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

Annaert Jan jan.annaert at uantwerpen.be
Wed Jun 3 11:43:40 CEST 2015

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

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

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

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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