Robust Portfolio Optimisation and Estimation Error

Bernd Scherer


Estimation error has always been acknowledged as a substantial problem in portfolio construction. Various approaches exist that range from Bayesian methods with a very strong rooting in decision theory to practitioner-based heuristics with no rooting in decision theory at all as portfolio resampling. Robust optimisation is the latest attempt to address estimation error directly in the portfolio construction process. We will show that robust optimisation is equivalent to Bayesian shrinkage estimators and offer no marginal value relative to the former. The implied shrinkage that comes with robust optimisation is difficult to control. Consistent with the ad hoc treatment of uncertainty aversion in robust optimisation, we will see that out-of-sample performance largely depends on the appropriate choice of uncertainty aversion, with no guideline on how to calibrate this parameter or how to make it consistent with the better known risk aversion. Virtually all attempts to address estimation error in portfolio construction have been around the refinement of expected returns before they enter the portfolio construction process. The error maximising property of traditional

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