkage and principal component analysis in combination with random matrix theory. Our empirical results implies that such an approach is better than all those previously proposed.