Comparing Financial Portfolio Style Through Quantile Regression

Laura Attardi, Domenico Vistocco
(2006) Statistica Applicata - Italian Journal of Applied Statistics, Vol. 18, Number 2, 6-16, ISSN 1125-1964


The main goal of style analysis is to assess and compare the performance of different financial products. Style analysis models decompose the portfolio performance with respect to a set of known indexes (constituents). The model estimates the quotas of such indexes in the portfolio, with the aim to separate out their attribution to return. The estimated compositions are interpretable in terms of sensitivity of portfolio expected returns to constituents returns: the style of the products is determined by the way constituents exposure influences expected returns.

The classical model is based on a least squares constrained regression model (Sharpe 1992). Model constraints allow the coefficients to be exhaustive and non negative and to interpret the estimated coefficients in terms of composition quotas.

Quantile regression, as introduced by Koenker and Basset (Koenker & Basset 1978), may be viewed as an extension of classical least squares estimation of conditional mean models for conditional quantile functions. It then offers an useful look at the style analysis problem from a different point of view, allowing to obtain information on the entire returns distribution of analyzed products. Through these additional features, a more detailed comparison of the financial products is then obtainable, by combining classical model results and quantile regression results.