A Tale of Tails: Improving Financial Risk Measures Through Advanced Distribution Modelling

Mads Thers Christiansen & Sisse Olsson

Student thesis: Master thesis


This paper provides suggestions for improvement of the portfolio risk measures: Value-at-Risk and Expected Shortfall. Specifically, this master thesis seeks to improve the accuracy of portfolio risk measures through modelling of non-normality in asset returns with a GARCH-EVT-Copula framework. The applied statistical methods are AR(p)-GJR-GARCH(p,q), Extreme Value Theory and student’s t copula. Combined these statistical tools allow the authors to account for non-normal distribution patterns in relation to skewness, excess kurtosis, heavy tails, volatility clustering and non-linear correlations. The calculations are performed based on a portfolio representing a broad selection of European asset classes including equity, high yield bonds and government bonds. Given this portfolio, the authors document that assuming normality leads to a risk underestimation of more than 35% in several cases. Further investigation reveals that the risk underestimations are of similar nature for risk conservative and risk seeking investors whereby making the modelling concerns of relevance to a broad audience. In sum, the results of the analysis clearly demonstrate the inappropriateness of assuming normality and at the same time document the significant estimation improvements associated with the suggested GARCH-EVT-Copula framework.

EducationsMSc in Applied Economics and Finance, (Graduate Programme) Final Thesis
Publication date2016
Number of pages113
SupervisorsSøren Plesner