Portfolio style: Return-based attribution using quantile regression

Return-based classification identifies a portfolio's style signature in the time series of its returns. Detection is based on a regression of portfolio returns on returns of factor mimicking indices. The method is easy to apply and does not require information about portfolio composition. Classification using least squares means that style is determined by the way factor exposure influences expected returns. We introduce regression quantiles as a complement to the standard analysis. The regression quantiles extract additional information from the time series of returns by identifying the way style affects returns at places other than the expected value. This allows discrimination among portfolios that would be otherwise judged equivalent based on conditional expectations. It also provides direct information about the impact of style on the tails of the conditional return distribution. Simple examples are presented to illustrate regression quantile classification.