Skip to content

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

A bank's 250 daily PIT values are transformed to z_t = Φ^-1(u_t). The sample mean of z_t is 0, the sample standard deviation is 1.40, and the lag-1 autocorrelation is near zero. Which conclusion is best supported, and what is the approximate ratio of the model's predicted standard deviation to the realized dispersion?

The model understates risk. Correct forecasts produce transformed PIT values with standard deviation 1, but the observed 1.40 shows realized outcomes are more dispersed than predicted. The predicted spread is roughly 1/1.40, about 0.71, of the realized spread, despite zero mean and no autocorrelation.

  1. ARisk is understated; the predicted spread is about 0.71 (1/1.40) of the realized spreadCorrect
  2. BRisk is overstated; the predicted spread is about 1.40 times the realized spread
  3. CRisk is understated; the predicted spread is about 1.40 times the realized spread
  4. DThe model is acceptable because the mean and autocorrelation are zero

Explanation

If the model were right, z_t would have standard deviation 1. A sample value of 1.40 means realized outcomes are more dispersed than predicted, so risk is understated. The predicted-to-realized ratio is 1/1.40 ≈ 0.714. Zero mean and autocorrelation do not offset the variance failure, so the model is not acceptable.

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