101 Concepts for the Level I Exam

Essential Concept 94: Value at Risk

Value at risk (VaR) is the minimum loss that would be expected to be incurred a certain percentage of the time over a certain period of time given assumed market conditions.

Consider a $400 million portfolio. The VaR statement for this portfolio might be as follows: “The 5% VaR is$2.2 million over a one-day period.”  Notice that the VaR measure has three important elements:

• Minimum loss – In our example the minimum expected loss is $2.2 million. The minimum loss can be expressed in either currency units or percentage terms. • Time horizon – In our example the time horizon is one day. This is the time period over which the minimum loss can be expected. • Frequency – In our example the frequency is 5%. This can be interpreted as ‘a loss of$2.2 million or more is expected 5% of the time’ or ‘95% of the time, the loss will be less than \$2.2 million.’

There are three methods to estimate VaR:

1. Parametric (variance – covariance) method
2. Historical simulation method
3. Monte Carlo simulation method