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FRM Part II · FRM Exam Part II · Backtesting VaR

A bank backtests a 99% one-day VaR over 500 days and observes 12 exceptions. The expected number is 5. A review finds that the model assumes normal returns, and the exceptions' losses were on average 2.3 times VaR. The risk committee proposes four responses. Which is most consistent with the evidence?

The model underestimates tail risk. Twelve exceptions versus five expected is about 3.15 standard deviations above the mean, which is too many to be chance, and the large exceedances suggest fat tails. Fat-tailed methods such as historical simulation, Student-t or extreme value theory should be considered, along with checking clustering.

  1. ATreat the model as accurate because 12 is close to 5 given sampling error
  2. BRecognize that the model underestimates tail risk, and consider fat-tailed approaches such as historical simulation, Student-t or extreme value theory, while also checking clusteringCorrect
  3. CRaise the confidence level to 99.9% under the same normal assumption, since that will remove the fat-tail problem
  4. DShorten the horizon to one hour so exceptions become rarer

Explanation

Under the null the count is Binomial(500, 0.01) with mean 5 and standard deviation sqrt(500*0.01*0.99)=2.22. Twelve is (12-5)/2.22 = 3.15 standard deviations above, so it is not just sampling error. Large average exceedances point to a fat-tailed reality, so fat-tailed methods such as EVT or Student-t help. Raising the confidence level under normality still understates tails.

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