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VaR

2 messages · david.jessop at ubs.com, Enrico Schumann

Original
david.jessop at ubs.com
# 
Hi

A very simple (if somewhat artificial) example.  Suppose you have an
option which pays off zero 96% of the time and -10 4% of the time.  The
95% VaR is zero (obviously).  Now suppose you have another similar
option on an uncorrelated event, the VaR of this is also zero.  Now
combine them together.  There is a 92.2% probability of getting zero,
0.2% of getting -20 and 7.6% of getting -10. Hence the VaR of the
combined portfolio is -10.  

In the case of equities or anything with a reasonable distribution this
type of thing is unlikely to happen. 

Regards,

David


Message: 1
Date: Tue, 3 Mar 2009 03:20:55 -0800 (PST)
From: Bogaso <bogaso.christofer at gmail.com>
Subject: [R-SIG-Finance] [R-sig-finance] VaR
To: r-sig-finance at stat.math.ethz.ch
Message-ID: <22306743.post at talk.nabble.com>
Content-Type: text/plain; charset=us-ascii


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
Enrico Schumann
# 
sorry, i did not follow this thread closely, so maybe i repeat something
that has already been said.

to quote david: "In the case of equities or anything with a reasonable
distribution this type of thing is unlikely to happen."  theoretically,
"reasonable" is elliptical distributions, for which var actually is a
coherent risk measure. a very readable paper describing this can be found
here http://www.math.ethz.ch/~strauman/light/risk.pdf

regards
enrico


-----Urspr?ngliche Nachricht-----
Von: r-sig-finance-bounces at stat.math.ethz.ch
[mailto:r-sig-finance-bounces at stat.math.ethz.ch] Im Auftrag von
david.jessop at ubs.com
Gesendet: Mittwoch, 4. M?rz 2009 12:41
An: r-sig-finance at stat.math.ethz.ch
Betreff: Re: [R-SIG-Finance] [R-sig-finance] VaR

Hi

A very simple (if somewhat artificial) example.  Suppose you have an option
which pays off zero 96% of the time and -10 4% of the time.  The 95% VaR is
zero (obviously).  Now suppose you have another similar option on an
uncorrelated event, the VaR of this is also zero.  Now combine them
together.  There is a 92.2% probability of getting zero, 0.2% of getting -20
and 7.6% of getting -10. Hence the VaR of the combined portfolio is -10.  

In the case of equities or anything with a reasonable distribution this type
of thing is unlikely to happen. 

Regards,

David


Message: 1
Date: Tue, 3 Mar 2009 03:20:55 -0800 (PST)
From: Bogaso <bogaso.christofer at gmail.com>
Subject: [R-SIG-Finance] [R-sig-finance] VaR
To: r-sig-finance at stat.math.ethz.ch
Message-ID: <22306743.post at talk.nabble.com>
Content-Type: text/plain; charset=us-ascii


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
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