Value-at-Risk: An Empirical Analysis of the Market-Price-Risk Estimation

Daniel Heeschen & Alex Noyes Kopischke

Student thesis: Master thesis


Given the increased regulatory and societal pressures, there has been a growing need for managing and predicting financial risk. In this study we evaluate and compare the daily returns of both the Dow Jones Industrial Average (DowJones) and the Deutscher Aktienindex (DAX) from over 30 years of performance. The researched Value-at-Risk models are Historical Simulation, Variance- Covariance Simulation, and Monte-Carlo Simulation. These methods were selected because of their prevalence and popularity in both industry and academic settings. The daily Value-at-Risk for each of these indexes was computed using all three models at both the 95 and 99 percent confidence intervals. The results were evaluated using Christoffersen’s backtesting methods to allow for comparability and evaluation. Each of the models was found to be inadequate in terms of losses not exceeding the Valueat-Risk at the rate specified in the confidence interval. However, the findings resulted in Historical Simulation faring the best under our test conditions, followed by Variance-Covariance – Moving-Average, Variance-Covariance – Exponential Weighted Moving-Average, and Monte-Carlo respectively. The analysis also introduces Basel II methods for evaluating the success of Value-at-Risk models, which is often used for regulatory requirements. This model involved categorizing the success of models into three separate categories of ‘green,’ ‘yellow,’ and ‘red,’ ranging from good to poor respectively. Using this framework, our models appear to be in a more acceptable range. As an area of future research, it would an area of intrigue to analyze if some of the other more sophisticated varieties of the Variance-Covariance and Monte-Carlo method could exceed the performance of the Historical Simulation method.

EducationsMSc in Accounting, Strategy and Control, (Graduate Programme) Final Thesis
Publication date2018
Number of pages111