## Tuesday, July 24, 2012

### Meet two beasts of risk management - VaR and CVaR

Value-at-Risk (VaR) is a commonly used risk measure.

It says what is a minimum amount of money that can be lost over a certain period at a given probability level, based on the historical returns.

So, a daily VaR equal to \$100 million at 5% probability, means, there is a 1 in 20 chance of losing \$100 million or more in a single future day.

The first important thing about VaR is that it specifies only a minimum amount that can be lost. Hence, virtually any larger loss is possible.

To take this limitation into account, a related measure called Conditional VaR or Expected Shortfall is used.

Conditional VaR says, what is the expected (i.e. average) loss in case the return is among a certain portion (such as 1% or 5%) of the worst historical cases. Therefore CVaR combines both VaR at a certain level and all worst cases, weighted by their probability of occurrence.

Below chart show density of normally distributed returns together with 5% and 1% VaR and CVaR values.
Chart: ND Returns Density together with VaR and CVaR

There is however one serious problem with both VaR and CVaR I'm going to address in the next post.