Antwort: Re: Antwort: [R-sig-finance] VaR
Hi
thats what I ment with the second paragraph. If any of the return
distributions is not normal or shifted/skewed or whatever, you usually have
a serious problem finding the quantile.
Cheers
Matthias
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03.03.2009 13:23 Re: [R-SIG-Finance] Antwort:
[R-sig-finance] VaR
Matthias and others,
Indeed, correlation possibly has something to do with it. But it's not the
whole story. VaR is a quantile of a distribution and you can draw up
examples that go wrong specifically there, regardless of correlation. I
constructed or adapted one, which must have been about three years ago I
think, based on an example which came from IIRC F?llmer's book "Stochastic
Finance" or "Quantitative Risk Management" by McNeil, Frey and Embrechts. I
would have to do some serious digging to be sure... The example was based
on
a very simple example of defaults in a loan portfolio. Explicitly showing
the quantiles in the loss distribution you could show that subadditivity
did
not hold when VaR is used as a risk measure.
Kind regards,
Micha Keijzers
2009/3/3 <Matthias.Koberstein at hsbctrinkaus.de>
Hi Christofer, I think the analogy is allowed if you assume normal distributions for the assets. Since then the VaR is dependent on the volatility. The variance of two random variables (combined assets in this case) is given by Var(x+y)= E((x+y)^2) - E(x+y)^2 which transforms to Var( x+y) = Var(x) + Var(y) + 2 * Covariance(x, y) So it all depends on the covariance of x to y. To give it a better feel this can be expressed in Correlation Var(x+y)= Var(x) + Var(y) + 2 * Vol(x) * Vol(y) * Correlation To better see the effect throw some weights in w1, and w2 which combine
to
one. Then Var( w1 x + w2 y)= Var(x) w1^2 + Var(y) w2^2 + 2 * w1 * w2 * Vol(x) * Vol (y) * Correlation the volatility used to estimate VaR is the square root of the variance. So you see that if correlation is 1 VaR is not sub-additive. Another point is if the distributions you use for the assets are not the same, the VaR can not even been combined easily but you have to find the
combined
distributions of the assets in the portfolio (which can be quite
painful).
I hope that helps. All the best Matthias **** Ressourcen schonen, weniger drucken - Think before you print! **** --------------------------------------------------------------------- Diese E-Mail sowie eventuelle Anh?nge enthalten vertrauliche und / oder rechtlich gesch?tzte Informationen. Wenn Sie nicht der richtige Adressat sind oder diese E-Mail irrt?mlich erhalten haben, informieren Sie bitte sofort den Absender und vernichten Sie diese Mail. Das unerlaubte
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[R-SIG-Finance] [R-sig-finance]
Fax-Deckblatt: VaR
HSBCTuB
03.03.2009 12:24
I frequently hear Value at risk i.e. VaR is not a coherent risk measure
because, sum of VaR for two individual assets may be LOWER than VaR of
portfolio consists of that two aseets i.e. VaR may not be sub-additive.
However when I calculate VaR for general assets like Equity, commodity
etc,
I see that VaR is actually sub-addtive i.e. portfolio VaR is always less than sum of individuals, which is reported as "diversification benefit". Can anyone give me a particular example why VaR is not sub-additive? Thanks -- View this message in context: http://www.nabble.com/VaR-tp22306743p22306743.html Sent from the Rmetrics mailing list archive at Nabble.com.
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