Framework for VAR allocation among traders
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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