Robust estimation of style analysis coefficients
Michele La Rocca and Domenico VistoccoAbstract.Style analysis, as originally proposed by Sharpe, is an asset class factor model aimed
at obtaining information on the internal allocation of a financial portfolio and at comparing
portfolios with similar investment strategies. The classical approach is based on a constrained
linear regression model and the coefficients are usually estimated exploiting a least squares
procedure. This solution clearly suffers from the presence of outlying observations. The aim of
the paper is to investigate the use of a robust estimator for style coefficients based on constrained
quantile regression. The performance of the novel procedure is evaluated by means of a Monte
Carlo study where different sets of outliers (both in the constituent returns and in the portfolio
returns) have been considered.Key words:style analysis, quantile regression, subsampling1 Introduction
Style analysis, as widely described by Horst et al. [12], is a popular and important
tool in portfolio management. Firstly, it can be used to estimate the relevant factor
exposure of a financial portfolio. Secondly, it can be a valuable tool in performance
measurement since the style portfolio can be used as a benchmark in evaluating the
portfolio performance. Finally, it can be used to gain highly accurate future portfo-
lio return predictions since it is well known from empirical studies [12] that factor
exposures seem to be more relevant than actual portfolio holdings.
The method, originally proposed by Sharpe [25], is a return-based analysis aimed
at decomposing portfolio performance with respect to the contribution of different
constituents composing the portfolio. Each sector is represented by an index whose
returns are available. The model regresses portfolio returns on constituent returns
in order to decompose the portfolio performance with respect to each constituent.
Indeed, in the framework of classical regression, the estimated coefficients mean the
sensitivity of portfolio expected returns to constituent returns. The classical approach
is based on a linear regression model, estimated by using least squares, but different
constraints can be imposed on the coefficients.M. Corazza et al. (eds.), Mathematical and Statistical Methodsfor Actuarial Sciencesand Finance
© Springer-Verlag Italia 2010