Encyclopedia of Financial Models
Over the last couple of years financial markets around the world have exhibited increasing volatility, thereby demanding high skills of risk managers and investors seeking a profit. It appears that market risk, defined as losses owing to unfavorable movements in financial variables, seems to be the dominant factor in this turbulent environment. The implications of these sudden fluctuations are clear: Several financial institutions have faced the consequences of an inadequate risk management,
... cing some into bankruptcy. In times like these, the need for proper risk management, by means of choosing an effective risk metric, is greater than ever. Over the past decade Value-at-Risk (VaR) has become a standard measure of risk. It is constructed as a tool to indentify and control financial risk to which, practically all companies are exposed. In short, VaR is a risk metric measuring the worst loss a position can suffer over a horizon with a chosen level of confidence. Recently VaR has been applied to portfolio management with great success and is widely used today by investment companies, pension companies etc. because of its simple interpretation. Especially banks have fully adopted the risk metric. This is mostly due to the fact, that the Basle Committee on Bank Supervision allows internal VaR-based risk models to calculate the market risk charge for economic capital. Motivated by the discussion above, this thesis investigates the applicability of VaR as a risk metric on an efficient portfolio. The goal was to find out, if VaR could fully capture the portfolios risk and if so, which VaR model produced the most valid and efficient results. The analysis included various risk horizons and levels of confidence in order to determine, if differences in choice of parameters had an effect on the outcomes. The data used, was picked from the Danish stock and bond market. An optimal portfolio was found consisting of three stocks, two bonds and two exchange rate positions. A preliminary data analysis was conducted to decide, which models should be included in the analysis. As seen in the majority of financial research, the portfolio return series suffered from leptokurtic properties, making the tails of the return distribution fat. Therefore a student-t VaR model was included. Additional tests proved the existence of volatility clustering, better known as ARCH-effects. This justified the use of EWMA, GARCH and EGARCH as forecasting models -specified to handle time varying volatility. A GARCH(1,1) and EGARCH(1,1), both based on student-t distributed errors, showed to fit the data best. ii A thorough analysis of the estimated VaR models was undertaken in the last part of the thesis. The models were evaluated using a range of statistical backtesting techniques and efficiency criterias. The major findings suggested that model performance did in fact differ with regards to the choice of parameters. Generally the models captured portfolio risk very well at a short horizon and low levels of confidence. At a higher confidence level and longer risk horizon most models could not be validated. In terms of distributions, the student-t versions displayed a slightly better performance than the normal ones. With regards to choice of forecasting model the traditional GARCH outperformed both EWMA and EGARCH in most cases.