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

[elton wang]

Brian,
In case I have doubt with observed moments, I will not
using these numbers on VaR modification; a simple non
paremetric distriubtion will catch the tail risk in a
more reliable way.

it is not the  case "> but I think that's all you
could do with any confidence." No one forces us to use
these higher moments even admitting non normal tail
risks, we have other ways.

The example of t distribution with DOF=4 is not
arguing one or another particular ideal distrubtion,
it is to show that it is totally possible that
underlying kurtosis does not converge/exist at all.
when you cleaning the data, the number change; when
you get more data, the number change.





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

> elton wang 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 distribution. 
> > How can you rule out this possibility of
> underlying
> > distribution?
> 
> I am not in general a believer that real returns are
> generated by 
> mathematically ideal distributions.  Ideal
> distributions may make good 
> estimators (thus the rationale for any parametric
> estimation method), 
> but are rarely if ever the actual generator of
> returns.
> 
> You can't rule out the possibility that the
> "generating" distribution 
> has different moments from the observed
> distribution.  You might be able 
> to cast doubt on the observed moments by fitting
> various distributions, 
> but I think that's all you could do with any
> confidence.
> 
> One of the reasons I prefer the Cornish-Fisher
> expansion over most other 
> fitted distributions is precisely because it
> directly utilizes the 
> observable moments of the distribution.  These
> moments have intuitive 
> financial as well as mathematical meaning.  As I
> discussed below, if the 
> magnitude of the observed higher moments are small,
> the effect on the 
> estimate will also be small.
> 
> If you believe that you have a better estimator of
> the moments for your 
> data than the observed moments (possibly via fitting
> to an ideal 
> distribution) you can plug those into the Cornish
> Fisher expansion and 
> still take advantage of the component decomposition
> offered via the CF 
> process.
> 
> Again, thank you for your thoughtful commentary.
> 
> Regards,
> 
>    - Brian
> 
> > --- "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 post, 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:
> 
=== message truncated ===



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