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

[elton wang]

My point is,
when underlying is non normal, any sample higher
moments may highly sensitive to outliers; without a
study of sample moments sensitity and converegence to
outliers, you can not justify the quality of VaR
modification.


you tested/simulated one skewed t distribution, but
you can not rule out all other underlying distribution
possibilities even within t-distribution with
different DOF.

These higher momonents mod on VaR are overdone IMHO.


--- elton wang <ahala2000 at yahoo.com> wrote:

> 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
> >  >>
> >  >> _______
> > 
> 
> 
> 
>      
>
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> 



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