Skip to content

Portfolio VaR and Asset VaR

6 messages · Christofer Bogaso, Annaert Jan, Brian G. Peterson +3 more

#
Hi again,

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,
#
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

UNIVERSITEITANTWERPEN | Faculty of Applied Economics (TEW) | Dept.
Accounting & Finance
Room  S.B.335 | Prinsstraat 13 | B-2000 Antwerp  | Belgium
Phone +32 32654163 |Fax +32 32654064
https://www.uantwerp.be/en/staff/jan-annaert/
http://ssrn.com/author=143473



From:  Christofer Bogaso <bogaso.christofer at gmail.com>
Date:  woensdag 3 juni 2015 05:55
To:  "r-sig-finance at r-project.org" <r-sig-finance at r-project.org>
Subject:  [R-SIG-Finance] Portfolio VaR and Asset VaR


Hi again,

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,

_______________________________________________
R-SIG-Finance at r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-finance
-- Subscriber-posting only. If you want to post, subscribe first.
-- Also note that this is not the r-help list where general R questions
should go.
#
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:
#
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:
_______________________________________________
R-SIG-Finance at r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-finance
-- Subscriber-posting only. If you want to post, subscribe first.
-- Also note that this is not the r-help list where general R questions should go.
#
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:

            

  
  
#
Actually in some cases portfolio VaR may be greater than the sum of the individual VaRs. Hence it doesn't have the property of being sub-additive, and is not a coherent risk measure.

There's an example on wikipedia

http://en.wikipedia.org/wiki/Coherent_risk_measure

Thanks

Peter
www.returnandrisk.com



---- On Wed, 03 Jun 2015 10:20:24 +0000 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,
 > 
 > _______________________________________________
 > R-SIG-Finance at r-project.org mailing list
 > https://stat.ethz.ch/mailman/listinfo/r-sig-finance
 > -- Subscriber-posting only. If you want to post, subscribe first.
 > -- Also note that this is not the r-help list where general R questions should go.
 > 
 > 
 > 
 > [[alternative HTML version deleted]]
 > 
 > _______________________________________________
 > R-SIG-Finance at r-project.org mailing list
 > https://stat.ethz.ch/mailman/listinfo/r-sig-finance
 > -- Subscriber-posting only. If you want to post, subscribe first.
 > -- Also note that this is not the r-help list where general R questions should go.