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Value-at-risk

4 messages · Brian G. Peterson, sadako

sadako
# 
I'm ok with the notions of component and marginal VaR but can't retrieve
results from marginal.

First what is the PortfolioVaR with the portfolio_method="marginal" ?
Except the sign, the 2 figures I get from these functions for PortfolioVaR
are differents :
VaR(tsdata,method="gaussian",portfolio_method="marginal")
VaR(tsdata,method="gaussian",portfolio_method="component")$VaR


Second -and it is maybe be related - how is the marginal VaR computed ?
I tried the following but the result is different from the function (here it
is the 5th marginal) :

VaR(tsdata,method="gaussian",portfolio_method="component")$VaR-VaR(tsdata[,-5],method="gaussian",portfolio_method="component")$VaR

Many thanks for any helpful comment,

PS : tsdata is any valid timeSeries.

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Brian G. Peterson
#
On Sun, 2011-06-19 at 03:19 -0700, sadako wrote:
Marginal and component VaR *are* different.  So I'm not sure I
understand what you're asking, entirely.

Component VaR is a coherent risk measure per Artzner.  The component
risks will add up to the univariate VaR of the entire portfolio.  The
univariate portfolio VaR is given in the $VaR slot you reference in your
code.  The additive measures are available two different ways, in the
$contribution slot (which will add up to the univariate portfolio VaR)
and in the $pct_contrib_VaR slot which will add up to 1(100%)
Marginal VaR is the difference between the univariate portfolio VaR of a
a portfolio with the instrument in question and the VaR of the portfolio
without that instrument.  It is not guaranteed to add up to anything.
Frankly, I think it is a useless measure *unless* you are comparing two
otherwise similar instruments for inclusion in a portfolio, and want to
see which of those two instruments would add less risk to the portfolio
"at the margin".
Component VaR and marginal VaR aren't interchangeable, as described
above, and as described in the documentation.

simple subtraction doesn't work, because the portfolio (capital) needs
to be redistributed.

The weighting factor is

weightfactor = sum(weightingvector)/sum(t(weightingvector)[, -column])

you can see the code with:

PerformanceAnalytics:::VaR.Marginal
I hope this helps,

    - Brian
sadako
#
braverock wrote:
Actually I didn't mean to compare marginal and component : I just use the
portfolio_method="component" to get the univariate VaR of the portfolio
($VaR slot). 
I have the same number using calculation like
qnorm(0.95,0,1)*sqrt(t(wghts)%*%var(tsdata)%*%wghts)-t(wghts)%*%colMeans(tsdata).

I would have expect to have the same number for this univariate portfolio
VaR in the "PortfolioVaR" column of VaR(...,portfolio_method="marginal"), -
all other parameters being equal - but this is not the case. 

Both should represent the univariate portfolio VaR aren't they ?
Nota : here again I just use the $VaR slot of component to get access to the
univariate VaR of portfolio.

I think I got the weight factor right implicitly since I don't set any
special weights vectors : the VaR functions sets these weights equally in
both members of my equation. 

Assume I'm working with 5 assets : 
- the univariate VaR of the portfolio :
VaR(tsdata,method="gaussian",portfolio_method="component")$VaR is computed
with default weights=c(0.2,0.2,0.2,0.2,0.2)
- the VaR of the portfolio without the asset 5 :
VaR(tsdata[,-5],method="gaussian",portfolio_method="component")$VaR is
computed with equally-weighted default weights=c(0.25,0.25,0.25,0.25). These
are indeed the weights of the 5-assets portfolio taking into account the
weight factor of sum(weightingvector)/sum(t(weightingvector)[, -5])=1.25


Marginal VaR is the difference between the univariate portfolio VaR of a
So with no weight specification, the stricto-sensu calculation :

VaR(tsdata,method="gaussian",portfolio_method="component")$VaR-VaR(tsdata[,-columnAsset],method="gaussian",portfolio_method="component")$VaR 

should work or this is non-sense ?
I'm having a look, maybe the difference stems from the application of
Return.portfolio in the marginal case...
It did, thank you very much Brian !

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sadako
#
sadako wrote:
I think we don't get the same univariate portfolio VaR with the two
portfolio_method "marginal" and "component" because of :

- in PerformanceAnalytics:::VaR.Marginal, the Return.portfolio are
calculated without the optional argument geometric (geometric=FALSE would
eventually match the stdev I compute).

- in PerformanceAnalytics:::VaR.Marginal, when calling the
portfolio_method="single" to compute the univariate portfolio VaR, we end up
in the PerformanceAnalytics:::VaR.Gaussian function. 
This function uses the PerformanceAnalytics:::centeredmoment function, which
uses the mean function. 
This does not give the same variance as stdev for instance since there's not
the ajustement of the estimator (division by n-1 instead of n if data set
has n observations). 
If we set m2 = centeredmoment(r, 2)*dim(r)[1]/(dim(r)[1]-1), it looks ok.

With these two modifications, I have the impression the univariate portfolio
VaR computed from portfolio_method="marginal" and
portfolio_method="component" are consistant.

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