[R-SIG-Finance] Framework for VAR allocation among traders

[Brian G. Peterson]

elton wang wrote:
> Brian,
> I have a question on your paper:
> If you use skewness and kurtosis in the VaR
> calculation, you want to make sure:
 >
> 1. these are exist if the underlying distribution is
> non-normal.

At least one of skewness!=0 or kurtosis!=3 exist if the underlying 
distribution is non-normal.  Perhaps I don't understand your first point?

If skewness=0 and kurtosis=3, the Cornish-Fisher expansion does not 
change the Gaussian normal distribution.  So it should have no adverse 
consequences if utilized even if all portfolio assets were normal (which 
seems a highly unlikely circumstance).

> 2. your sample skewness and kurtosis is good estimates
> of true skewness and hurtosis.

While it is possible to fit many different fat-tailed distributions to 
the sample, and derive skewness and kurtosis from these, I don't see how 
this is a better approach than utilizing the sample skewness and 
kurtosis.  We did show in the paper how to test the Cornish Fisher and 
Edgeworth expansion against a very skewed and fat-tailed Skew Student-t 
distribution.

Another problem with utilizing a fitted distribution is that many fitted 
distributions would  not carry the same properties of being 
differentiable by the weight (properties of the Gaussian normal and 
Cornish Fisher distributions) in a portfolio to obtain a good estimator 
of Component Risk in a portfolio.

In the main, the data cleaning method is most valuable for adding 
stability to the effects of the co-moments in decomposing the risk to 
avoid undue influence by a small number of extreme events.  The method 
was developed to specifically not change observations that were not "in 
the tail", and to keep the direction (but not the absolute magnitude) of 
the extreme events.  As I discussed in the text of the paper, I do not 
believe that you would ever use the cleaning method for measuring VaR or 
ES ex port, but only to stabilize the predictions of contribution on a 
forward-looking ex ante basis.

> In part 5 you discussed the Robust estimation but it
> could be stronger argument IMHO. For example, do you
> have convergence/sensitivity analysis on estimated
> skewness/kurtosis results for your cleaning method? 

I agree that a sensitivity analysis would be a good addition.  I will 
start thinking about how to add that.

Regards,

   - Brian


 > --- "Brian G. Peterson" <brian at braverock.com> wrote:
 >
 >> On Thursday 13 March 2008 22:32:59
 >> adschai at optonline.net wrote:
 >>> Hi,I'm looking for VAR allocation framework among
 >> traders. I saw some
 >>> papers but none of which (at least that I saw)
 >> look practical. I am
 >>> wondering if anyone can hint me some idea or some
 >> reference? The situation
 >>> is if at the desk level you were given a certain
 >> amount of VAR limit, how
 >>> should one allocate the number among traders?
 >> Thank you.adschai
 >>
 >> Calculate Component VaR.
 >>
 >> The first definition (as far as I know) is in Garman
 >> in Risk Magazine.  The
 >> article may be found here:
 >>
 >> Garman, Mark, "Taking VaR to Pieces (Component
 >> VaR)," RISK 10, 10, October
 >> 1997.
 >> http://www.fea.com/pdf/componentvar.pdf
 >>
 >> He also has a longer working paper on the topic
 >> here:
 >>
 >>
 > http://www.gloriamundi.org/detailpopup.asp?ID=453055537
 >> We implemented Component VaR for assets with
 >> non-normal distribution in our
 >> recent paper here:
 >>
 >> Boudt, Kris, Peterson, Brian G. and Croux,
 >> Christophe, "Estimation and
 >> Decomposition of Downside Risk for Portfolios With
 >> Non-Normal Returns"
 >> (October 31, 2007).
 >> http://ssrn.com/abstract=1024151
 >>
 >> All code for our paper was implemented in R, and is
 >> available.  We will also
 >> be cleaning up and documenting the functions in the
 >> next version of
 >> PerformanceAnalytics.
 >>
 >> Regards,
 >>
 >>     - Brian
 >>
 >> _______