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Revere Street Working Paper Series Financial Economics 272-18

Mean-Variance Analysis versus Full-Scale Optimization Out of Sample
First Version: November 11, 2005 This Draft: December 13, 2005
Timothy Adler
Windham Capital Management, LLC 5 Revere Street Cambridge, MA 02138 617 234-9459 tadler@windhamcapital.com Abstract For three decades, mean-variance analysis has served as the standard procedure for constructing portfolios. Recently, investors have experimented with a new optimization procedure, called full-scale optimization, to address certain limitations of mean-variance optimization. Specifically, mean-variance optimization assumes that returns are normally distributed or that investor preferences are well approximated by mean and variance. Full-scale optimization relies on sophisticated search algorithms to identify the optimal portfolio given any set of return distributions and based on any description of investor preferences. Full-scale optimization yields the truly optimal portfolio in sample, whereas the mean-variance solution is an approximation to the insample truth. Both approaches to portfolio formation, however, suffer from estimation error. Mean-variance analysis requires investors to estimate the means and variances of all assets and the covariances of all asset pairs. To the extent the out-of-sample experience of these parameters departs from the in-sample parameter values, the mean-variance approximation will be even less accurate. Full-scale optimization requires investors to estimate the entire multivariate return distribution. To the extent it varies from the insample distribution, full-scale optimization will also yield sub-optimal results out of sample. We employ a bootstrapping procedure to compare the estimation error of fullscale optimization to the combined approximation and estimation error of mean-variance analysis. We find that, to a

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