Mean–variance versus full-scale optimisation: In and out of sample

Abstract

We present a recent innovation to portfolio construction called full-scale optimisation. In contrast to mean–variance analysis, which assumes that returns are normally distributed or that investors have quadratic utility, full-scale optimisation identifies the optimal portfolio given any set of return distributions and any description of investor preferences. It therefore yields the truly optimal portfolio in sample, whereas mean–variance analysis provides an approximation to the in-sample truth. Both approaches, however, suffer from estimation error. We employ a bootstrapping procedure to compare the estimation error of full-scale optimisation to the combined approximation and estimation error of mean–variance analysis. We find that, to a significant degree, the in-sample superiority of full-scale optimisation prevails out of sample.