[R-SIG-Finance] CVaR, fExtremes

[Markus Gesmann]

Hi all,

I struggle to understand the output of the CVaR function in the fExtremes package.
The output of VaR (Value at Risk) gives me results I expect to see. However the output of CVaR is less than the output of VaR. From my understanding CVaR gives the mean over a given threshold and should therefore always be bigger than VaR.
The fowling example shows the output of VaR and CVaR:

library(fExtremes)
n <- 1000000
loss.ratio <- rlnorm(n, -0.3479, 0.104)
VaR(loss.ratio, 0.995) # same as quantile(loss.ratio, 0.995)
#    99.5%
# 0.9588572
CVaR(loss.ratio, 0.995)
#    99.5%
#0.7088572

I expected an output more like this:
mean(loss.ratio[loss.ratio > 0.995])
# 1.021089
mean(loss.ratio[loss.ratio > 0.995]) - VaR(loss.ratio, 0.995)
#  99.5%
#0.09783733

Maybe I am just a little bit confused and mix up terminologies.


Markus



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