[R-SIG-Finance] Portfolio VaR and Asset VaR

[Prashant Sethi]

Any portfolio on the efficient frontier will have the least variance for a
given expected return, however not necessarily less than each individual
asset.

One such efficient portfolio is known as the global minimum portfolio. This
global minimum portfolio has the portfolio variance (thus portfolio VaR) as
the lowest possible variance, which is less than each of the individual
assets in the portfolio, provided there is no restriction on short
condition of assets.

Thanks and regards,
Prashant Sethi
 On 3 Jun 2015 15:51, "AIE ATUMA via R-SIG-Finance" <
r-sig-finance at r-project.org> wrote:

> Dear Brian,
> The Portfolio VaR is expected to be lower than the sum of the individual
> asset VaRs. This is made possible due to correlation between the individual
> assets. Thank You and Best Regards,
>
> Emeka .I. A
> Integrity is work your talk don't talk your work
>
>
>      On Wednesday, 3 June 2015, 11:03, Brian G. Peterson <
> brian at braverock.com> wrote:
>
>
>  Jan is correct.  Value at Risk does not have the property of being
> 'coherent' in the sense described in Artzner's papers.
>
> R does have a coherent portfolio VaR available.  You can call
> portfolio_method='component' in the VaR function in PerformanceAnalytics
> which will give you the portfolio VaR and how much each asset
> contributes to the overall portfolio VaR.
>
> Regards,
>
> Brian
>
>
> On 06/03/2015 04:43 AM, Annaert Jan wrote:
> > I think this is perfectly possible. For instance, if A to E are
> individual
> > stocks and P is, say, an equally weighted portfolio of these stocks. If
> > firm-specific risk is high relative to systematic risk (which is
> typical),
> > firm-specific risk may be to a large extent diversified away in P. As a
> > consequence, VaR of P may be (much) smaller than each of the individual
> > VaRs.
> > HTH,
> >
> >
> > Jan Annaert
> >
> > From:  Christofer Bogaso <bogaso.christofer at gmail.com>
> > Date:  woensdag 3 juni 2015 05:55
> >
> > Let say I have a diversified portfolio of 5 assets. The individual
> > Asset VaRs for them are $A, $B, $C, $D, & $E. And the overall
> > portfolio VaR is $P. Assumed all VaR numbers are reported in absolute
> > number
> >
> > It appears that P is less than all 5 individual VaRs.
> >
> > Can that happen? I know that P < (A+B+C+D+E). However here in my
> > calculation what happened is P is less than each asset VaR.
> >
> > Appreciate your view.
> >
> > Thanks and regards,
>
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