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

[elton wang]

For example, if underlying is a t distribution with
DOF=4, then kurtosis does not exsit. Any sample
kurtosis (with any cleaning tech or not) would be a
false stat of underlying didstribution. 
How can you rule out this possibility of underlying
distribution?

--- "Brian G. Peterson" <brian at braverock.com> wrote:

> 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
>  >>
>  >> _______
>