[R-SIG-Finance] Value-at-risk
Bogaso Christofer
bogaso.christofer at gmail.com
Fri May 20 17:38:52 CEST 2011
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)
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.
I suggest you start with
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
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