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**Conditional Tail Expectation or Conditional VaR**

**Applies to:** @RISK 5.x–7.x

How can I use @RISK to calculate the conditional tail expectation (conditional value at risk, CVaR) of a simulated output?

Beginning with @RISK 5.5, you can compute statistics for part of a distribution by value or by percentile; @RISK 5.0 can compute statistics for a distribution delimited by value only. To compute your statistics, you insert the property function RiskTruncate( ) in an @RISK statistics function such as RiskMean( ).

For example, suppose you have a simulated output in cell C11, and you want the conditional value at risk for the left-hand 5% tail. That is equivalent to the mean value of just the lowest 5% of the distribution, and you compute it like this:

@RISK 5.5 and later: =RiskMean(C11, RiskTruncateP( , 0.05) )

@RISK 5.0: =RiskMean(C11, RiskTruncate( , RiskPtoX(C11,0.05) ) )

You can also compute expected value for the upper tail. For example, the upper 5% is above the 95th percentile, so you set the 95th percentile as a lower limit and compute the expected value of the 5% right-hand tail like this:

@RISK 5.5 and later: =RiskMean(C11, RiskTruncateP(0.95, ) )

@RISK 5.0: =RiskMean(C11, RiskTruncate( RiskPtoX(C11,0.95), ) )

The value will be approximate if you're calculating conditional tail expectation on a *theoretical* distribution. See About accuracy of theoretical statistics in Statistics for Just Part of a Distribution.

In @RISK help or the manual, see the section "Calculating Statistics on a Subset of a Distribution".

Last edited: 2017-09-01

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