A Practitioner's Guide to Asset Allocation

CHAPTER 5Error Maximization

FALLACY: OPTIMIZED PORTFOLIOS ARE HYPERSENSITIVE TO INPUT ERRORS

Mean‐variance analysis requires investors to estimate expected returns, standard deviations, and correlations whose future realizations will vary from their estimated values. The process of optimization, by construction, will overallocate to asset classes for which expected returns are overestimated and for which standard deviations and correlations are underestimated, and it will underallocate to asset classes for which the opposite occurs. Moreover, the effect of estimation error is not diversified away as more asset classes are added; it usually becomes worse.

The effect of this problem is twofold: The weights of the efficient portfolios are misstated, and their expected returns and risk are incorrect. The question arises, therefore, as to the seriousness of this problem. Are optimizers so sensitive to errors as to be of little or no value, or are critics of optimization overstating this problem? We believe the latter is true. In most cases, and in particular, for applications to asset allocation, optimization is reasonably robust to estimation error.

THE INTUITIVE ARGUMENT

The intuition of our argument is straightforward. Consider optimization among asset classes that have similar expected returns and risk. Small errors in the estimates of these values may substantially misstate efficient allocations. Despite these misallocations, however, the return distributions of the correct ...