[R-SIG-Finance] Value-at-risk

Brian G. Peterson brian at braverock.com
Fri May 20 18:31:40 CEST 2011

You can't do what you're trying to do, in the way you are trying to do
it.

Since your weights are obviously dollar weights, I assumed that you were
trying to get the *entire* portfolio, knowing that these weights don't

If you want to work in returns space, and be able to make apples to
apples portfolio comparisons, then your weights should be a vector that
taking a \$734M position out of the portfolio, you're replacing it with
something....  cash, spreading the money to other things, whatever...

That position, in your example, is the largest position you have by far,
and contributes 95% of the total portfolio risk.  This shouldn't be
entirely surprising, as it is three times the size of your biggest short
position.

If you're going to *rebalance* the portfolio and see what the new VaR
is, you need to adjust more than just one weight.

If you really want Marginal VaR, then use Marginal VaR.  Please don't
try to permute component VaR into something it is not.

Regards,

- Brian

On Fri, 2011-05-20 at 21:52 +0530, Bogaso Christofer wrote:
> Thanks Brian, for your mail:
>
> On regard of the 1st asset your said: " Removing it would be expected to increase the portfolio VaR, as you report below "
>
> Therefore, if I consider 2nd asset, it has +ve sign. Therefore there is not diversification effect for this 2nd asset. Hence ** Removing it would be expected to "decrease" the portfolio VaR **. Right? However in reality I see different thing:
>
> > VaR(R = Ret, p = 0.05, method = "gaussian", portfolio_method = "component", weights = WtVector)
> \$VaR
>         [,1]
> [1,] 5434285
>
> \$contribution
>       Ret1       Ret2       Ret3       Ret4       Ret5       Ret6       Ret7
> -316156.24 5211014.96  266249.91  -50021.42  260904.17  149986.52  -87692.49
>
> \$pct_contrib_VaR
>         Ret1         Ret2         Ret3         Ret4         Ret5         Ret6         Ret7
> -0.058178070  0.958914480  0.048994465 -0.009204784  0.048010759  0.027600044 -0.016136894
>
> >
> > WtVector1 <- WtVector; WtVector1[2] <- 0 ## I remove 2nd asset, therefore portfolio VaR is expected to decrease
> > VaR(R = Ret, p = 0.05, method = "gaussian", portfolio_method = "component", weights = WtVector1)
> \$VaR
>         [,1]
> [1,] 7340057
>
> \$contribution
>       Ret1       Ret2       Ret3       Ret4       Ret5       Ret6       Ret7
>  868217.23       0.00 -260061.45   41235.95 4359025.20 2505891.43 -174251.63
>
> \$pct_contrib_VaR
>         Ret1         Ret2         Ret3         Ret4         Ret5         Ret6         Ret7
>  0.118284812  0.000000000 -0.035430442  0.005617933  0.593868053  0.341399463 -0.023739820
>
> With 2nd asset, port VaR is 5434285, and without 2nd asset port VaR is 7340057. How can it be justified?
>
> Here I plotted the relationship between port VaR with the 2nd asset weight:
>
> Mod_Wt <- seq(0, abs(WtVector[2]), by = 150000)
> VaRi <- vector(length = length(Mod_Wt))
> for (i in 1:length(VaRi)) {
> 					Wt1 <- WtVector; Wt1[2] <- 1 * Mod_Wt[i]
> 					VaRi[i] <- VaR(R = Ret, p = 0.95,  method = "gaussian", portfolio_method = "component", weights = Wt1)\$VaR
>                 }
> tail(Mod_Wt)
> tail(VaRi)
> plot(Mod_Wt, VaRi, type = "l")
>
>
> -----Original Message-----
> From: Brian G. Peterson [mailto:brian at braverock.com]
> Sent: 20 May 2011 21:07
> To: Bogaso Christofer
> Cc: r-sig-finance at stat.math.ethz.ch
> Subject: Re: [R-SIG-Finance] Value-at-risk
>
> On Fri, 2011-05-20 at 21:08 +0530, Bogaso Christofer wrote:
> > Hi,
> >
> > After Emmanuel's post in R-finance and the reply from Brian, I spent
> > few times on the VaR() function and on the underlying theory. Just to
> > admit that, this is great. However, I don't think I could understand
> > the theory of component VaR calculation, although it seems the coding
> > within the VaR() function for the same is completely okay.
> >
> > My problem is, how should I interpret component VaR? Having searched
> > over net and after going through few materials, I understand that, I
> > can read CVaR as the change of PVaR if underlying asset is removed
> > from the portfolio. Here my problem of interpretation starts from!
> > Please consider following hypothetical return (a zoo object, as needed
> > for VaR())
> >
> > > Ret
> >                     Ret1         Ret2         Ret3          Ret4
> > Ret5         Ret6         Ret7
> > 2010-04-15 -0.0009783093  0.000000000 -0.003752350 -0.0006021985
> > -0.012384059 -0.012539349 -0.034979719
> > 2010-04-16 -0.0004805344  0.003863495  0.003752350  0.0009617784
> > 0.003110422  0.003149609  0.003231021
> > 2010-04-19 -0.0273642188 -0.010336009 -0.003752350 -0.0104916573
> > -0.009360443 -0.009478744 -0.006472515
> > 2010-04-20  0.0154788565 -0.002600782 -0.007547206 -0.0036357217
> > -0.006289329 -0.006369448  0.006472515
> > 2010-04-21 -0.0094613433  0.000000000  0.000000000  0.0005484261
> > 0.000000000  0.000000000  0.000000000
> > 2010-04-22  0.0062536421  0.000000000  0.003780723 -0.0001143766
> > 0.009419222  0.009539023  0.006430890
> > 2010-04-23  0.0237922090  0.015504187  0.007518832  0.0097156191
> > 0.006230550  0.006309169  0.000000000
> > 2010-04-26  0.0133441736  0.012739026  0.003738322  0.0049317586
> > 0.018462063  0.018692133  0.012739026
> > 2010-04-28 -0.0105522323  0.000000000  0.000000000 -0.0037038049
> > -0.006116227 -0.006191970  0.000000000
> > 2010-04-29  0.0030733546 -0.006349228 -0.011215071 -0.0071195792
> > -0.003072199 -0.003110422  0.000000000
> >
> >
> > I have a long-short portfolio, I want to estimate component VaR for
> > the 2nd asset, using VaR() function:
> >
> >
> > > WtVector <- c( -49895159,  734677735,   51037536,   -7126937, -283834066,
> > -161147892,   13652772)
> > > VaR(R = Ret, p = 0.05, method = "gaussian", portfolio_method =
> > "component", weights = WtVector)
> > \$VaR
> >         [,1]
> > [1,] 5434285
> > \$contribution
> >       Ret1       Ret2       Ret3       Ret4       Ret5       Ret6       Ret7
> >
> > -316156.24 5211014.96  266249.91  -50021.42  260904.17  149986.52
> > -87692.49 \$pct_contrib_VaR
> >         Ret1         Ret2         Ret3         Ret4         Ret5
> > Ret6         Ret7
> > -0.058178070  0.958914480  0.048994465 -0.009204784  0.048010759
> > 0.027600044 -0.016136894
> >
> > This says (if my interpretation is correct) that if I remove my 1st
> > asset then, portfolio VaR will increase by -316156.24 (negative sign
> > tells to have hedging effect)
>
> You're speaking of *marginal* VaR, not component VaR.
>
> Marginal (or Incremental) VaR is the contribution of that instrument to the VaR of the portfolio "at the margin" (this is how I keep them straight).  Marginal VaR is not additive, it may add up to more than 100% of the total portfolio VaR.  I find it to be a relatively poor risk measure overall, and generally don't recommend using it (there are some exceptions that are mentioned in the documentation for the VaR function).  Your description describes Marginal VaR, not Component VaR.
>
> Component VaR is the *contribution* to the portfolio VaR of each component in the portfolio.  It adds up to the value of the entire portfolio VaR. The value returned has three slots.
> \$VaR # the portfolio VaR
> \$contribution
>   the scalar contributions of each instrument,
>   this adds up to the portfolio VaR
> \$pct_contribution_VaR
>   the percentage contributions to VaR,
>   this adds up to 1
>   negative numbers are diversifiers, *decreasing*
>   the total portfolio VaR
>
> So, given that this is component VaR we're looking at, not marginal VaR, asset 1 is your *largest diversifier*.  Removing it would be expected to increase the portfolio VaR, as you report below.
>
> Hopefully this clears things up...
>
> Regards,
>
>    - Brian
>
> > So I recalculate the portfolio VaR without having 1st asset:
> > > WtVector <- c( 0,  734677735,   51037536,   -7126937, -283834066,
> > -161147892,   13652772)
> > > VaR(R = Ret, p = 0.05, method = "gaussian", portfolio_method =
> > "component", weights = WtVector)
> > \$VaR
> >         [,1]
> > [1,] 5849476
> > \$contribution
> >       Ret1       Ret2       Ret3       Ret4       Ret5       Ret6       Ret7
> >
> >       0.00 5987199.26  274456.46  -55685.39 -185776.60 -106798.21
> > -63919.72 \$pct_contrib_VaR
> >         Ret1         Ret2         Ret3         Ret4         Ret5
> > Ret6         Ret7
> >  0.000000000  1.023544581  0.046919839 -0.009519723 -0.031759529
> > -0.018257741 -0.010927428
> >
> > I am just surprised to see that, my portfolio VaR indeed
> > ***increased!!!***
> >
> > I have found that, this kind of discrepancy comes as possible
> > non-linear relationship between VaR and it's constituent assets. It
> > happens that x-y plot for VaR and weight for the 1st asset is highly
> > non-linear. sign of the Slope changes if I move from current point
> > (resemble to weight for 1st
> > asset) to origin (i.e. no 1st asset in the portfolio.)
> >
> > So My question is, how can I trust on the sign (at least) of component VaR.
> > Isn't it is giving completely misleading figure? How risk managers
> > handle these issue? Does the solution like:
> > 1. I should include higher term of the Taylor's expansion of the
> > portfolio VaR function 2. Do not simply trust those component VaR
> > figures. I should completely re-estimate my VaR number with and
> > without having underlying asset.
> >
> > Any thoughtful point(s) will be highly appreciated.
> >
> > Thanks and regards,
> >
> > -----Original Message-----
> > From: r-sig-finance-bounces at r-project.org
> > [mailto:r-sig-finance-bounces at r-project.org] On Behalf Of Brian G.
> > Peterson
> > Sent: 12 May 2011 17:28
> > To: Emmanuel Senyo
> > Cc: r-sig-finance at stat.math.ethz.ch
> > Subject: Re: [R-SIG-Finance] Value-at-risk
> >
> > There is over 100 pages of documentation available with
> > PerformanceAnalytics.
> >
> >
> > install.packages("PerformanceAnalytics")
> > #you only need to do the install the first time
> >
> > require(PerformanceAnalytics)
> > ?VaR
> >
> > from the R prompt.  See the examples at the bottom of the VaR documentation.
> >
> > Hopefully that will get you started.  If you have trouble, you may
> > email the R-SIG-Finance list or me with an example of what you're trying to do.
> > Ideally, start with some publicly available data (use the edhec or
> > managers data in Performanceanalytics, or use getSymbols to pull stock
> > data from Yahoo or Google) so that others can replicate what you're
> > trying to do and help you with code rather than vague suggestions.
> >
> > Regards,
> >
> >    - Brian
> >
> > On Thu, 2011-05-12 at 13:47 +0200, Emmanuel Senyo wrote:
> > > Dear Brian,
> > > Thanks for the mail, I have now located the PerformanceAnalytics.
> > > Could you please elaborate on it how I could use this package, the
> > > fact is that I am new to R, how i would like compute value at risk
> > > for prices and volumes. If I can get a sample scripts with
> > > explanation that would be very helpful to me to enable me build my own scripts.
> > > Regards
> > > Emma
> > >
> > > On Thu, May 12, 2011 at 1:21 PM, Brian G. Peterson
> > > <brian at braverock.com> wrote:
> > >
> > >         On Thu, 2011-05-12 at 12:38 +0200, Emmanuel Senyo wrote:
> > >         > Dear All,
> > >         > I am currently work on Value-at-risk and would like to know
> > >         the package that
> > >         > is helpful in this regard. It consist of three method, that
> > >         is variance
> > >         > covariance method, Monte carlo simulation, and Historical
> > >         simulation.
> > >         > Regards
> > >         > Em
> > >
> > >
> > >         The Gaussian and Historical methods are available in
> > >         PerformanceAnalytics.
> > >
> > >         You can easily use the Monte Carlo method of your choice to
> > >         create a
> > >         longer sample, and then use PerformanceAnalytics to calculate
> > >         the VaR.
> > >
> > >         There are also several bootstrap Monte Carlo methods in
> > >         PerformanceAnalytics that have been contributed by Eric Zivot,
> > >         but which
> > >         we have not yet documented and exposed.
> > >
> > >         Regards,
> > >
> > >           - Brian
> > >
> > >         --
> > >         Brian G. Peterson
> > >         http://braverock.com/brian/
> > >         Ph: 773-459-4973
> > >         IM: bgpbraverock
> > >
> > >
> >
> > --
> > Brian G. Peterson
> > http://braverock.com/brian/
> > Ph: 773-459-4973
> > IM: bgpbraverock
> >
> > _______________________________________________
> > 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.
> >
> > _______________________________________________
> > 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.
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>
> --
> Brian G. Peterson
> http://braverock.com/brian/
> Ph: 773-459-4973
> IM: bgpbraverock
>
> _______________________________________________
> 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.

--
Brian G. Peterson
http://braverock.com/brian/
Ph: 773-459-4973
IM: bgpbraverock