[R-SIG-Finance] VaR and ES in PerformanceAnalytics

[Brian G. Peterson]

On Mon, 2011-10-24 at 11:49 -0400, financial engineer wrote:
> I ran the VaR and ES using the below, and am trying to understand why the VaR(99%) 
> is exactly equal to ES(99%). Is that how it is supposed to be.....

You didn't include your data to make this reproducible, so I need to
speak in generalities.

>From the documentation:

 Modified expected shortfall should always be higher than modified
 Value at Risk. Due to estimation problems, this might not always
 be the case. Set operational = TRUE to replace modified ES with
 modified VaR in the (exceptional) case where the modified ES is
 smaller than modified VaR.

If you're seeing this, I expect your data is highly skewed and/or
kurtotic.

Cornish Fisher Modified VaR can exhibit what Jorion referred to as
'wrong tailed  behavior', migrating rapidly to zero or infinity.  While
this is a problem, it is only a problem if you aren't paying attention.
I use this as an indicator that I either don't have enough data or that
my data is likely unreliable.  It is also often an indication that your
preferred probability (99%) is too high for a reliable answer.

Look at function chart.VaRSensitivity to see how the VaR and ES play out
at different probability thresholds. 

The good news is that it's really obvious when this happens, you can
easily see it in the chart, and tell where you don't and probably
shouldn't have confidence in your estimating powers.

Just because some other methodologies will give you an answer that
claims to be precise doesn't mean that they are truly doing so.  Many
many people have written about the pitfalls of looking for too high a
precision in VaR/ES estimates.  I, for example, find 95% to be a good
number on daily return data, as this indicates a 1 in 20 'bad day', so
you can interpret the 95% ES as approximately your 'average one really
bad day a month' on daily return data.  I have a colleague who uses 92%
on monthly return data to estimate the 'average really bad month once a
year' on his portfolios.

I prefer 'approximately correct' to 'precisely wrong' statistics.

I could speak in more specifics about the characteristics of your data
with a reproducible example.

Regards,

  - Brian   

-- 
Brian G. Peterson
http://braverock.com/brian/
Ph: 773-459-4973
IM: bgpbraverock