FRM Part II · FRM Exam Part II · Backtesting VaR
Over a backtest, a model produced 100 days after a non-exception day, of which 4 were exceptions, and 20 days after an exception day, of which 4 were exceptions. What are the estimated conditional probabilities π01 (exception following a non-exception) and π11 (exception following an exception)?
π01 is 0.04 and π11 is 0.20. Each is the number of exceptions following a given state divided by the number of days following that state: 4 of 100 and 4 of 20. The much higher π11 indicates exceptions cluster.
- Aπ01 = 0.04, π11 = 0.20Correct
- Bπ01 = 0.20, π11 = 0.04
- Cπ01 = 0.04, π11 = 0.04
- Dπ01 = 0.08, π11 = 0.20
Explanation
π01 = 4/100 = 0.04 and π11 = 4/20 = 0.20. Under independence these would be equal, so π11 far above π01 suggests clustering. Reversing the two gives the second option.
Did you get it right without looking?
One question tells you little. A timed set on Backtesting VaR shows your real accuracy, how long you take and where you lose marks.
More Backtesting VaR questions
- Assume a bank's VaR model is truly accurate at 99% over 250 days, so exceptions are binomial with p = 0.01. The probability of 4 or fewer ex…
- A bank's 99% one-day VaR shows 9 exceptions over 250 days. Investigation shows the VaR model prices an exotic option using a delta-only appr…
- A bank's 99% one-day VaR model is backtested over 250 trading days and produces 1 exception. The head of risk argues that this proves the mo…
- A bank backtests a 99% VaR model over 250 days and rejects it if there are 5 or more exceptions. The true exception probability is 1%, and t…
- A risk manager finds that a bank's 99% VaR had 4 exceptions in 250 days, all occurring within a single two-week period of market stress, and…
- A bank backtests a 99% one-day VaR over 500 days and observes 12 exceptions. The expected number is 5. A review finds that the model assumes…