Title:

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

Abstract:

Mean-Variance (MV) portfolio selection is based on assumptions
involving parameters that have to be estimated using historical
data. The usual sample estimates introduce a great deal of
estimation error. One way of reducing estimation error is to
impose some form of structural assumptions, but since little is
known about the actual mechanisms of financial markets, such
assumptions will instead introduce specification error. Thus we
are faced with a trade-off between estimation error and
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 our estimates as good as possible, in order to avoid as much
as we can of this ambiguity.

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 shows that such an approach outperforms all
previously proposed estimators