The impact of distribution on value-at-risk measures

Value at risk is a popular approach to aid financial risk management. Questions about the appropriateness of the measure have arisen since the related 2008 bubble collapses in some US housing markets and the global financial market. These questions include the presence of fat tails and their impact. This paper compares results based upon assumptions of normality and logistic distributions, comparing portfolios generated with various probabilistic models. Computations are applied to real stock data. Optimization models are described, with simulation models evaluating comparative model performance. Chi-square tests indicated that logistic distribution better fit the data than the normal distribution. The error implied by value-at-risk assumptions is demonstrated through Monte Carlo simulation.