Web appendix for the research paper Why risk is so hard to measure on Jon Danielsson's ModelsandRisk.org

Why risk is so hard to measure

Why Risk is so Hard to Measure

Jon Danielsson and Chen Zhou


Tables and plots

The results in the paper are a subset of the tables and figures here. The tables here contain results from the Pareto distribution and cases were both VaR and ES have the same 99% probability.

We simulated from the student and the Pareto, calculating VaR and ES of both 97 5% probability and 99% probability. We repeat this $$10^7$$ times, so can use those $$10^7$$ realizations of the risk measures to formulate some interesting statistics. In particular, we report the mean, standard error and the 99% empirical confidence interval. The last is calculated by taking the 0.5% and 99.5% quartiles across the realized risk measurements.

The results in the paper are reported slightly differently, there we adjusted the numbers by the true values, but not below.