Skip to content

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

An analyst transforms PIT values u_t into z_t = Φ^-1(u_t) to test a VaR model's full distribution. Which statement best describes the advantage of this step and the expected outcome under a correct model?

Under a correct model, the transformed values z_t should be i.i.d. standard normal. This lets the analyst apply powerful parametric tests, such as the Berkowitz likelihood ratio test of zero mean, unit variance and no autocorrelation, using the full distribution rather than only exceedances.

  1. Az_t should be i.i.d. standard normal, allowing standard normality and independence tests such as the Berkowitz likelihood ratio testCorrect
  2. Bz_t should be uniform on [-1, 1], allowing a Kupiec proportion-of-failures test
  3. Cz_t should equal the VaR exceedance indicator, allowing a binomial test
  4. Dz_t should be chi-square distributed, allowing a test of tail loss magnitude only

Explanation

Applying the inverse normal CDF to i.i.d. uniform PITs gives i.i.d. standard normal variates under a correct model. This enables a likelihood-ratio test of mean zero, variance one and zero autocorrelation (Berkowitz). Exceedance-only tests like Kupiec use just the binary hit indicator.

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