Value-at-risk

On Sun, 2011-06-19 at 03:19 -0700, sadako wrote:

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

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.

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.

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 ?

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

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])

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

a portfolio with the instrument in question and the VaR of the portfolio 
without that instrument.

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 ?

you can see the code with: PerformanceAnalytics:::VaR.Marginal

I'm having a look, maybe the difference stems from the application of
Return.portfolio in the marginal case...

Many thanks for any helpful comment,

I hope this helps,
    - Brian

It did, thank you very much Brian !

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