Title: Joint inference on market and estimation risks in dynamic portfolios
Authors: Jean-Michel Zakoian - CREST (France) [presenting]
Christian Francq - CREST and University Lille III (France)
Abstract: The purpose is to study the estimation risk induced by univariate and multivariate methods for evaluating the conditional Value-at-Risk (VaR) of a portfolio of assets. The composition of the portfolio can be time-varying and the individual returns are assumed to follow a general multivariate dynamic model. Under ellipticity of the conditional distribution, we introduce in the multivariate framework a concept of VaR parameter, and we establish the asymptotic distribution of its estimator. A multivariate Filtered Historical Simulation method, which does not rely on ellipticity, is studied. We also consider two univariate approaches based on past real or reconstituted returns. We derive asymptotic confidence intervals for the conditional VaR, which allow to quantify simultaneously the market and estimation risks. Potential usefulness, feasibility and drawbacks of the different univariate and multivariate approaches are illustrated via Monte Carlo experiments and an empirical study based on stock returns.