Measuring Value at Risk of Portfolios Under the Edgeworth-Sargan Distribution

Abstract

This paper sheds light on the evaluation of portfolio risk by assuming a distribution capable of incorporating the behaviour of most financial variables, especially at the tails: the so called Edgeworth-Sargan distribution. This density is preferable over other distributions, such as the Student's t, when fitting high frequency financial variables, because of its flexibility for improving data fits by adding more parameters in a natural way.

Furthermore, this distribution is easy to be generalised to a multivariate context and, therefore, correlation coefficients among variables can be estimated efficiently. This article thus provides new insights into VaR methodology by estimating the joint density of portfolio variables, and by calculating the right critical values of the underlying portfolio density as well. The empirical examples include the estimation and evaluation of different volatility and weight scenarios for portfolios composed of stock indices and interest rates for major financial markets.

Keywords: Value at Risk, portfolio choice, joint distribution, Edgeworth-Sargan distribution, GARCH models, optimal weighting

JEL Classification: G10, G11, C13