[R-SIG-Finance] Framework for VAR allocation among traders
Brian G. Peterson
brian at braverock.com
Mon Mar 17 15:55:32 CET 2008
elton wang wrote:
> 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.
I agree that the sample moments (and especially the co-moments) are
highly sensitive to outliers. This is why we developed a cleaning
method to decrease the sensitivity.
I also agree that it could make sense to test for the sensistivity of
the estimates of the moments. I can envision how to test this using
Baysian methods. I would appreciate any insight you might have on other
more computationally tractable sensitivity tests for skewness and kurtosis.
> 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.
Many other papers have shown that the Cornish fisher expansion is a good
estimator even when compared to multiple other ideal fitted
distributions. We did not feel the need to redo that work.
> These higher momonents mod on VaR are overdone IMHO.
That might be true if the data you are working with approximate the
normal distribution, or are otherwise well-behaved. When basically all
the series that you look at are significantly non-normal, as is the case
with hedge fund returns, then some method of accounting for that
non-normality is also required.
Regards,
- Brian
> --- 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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