Framework for VAR allocation among traders

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:
 >>
 >>

 >

 >> We implemented Component VaR for assets with
 >> non-normal distribution in our
 >> recent paper here: