168 M. La Rocca and D. Vistocco
Fig. 1.Comparison of the least-squares (LS) estimators and of the median estimators through
quantile regression (QR) forT=250. The different subpanels of the two plots refer to the
portfolio constituents (rows) and to the different cases of presence of outliers (columns). In
particular the first column depicts the situation with no outlying observation, the second and
third columns refer, respectively, to the presence of outliers in portfolio returns and outliers in
constituent returns, while the last column depicts the behaviour of LS and QR estimates when
outliers are considered both in portfolio returns and in constituent returns. Ineach panel the
left boxplot depicts the sampling distribution of the LS estimator while the right one refers to
the sampling distribution of the QR estimator
5 Conclusions and further issues
Style analysis is widely used in financial practice in order to decompose portfolio
performance with respect to a set of indexes representing the market in which the
portfolio invests. The classical Sharpe method is commonly used for estimating pur-
poses but requires corrections in case of the presence of outliers. In this paper we
compare this classical procedure with a robust procedure based on a constrained me-