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

[markleeds at verizon.net]

  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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