[R-SIG-Finance] Antwort: [R-sig-finance] VaR

Xiaochen Sun Xiaochen.Sun at brunel.ac.uk
Tue Mar 3 14:01:07 CET 2009


I fully agreed with Adams.
For example, to apply EVT to each marginal distribution of return and to apply copula to te dependence structure.
I think this has been also addressed in the book "Introduction to Modern Portfolio Optimization with NuOPT" by Bernd Scherer.
Regards,
Michael

________________________________

From: r-sig-finance-bounces at stat.math.ethz.ch on behalf of Adams, Zeno
Sent: Tue 03/03/2009 12:34
To: Micha Keijzers; Matthias.Koberstein at hsbctrinkaus.de
Cc: r-sig-finance at stat.math.ethz.ch; Bogaso
Subject: Re: [R-SIG-Finance] Antwort: [R-sig-finance] VaR



I don't know what you think about the topic but I feel that this matter of subadditivity is strongly overemphasized. Many authors argue in their papers that they will use the CVaR instead of the VaR because of the subbaditivity property (which goes back to Artzner, 1999). From my point of view the matter of getting the return distribution right, especially its variation over time, as well as the dependence structure between asset returns if the distribution is not elliptic is far more important for modeling the VaR adequately.

-----Ursprüngliche Nachricht-----
Von: r-sig-finance-bounces at stat.math.ethz.ch [mailto:r-sig-finance-bounces at stat.math.ethz.ch] Im Auftrag von Micha Keijzers
Gesendet: Dienstag, 3. März 2009 13:22
An: Matthias.Koberstein at hsbctrinkaus.de
Cc: r-sig-finance at stat.math.ethz.ch; Bogaso
Betreff: 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 Föllmer'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
>
>
>
>
>
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>                                         [R-SIG-Finance] [R-sig-finance]
>             Fax-Deckblatt:              VaR
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>             03.03.2009 12:24
>
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>
>
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>
> 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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