On the accuracy of VaR estimates based

on the Variance-Covariance approach

Rakhal D. Davé

Olsen

Seefeldstrasse 233, 8008 Zurich, Switzerland

Gerhard Stahl

Federal Banking Supervisory Office

Gardeschützenweg 71-101, 12203 Berlin, Germany

(The views expressed herein should not be construed as being endorsed by the Federal Banking Supervisory Office)

Abstract

We present a thorough empirical study (based on over 8 years of daily data) of candidate models for forecasting losses in relation to positions held against individual risk factors as well as losses in relation to a portfolio of risk factors. As part of the study, we also define various measures and visualization techniques to evaluate the performance of the candidate models in the context of risk management and introduce two innovations: 1) tail emphasized model optimization and 2) implied covariance forecasting. Finally, we highlight the important issue of the estimation error of the covariance matrix in relation to its dimension and the number of datum from which it is estimated and outline a framework for handling this problem.