Robust portfolio optimization
Markowitz portfolios and their application in were introduced in Chapter 5. The problems that one might encounter by directly optimizing portfolios of this kind were addressed. In particular, it was stated that the use of sample estimators for the expected returns and the covariance matrix can result in sub-optimal portfolio results due to estimation error. Furthermore, extreme portfolio weights and/or erratic swings in the asset mix are commonly observed in ex post simulations. In general, this empirical fact is undesirable because of transaction costs. From a statistical point of view, these artefacts can mainly be attributed to the sensitivity of the ordinary sample estimators with respect to outliers. These outlying data points influence the dispersion estimates to a lesser extent than the means, ceteris paribus. Hence, but not only for this reason, minimum-variance portfolios are advocated compared to mean–variance portfolios (see the references in Chapter 5). It would therefore be desirable to have estimators available which lessen the impact of outliers and thus produce estimates that are representative of the bulk of sample data, and/or optimization techniques that incorporate estimations errors directly. The former can be achieved by utilizing robust statistics and the latter by employing robust optimization techniques.