How model risk and alpha dispersion affect portfolio efficiency

Abstract

The traditional mean-variance problem of maximising return while minimising the standard deviation of returns is not practical owing to sampling error. Reasonable solutions to overcome sampling errors have been proposed, but fail to offer an alternative definition for efficiency. A measure of a portfolio's efficiency should take into account modelling errors as well as pure market effects in assessing a strategy. The investor's objective function should be stated in terms of total forecast risk rather than focusing purely on return variance. In minimising total forecast risk, the efficient frontier has to be adjusted. Portfolios that might have looked attractive using a model that assumes the parameters are determinate and known, no longer look that attractive. Portfolio construction methodologies that do not take into account model uncertainties are almost certain to produce inferior portfolios; however, the difficulty of quantifying the alpha and beta estimation errors makes ‘true’ optimisation almost impossible, but strategies can be better evaluated knowing that model uncertainty exists.