Can robust portfolio optimisation help to build better portfolios?
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Bernd Scherer is Managing Director and Head of Quantitative Structured Products at Morgan Stanley Investment Management in London. Managing Director, Morgan Stanley, IM-Alternative Investments 20 Bank Street, Canary Wharf, E14 4QW, London. Tel: +44 20 7425-4016; Fax: +44 20 7425-8763; E-mail: [email protected]
Abstract 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. It will be shown 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, it can be seen 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 more well-known risk aversion. Journal of Asset Management (2007) 7, 374–387. doi:10.1057/palgrave.jam.2250049 Keywords: robust optimisation, Bayes, resampling, portfolio construction, estimation error
Introduction 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 portfolio optimisation (assets with positive estimation error are over-weighted, while assets with negative estimation error are under-weighted) has been felt as a major obstacle in achieving a more scientific approach to investing. Financial economists tried to control the variation in expected returns with some form of shrinkage to either equal returns (James–Stein approach) or implied market returns (Black–Litterman approach) in the hope to also control the variation in portfolio output (and hence to
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arrive at less extreme and more stable solutions). Success has been mixed. First, return estimates still show outlier dependency, whatever statistical method is used. Secondly, parameter ambiguity will always be present, even if we increase the amount of extra sample information. But this means that error maximisation still affects portfolio construction. Lately, engineers and operations research academics have become interested in the field of portfolio optimisation and suggested two variations to mainstream thinking. The first was the idea of robust statistics, which promotes the clever removal (or down-weighting) of what are thought to be extreme observations (outliers). While outliers are sometimes the only information we have got (eg, in hedge
Journal of Asset Management Vol. 7, 6, 374–387 & 2007 Palgrave Macmillan Ltd, 1470
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