Skip to content

FRM Part II · FRM Exam Part II · Beyond Exceedance-Based Backtesting of Value-at-Risk Models

A validator finds that a bank's VaR model passes the Kolmogorov-Smirnov test on its PIT values, but she suspects the model misstates extreme tail losses. Which test is better suited to this concern, and why?

Anderson-Darling is better suited, because it places extra weight on discrepancies in the tails of the distribution, whereas Kolmogorov-Smirnov looks at the maximum gap, which is usually driven by the center. Kupiec tests only the exceedance frequency at one level.

  1. AAnderson-Darling, because it weights discrepancies in the tails more heavily than KSCorrect
  2. BKolmogorov-Smirnov with a larger sample, because it is most sensitive in the tails
  3. CAnderson-Darling, because it only examines the central part of the distribution
  4. DKupiec proportion-of-failures test, because it tests the entire distribution shape

Explanation

KS measures the maximum gap, which is typically greatest near the center and is relatively insensitive to tail differences. Anderson-Darling applies a weighting that emphasizes the tails, making it more powerful against tail misspecification. Kupiec only tests the exceedance frequency at one confidence level.

Did you get it right without looking?

One question tells you little. A timed set on Beyond Exceedance-Based Backtesting of Value-at-Risk Models shows your real accuracy, how long you take and where you lose marks.

Practise Beyond Exceedance-Based Backtesting of Value-at-Risk ModelsFree diagnostic mock

More Beyond Exceedance-Based Backtesting of Value-at-Risk Models questions