Answer: 19

The risk manager is conducting a backtest on a 1-day 99.5% Value-at-Risk (VaR) model over a 10-year period at a 95% confidence level. The VaR model estimates the maximum potential loss over a given time period with a certain level of confidence. In this case, the 1-day 99.5% VaR means that there is a 0.5% chance (or 1 in 200) that the actual loss will exceed the VaR estimate on any given day. To determine if the model is calibrated correctly, the risk manager uses a statistical test that compares the observed number of losses exceeding the VaR to the expected number based on the model's confidence level. The formula used is: \[ x - \frac{pT}{1 - p} > z \] Where: - \( x \) is the observed number of losses exceeding the VaR. - \( p \) is the left tail level, which is \( 1 - 0.995 = 0.005 \) or 0.5%. - \( T \) is the total number of observations, calculated as \( 250 \) trading days/year \( \times 10 \) years = \( 2500 \). - \( z \) is the two-tail confidence level quantile, which is \( 1.96 \) for a 95% confidence level. Solving for \( x \) gives: \[ x > \frac{0.005 \times 2500 + 1.96^2}{0.005 \times (1 - 0.005) \times 2500} \] \[ x > 19.4 \] Since \( x \) must be a whole number, the maximum acceptable number of exceedances is \( 19 \). This means that if there are 19 or fewer days in 10 years where the loss exceeds the 1-day 99.5% VaR, the model can be considered calibrated correctly. The correct answer is A. 19.

Author: LeetQuiz Editorial Team