Question

Suppose that we back-test a VaR model using 300 days of data. The VaR confidence

level is 99% and we observe 10 exceptions. Do we reject the model?

Answer 1

No.

While we back test a Value at Risk model using 300 days of data and the confidence level is 99%, and we observe just 10 exeptions, the model can be accepted.

Value-at-risk (VaR) is a widely used measure of downside investment risk for a single investment or a portfolio of investments. VaR gives the maximum-dollar loss on a portfolio over a specific time period for a certain level of confidence. Often the confidence level is chosen so as to give an indication of tail risk; that is, the risk of rare, extreme market events.

Risk managers use a technique known as backtesting to determine the accuracy of a VaR model. Backtesting involves the comparison of the calculated VaR measure to the actual losses (or gains) achieved on the portfolio. A backtest relies on the level of confidence that is assumed in the calculation.A simple backtest stacks up the actual return distribution against the model return distribution by comparing the proportion of actual loss exceptions to the expected number of exceptions. The backtest must be performed over a sufficiently long period to ensure that there are enough actual return observations to create an actual return distribution. For a one-day VaR measure, risk managers typically use a minimum period of one year for backtesting.