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FRM Part II · FRM Exam Part II · Range of Practices and Issues in Economic Capital Frameworks

A bank validates its economic capital model by comparing the model's one-year 99.9% portfolio loss quantile against realized annual losses over 8 years. No realized loss exceeded the model quantile. A manager concludes the model is validated as accurate. Which critique is best?

Eight years without an exceedance is almost certain even for a poor model, since the probability is about 99.2% at a 99.9% level. Backtesting therefore has little power in the tail, so validation must also use benchmarking, sensitivity analysis and assumption review.

  1. AEight years with no exceedances is expected under a 99.9% level and carries little statistical power, so backtesting alone cannot validate the tail, and other methods such as benchmarking and sensitivity analysis are neededCorrect
  2. BZero exceedances proves the model is too aggressive and must be rejected
  3. CThe test is invalid because economic capital models cannot be compared with losses
  4. DEight observations are enough to confirm the 99.9% quantile to within one basis point

Explanation

At 99.9%, the chance of no exceedance in 8 years is about 0.999^8 ≈ 99.2%, so seeing none is expected whether or not the model is right. The test has very low power to detect underestimation. Validators therefore supplement it with benchmarking, stress and sensitivity analysis, and assumption review.

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