Portfolio Value at Risk: Concept, Implementation and Models Backtesting

This dissertation undertakes a comprehensive framework of the new risk management tool known as Value at risk, VaR. It introduces an in-depth study of the latest literature which is utilized in two different aspects. First, it studies the concept of VaR, origin, parameters, and compares it with other market risk measurements. Then, it defines, evaluates and compares the three most used approaches, historical simulation, variance-covariance, and Monte Carlo simulation to compute VaR. Finally, it addresses the concept of Backtesting VaR models for evaluating the accuracy and performance of such models. Second, parametric and non parametric types of VaR approaches are employed to 501 trading days of a stocks portfolio, a foreign exchange rates portfolio and a commodities portfolio to evaluate the models performance in estimating accurate value at risk measures. Descriptive analysis and statistical measurements of the portfolios data were presented. It inferred that VaR estimations rely on the observation horizon and chosen confidence level. Finally, this application found that non parametric VaRs and 95% confidence level VaRs are generally more accurate than parametric and 99% percentile VaRs. Overall, in a context of the 2008 financial recession, the VaR approaches did perform well and provided accurate and reliable estimates of potential losses under non parametric models for the stocks and FX portfolios. This VaR application confirmed that the methodology is indeed an added value in the field of risk management that would assess investors holding stocks and FX portfolio of their risk exposures and potential losses in a satisfying manner