Value at Risk vs. Conditional value at risk

(post from old site)

VaR
95% VaR is the 95th quantile of loss
Say it's = $1 mil. then it means 95% chance the loss is under $1 mil.

CVaR
Aka expected shortfall or tail conditional expectation
With the above 95% VaR, there is a 5% probability that the loss will be >= 1 mil.
Let's say if we fall into that 5%, what's the loss that we should expect?
Now, that's what CVaR is.

Think about it. 95% VaR is essentially the MINIMUM loss of the portfolio for the 5% worst case scenario.
CVaR will actually tell u the mean (expected) loss for the 5% worst case scenario.