Skip to content

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

A risk analyst notes that Value-at-Risk (VaR) is elicitable, whereas Expected Shortfall (ES) is not elicitable on its own. Which statement best describes the practical implication for backtesting?

VaR is elicitable, so a scoring function exists that lets forecasts be ranked by expected score. ES alone has no such function, so it cannot be compared that way on its own. ES can still be backtested, for instance jointly with VaR, and elicitability does not imply coherence.

  1. AES cannot be backtested in any form, so regulators must rely only on VaR exceedances
  2. BA single scoring function can rank competing VaR forecasts by expected score, but no such scoring function exists for ES aloneCorrect
  3. CES is elicitable only when the loss distribution is normal, so the problem disappears for parametric models
  4. DElicitability means a risk measure is coherent, so VaR is coherent while ES is not

Explanation

Elicitability means a risk measure is the minimiser of the expected value of some scoring function, which allows direct comparison of competing forecasts. VaR (a quantile) has such a function; ES alone does not. ES can still be backtested, for example jointly with VaR, so the first option is wrong. Elicitability is unrelated to coherence.

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