Why Risk Is So Hard to Measure

Abstract

This paper analyzes the robustness of standard techniques for risk analysis, with a special emphasis on the Basel III risk measures. We focus on the difference between value-at-risk and expected shortfall, their small sample properties, the scope for manipulating risk measures and how estimation can be improved. Overall, the paper find that risk forecasts are extremely uncertain at low sample sizes, with value-at-risk more accurate than expected shortfall, while value-at-risk is easily manipulated without violating regulations. Finally the implications for practitioners and regulators are discussed along with best practice suggestions.

Keywords: Value-at-Risk, expected shortfall, finite sample properties, Basel III

JEL Classification: C10, C15, G18