Conditional CAPM in financial risk management: a quantile autoregression approach

Abstract

The study aims to provide a comprehensive description of dependence pattern of a stock by studying a range of betas derived as quantiles of conditional return distribution using quantile regression based on moving window regression.We investigate predictability of various parts of the conditional return distribution in a linear, autoregressive framework. We also aim to capture a state of dependence at di erent quantiles of the conditional return distribution. A good (bad) state is associated with upper (lower) quantiles,thus the impact of lagged returns is di erent across quantiles. Our empirical ndings are based on daily returns of major European stocks-sample data. Lower quantiles exhibit positive dependence with past returns while upper quantiles are marked by negative dependence. Central quantiles exhibit weak dependence. Keeping the sign of returns, we discover that positive previous day's return leads to strong positive returns with today's positive return and marked negative with today's negative return. The opposite pattern is visible for past negative returns.