[R-SIG-Finance] [R-sig-finance] VaR
markleeds at verizon.net
markleeds at verizon.net
Tue Mar 3 12:34:01 CET 2009
Hi Christofer: I don't know if the analogy is allowed but this can
happen with regular statistical
variance so maybe it can happen with Value at Risk also ? if you have a
covariance matrix
of 2 assets with portfolio weights w_1 and w_2 and the 2 assets have
positive covariance, then the resulting variance of the portfolio will
be greater than the sum of the individual variances of the two assets
with weights w_1 and w_2. ( w_1*v_1 + w_2*v_2 ).
now I have no idea if the result for statistical variance holds for
Value at Risk ( i don't know the definition of Value at Risk ) but, if
it does, then that's probably the answer. Hopefully someone else will
tell us if the analogy is allowed ?
On Tue, Mar 3, 2009 at 6:20 AM, Bogaso wrote:
> 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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