A note on the sensitivity of the strategic asset allocation problem

The Markowitz mean–variance portfolio optimization problem is a quadratic programming problem whose first-order conditions require the solution of a linear system. It is well known that the optimal portfolio weights are sensitive to parameter estimates, particularly the mean return vector. This has generally been attributed to the interaction of estimation error and optimization. In this paper we present some examples that suggest the linear system produced by the first-order conditions is ill-conditioned and it is this property that gives rise to the sensitivity of the optimal weights.