Parametric Value at Risk models for hedge fund application

Recent events over the last year with regards to the US sub-prime crisis and the collapse of three major hedge funds, Bear Stearns, UBS's- Dillon Read Capital Management and Focus Capital, have highlighted that it is a common misconception within finance that extreme events have negligible probability. There is a widely repeated statistic in the hedge fund business that one in ten funds closes its doors each year. Since hedge fund returns often exhibit non linear option like exposures to standard asset classes (Fung and Hsieh, 2000a), traditional quantitative risk measures offer limited assistance in evaluating potential risk exposures. Not only are the investors, but also the managers of hedge funds themselves are now consequently looking for a more reliable risk measurement. Value at Risk (VaR) is believed to be one. In this paper, the author implements four principal methodologies to compute VaR forecasts, these being; Normal VaR, Log-Normal VaR, Student-t VaR and Extreme Value Theory VaR. Furthermore, for the models which directly incorporate a volatility parameter the author also implements a GARCH process to drive the estimated volatility term structure returns data. With the goal to evaluate the best performing model for each independent hedge fund strategy, and to also identify an overall best performing global model. In order to evaluate alternative VaR model forecasts, the methodology discussed by Lopez (1995) has been adopted which is based upon a probability forecasting framework. During the period from December 1993 to April 2008, the author finds that the relationship is almost monotonic across all indices, in that the overall best performing models are the Log-Normal and Normal VaR with an additionally incorporated conditional volatility model. Incorporating a conditional volatility model into VaR forecasts improves model performance by around 50% when compared to its unconditional equivalent