Skip to content

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

When using a scoring function to compare competing VaR forecasts, which property makes a scoring function 'strictly consistent' for the quantile?

A strictly consistent scoring function has an expected score that is uniquely minimized when the forecast equals the true quantile. This means honest VaR forecasts are rewarded, so lower average scores indicate a better model, as with the quantile (pinball) loss.

  1. AIts expected score is minimized only when the forecast equals the true quantileCorrect
  2. BIt always yields a score of zero for the correct model in every sample
  3. CIt counts exceedances and nothing else
  4. DIts score does not depend on the realized loss

Explanation

A strictly consistent scoring function for a quantile has an expected score uniquely minimized (for a loss-type score) at the true quantile. Truthful forecasting is therefore optimal, and a better model scores better on average. The pinball (quantile) loss is a standard example.

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