Why risk is so hard to measure

This paper analyses the accuracy and reliability of standard techniques for risk analysis used by the financial industry as well as in regulations. We focus on the difference between value–at–risk and expected shortfall, the small sample properties of these risk measures and the impact of using an overlapping approach to construct data for longer holding periods. Overall, we find that risk forecasts are extremely uncertain at low sample sizes. By comparing the estimation uncertainty, we find that value–at–risk is superior to expected shortfall and the time-scaling approach for risk forecasts with longer holding periods is preferable to using overlapping data.
 
Keywords: Value–at–risk, expected shortfall, finite sample properties, Basel III.
JEL classifications: C10, C15, G18.

Working paper no. 494.