The value at risk (VaR) uses both the confidence level and confidence interval. A risk manager uses the VaR to monitor and control the risk levels in a company's investment portfolio. VaR is a statistical metric measuring the amount of the maximum potential loss within a specified period with a degree of confidence. The VaR indicates that a company's losses will not exceed a certain amount of dollars over a specified period with a certain percentage of confidence.
The confidence level determines how sure a risk manager can be when he is calculating the VaR. The confidence level is expressed as a percentage, and it indicates how often the VaR falls within the confidence interval. If a risk manager has a 95% confidence level, it indicates he can be 95% certain that the VaR will fall within the confidence interval. For example, assume that a risk manager determines the 5% one-day VaR to be $1 million. This means that he has a 95% confidence level that the worst daily loss will not exceed $1 million.
Conversely, the confidence interval is a statistical measure that produces an estimated range of values that is likely to include an unknown population parameter. For example, suppose a risk manager is measuring the confidence interval of an investment portfolio. He finds it to be $2 million and $10 million at the endpoints.
Bridging the confidence interval and confidence level, the risk manager can calculate the value at risk. The confidence level of the VaR estimate is the quantile the risk manager uses to calculate the VaR. This, however, should not be confused with the confidence interval. The confidence interval is an interval that has a probability of including the VaR estimate.
For example, suppose a risk manager is evaluating the VaR of two different investment portfolios. The first portfolio has a one-day value at risk of $11 million and a confidence interval of $6 million to $17 million, whereas the second portfolio has a one-day VaR of $5 million with a confidence interval of $3 million to $7 million. The first portfolio has a 95% confidence interval, and the second portfolio has a 99% confidence interval. The first portfolio is riskier and has a higher level of uncertainty because the confidence interval and the VaR are much larger.
The confidence interval of the first portfolio includes the VaR of $11 million at 95% of the time. On the other hand, the confidence interval for the second portfolio includes the VaR of $5 million at 99% of the time.