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

Abstract

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.

A note on the relationships between some risk‐adjusted performance measures

“…To evaluate the effects of skewness on the relationships between Sharpe ratio and the two other ratios, we consider the Edgeworth-Sargan density; see, for example, Perote and Del Brio (2001). Let W ϭ (X Ϫ m)͞s.…”

Helium isotope separation by bi-layer membranes of g-C3N4

“…The use of Hermite polynomials has also found a place in economic problems. J. Perote et al [47][48][49] use Hermite polynomial methods to describe the behaviour of financial variables. Also, these polynomials can model non-Gaussian excitations which reflect models of numerous phenomena surrounding us.…”

Stress Testing

“…We can also model heavy-tailed distributions using other distributions. These include the Edgeworth-Sargan distribution (as inPerote and Del Brio (2001)) and other forms of elliptical and generalised hyperbolic distributions, besides the two elliptical distributions discussed in the text (i.e., the stable Lévy and Student t; for more on these, see, e.g.,,Eberlein et al (1998),Eberlein and Prause (2000), etc.). We deal with elliptical VaR in some detail in Chapter 5.…”