An empirical evaluation of Value-at-Risk during the financial crisis

In the latest financial crisis, risk management and forecasts of market losses played a crucial role in the area of finance. This thesis evaluates the theory of Value-at-Risk through a quantitative study of two non-parametric approaches and three parametric: Basic- and volatility-weighted Historical Simulation, Normal distribution, Log-normal distribution and Student’s t-distribution. The thesis compares 1-day VaR estimates predictive performance of market losses defined by the index of Standard & Poor’s 500 on a 99% and 95% confidence level. The study is made by a rolling window forecast between 2005-12-28 and 2008-12-31 which includes 786 observations that accommodate one tranquil and one crisis period. Performance is evaluated by backtesting, using the Kupiec’s test. The result shows that VaR as a risk measure is very imprecise in its forecasts; however the predictability is different across the five approaches. Under the tranquil period all approaches were significant on the 99% significance level on the 95% however some approaches were not, due to overestimates of the risk. Another finding among the approaches is that they fail to account for rapid shifts in risk. During the crisis period all VaR models included in the backtest was rejected at both confidence intervals. This means that VaR is proven to serious destabilizing during times of crisis. The failure of non-parametric approaches is mostly due to that they are determined by a historical distribution which reflects the past market climate that not always correspond with the climate tomorrow. We also conclude that the parametric approaches rely too heavily on unrealistic assumptions of future distribution and therefore fail as well