[R-SIG-Finance] CVaR and Penalty Augmented objective function
Brian G. Peterson
brian at braverock.com
Thu Oct 13 20:01:19 CEST 2016
Yes, agreed. This gets handled correctly, I think in
optimize.portfolio(), but when constrained_objective is called directly,
it looks like set.portfolio.moments doesn't merge arguments from ... or
the arguments=list correctly.
I think that the 'correct' way to deal with this would probably be to
handle it in dots, and make sure those get merged correctly. I think it
would be much more challenging to process it from the argument=list()
for an individual objective.
Regards,
Brian
--
Brian G. Peterson
http://braverock.com/brian/
Ph: 773-459-4973
IM: bgpbraverock
On Thu, 2016-10-13 at 12:54 -0500, Michael Weylandt wrote:
> The issue seems to be in the calculation of the co-skewness and co-kurtosis.
>
> In particular, when calling ES directly, the user-supplied mu gets
> used to calculate M3 and M4. When called through PortfolioAnalytics,
> M3 and M4 are calculated (without using mu) before calling ES.
>
> A pure PerformanceAnalytics example:
>
> ###### < BEGIN EXAMPLE > ######
> ## Marco's problem
> library(PerformanceAnalytics)
> data(indexes)
>
> R <- indexes[,1:4]
>
> w <- rep(1/4, 4)
> mu <- rep(0.01, 4)
>
> M2 <- cov(R)
> M3 <- M3.MM(R)
> M4 <- M4.MM(R)
>
> ES(R, portfolio_method="single", weights=w,
> sigma=M2, m3=M3, m4=M4, mu=mu, invert=FALSE)
>
> ES(R, portfolio_method="component", weights=w, mu=mu)$MES
>
> ## Adding mu to the calculation of M3, M4 gives consistent answers
> M2_mu <- cov(R)
> M3_mu <- M3.MM(R, mu=mu)
> M4_mu <- M4.MM(R, mu=mu)
>
> ES(R, portfolio_method="single", weights=w,
> sigma=M2, m3=M3_mu, m4=M4_mu, mu=mu, invert=FALSE)
>
> ES(R, portfolio_method="component", weights=w, mu=mu)$MES
>
> ##### < END EXAMPLE > ######
>
> It looks like PortfolioAnalytics::set.portfolio.moments does not
> attempt to pass a user supplied mu to PerformanceAnalytics::M3.MM and
> PerformanceAnalytics::M4.MM, even if its given as an argument to
> constrained_objective():
>
> >From https://github.com/cran/PortfolioAnalytics/blob/master/R/moment.functions.R#L327
>
> switch(method,
> sample = {
> if(is.null(momentargs$mu)) momentargs$mu = matrix(
> as.vector(apply(tmpR, 2, 'mean')), ncol=1);
> if(is.null(momentargs$sigma)) momentargs$sigma = cov(tmpR)
> if(is.null(momentargs$m3)) momentargs$m3 =
> PerformanceAnalytics::M3.MM(tmpR)
> if(is.null(momentargs$m4)) momentargs$m4 =
> PerformanceAnalytics::M4.MM(tmpR)
> },
>
> [Code for the current development version looks to behave similarly]
>
>
> Hope this helps,
> Michael
>
>
> On Wed, Oct 12, 2016 at 5:21 AM, Brian G. Peterson <brian at braverock.com> wrote:
> > I attach what I think is a syntactically correct version of the email, which
> > looks like it was pasted from HTML.
> >
> > We'll try to take a look.
> >
> > Regards,
> >
> > Brian
> >
> > On 10/12/2016 04:34 AM, Marco Mastrangeli wrote:
> >>
> >> Hi Michael,
> >>
> >> thanks for your reply, I apologize for the not full clarity of my
> >> question.
> >> In the following, I try to report a full example.
> >>
> >> #Library
> >> *library(PerformanceAnalytics)*
> >> *library(PortfolioAnalytics)*
> >>
> >> #Returns data present in "PortfolioAnalytics"
> >> *data(indexes)*
> >> *indexes <- indexes[,1:4]*
> >>
> >> #New Portfolio Object
> >> *Wcons <- portfolio.spec(assets=colnames(indexes))*
> >>
> >> #Add box constraints
> >> *Wcons <- add.constraint(portfolio=Wcons, type='box', min=0, max=1)*
> >>
> >> #Add the full investment constraint
> >> *Wcons <- add.constraint(portfolio=Wcons, type="full_investment")*
> >>
> >> #Add Objective specification: VaR with default parameter for vector "mu"
> >> (EXAMPLE 1)
> >> *VaRObjSpec <- add.objective(portfolio=Wcons, type="risk", name="VaR",
> >> arguments=list(p=0.95), enabled=TRUE)*
> >>
> >> #The value of the objective function is:
> >> *constrained_objective(w=rep(1/4,4), R=indexes, portfolio=VaRObjSpec)
> >> #* VaR
> >> *0.0499467*
> >>
> >> #This is the VaR of the equal-weight portfolio as computed by the function
> >> VaR in the PerformanceAnalytics package.
> >> *VaRout <- VaR(indexes, weights=rep(1/4,4), p=0.95,
> >> portfolio_method="component")*
> >> *VaRout$MVaR # *[1,]* 0.0499467*
> >>
> >> Now, I repet the VaR example with a user-defined vector for the parameter
> >> "mu".
> >>
> >> #User-defined vector "mu"
> >> *myMu = rep(0.01, 4)*
> >>
> >> #Add Objective specification: VaR with user-defined parameter for vector
> >> "mu"
> >> *myVaRObjSpec <- add.objective(portfolio=Wcons, type="risk", name="VaR",
> >> arguments=list(p=0.95, mu=myMu), enabled=TRUE)*
> >>
> >> #The value of the objective function is:
> >> *constrained_objective(w=rep(1/4,4), R=indexes, portfolio=myVaRObjSpec)
> >> #* VaR *0.04638622*
> >>
> >> #This is the VaR of the equal-weight portfolio as computed by the function
> >> VaR in the PerformanceAnalytics package with *mu=myMu.*
> >> *myVaRout <- VaR(indexes, weights=rep(1/4,4),
> >> p=0.95, mu=myMu, portfolio_method="component")*
> >> *myVaRout$MVaR # *[1,]* 0.04638622*
> >>
> >> So, using the default and user-defined parameter for "mu" there is
> >> corrispondence between constrained_objective and the function VaR of
> >> PerformanceAnalytics package.
> >> I repet the example but now adding CVaR as risk objective in Wcons
> >> portfolio.
> >>
> >> #Add Objective specification: CVaR with default parameter for vector "mu"
> >> (EXAMPLE 2)
> >> *CVaRObjSpec <- add.objective(portfolio=Wcons, type="risk", name="CVaR",
> >> arguments=list(p=0.95), enabled=TRUE)*
> >>
> >> #The value of the objective function is:
> >> *constrained_objective(w=rep(1/4,4), R=indexes, portfolio=CVaRObjSpec)
> >> #* ES
> >> *0.1253199*
> >>
> >> #This is the CVaR of the equal-weight portfolio as computed by the
> >> function
> >> ES in the PerformanceAnalytics package.
> >> *CVaRout <- ES(indexes, weights=rep(1/4,4), p=0.95,
> >> portfolio_method="component")*
> >> *CVaRout$MES # *[1,]* 0.1253199*
> >>
> >> Now, I repet the CVaR example with a user-defined vector for the parameter
> >> "mu".
> >>
> >> #User-defined vector "mu"
> >> *myMu = rep(0.01, 4)*
> >>
> >> #Add Objective specification: CVaR with user-defined parameter for vector
> >> "mu"
> >> *myCVaRObjSpec <- add.objective(portfolio=Wcons, type="risk", name="CVaR",
> >> arguments=list(p=0.95, mu=myMu), enabled=TRUE)*
> >>
> >> #The value of the objective function is:
> >> *constrained_objective(w=rep(1/4,4), R=indexes, portfolio=myCVaRObjSpec)
> >> #* ES *0.1217594*
> >>
> >> #This should be the CVaR of the equal-weight portfolio as computed by the
> >> function ES in the PerformanceAnalytics package with *mu=myMu.*
> >> *myCVaRout <- ES(indexes, weights=rep(1/4,4),
> >> p=0.95, mu=myMu, portfolio_method="component")*
> >> *myCVaRout$MES # *[1,]* 0.1235878*
> >>
> >> In this case, using the user-defined parameter for "mu" there is no
> >> corrispondence between the value of constrained_objective (0.1217594*)
> >> *and
> >>
> >> the result of function ES of PerformanceAnalytics package (0.1235878). Why
> >> there is no match in this case?
> >> This not the case for the matrix parameter (for portfolio) "sigma": if I
> >> use a user-defined sigma matrix, there is always corrispondence (without,
> >> obviosly, costraints that augment the penalty augmented objective
> >> function) between the value of constrained_objective (with VaR/CVaR risk
> >> objective) and the result of function VaR/ES of PerformanceAnalytics
> >> package.
> >>
> >> I hope my example is clear enough to illustrate the question.
> >> Thanks a lot for your attention.
> >> Marco
> >>
> >>
> >> On Wed, Oct 12, 2016 at 1:55 AM, Michael Weylandt <
> >> michael.weylandt at gmail.com> wrote:
> >>
> >>> Hi Marco,
> >>>
> >>> Can you put together a minimal reproducible example [1,2] so that it's
> >>> easier for others to answer your question?
> >>>
> >>> For this problem, I'd recommend using the edhec data distributed with
> >>> PerformanceAnalytics.
> >>>
> >>> Thanks,
> >>> Michael
> >>>
> >>> [1] http://stackoverflow.com/questions/5963269/how-to-make-
> >>> a-great-r-reproducible-example
> >>> [2] http://adv-r.had.co.nz/Reproducibility.html
> >>>
> >>> On Tue, Oct 11, 2016 at 11:46 AM, Marco Mastrangeli
> >>> <marco.mastrangeli at gmail.com> wrote:
> >>>>
> >>>> I have a question about the use of the "mu" parameter in the functions
> >>>> StdDev, VaR e CVaR.
> >>>> As reference data we can use data in the paper "Vignette: Portfolio
> >>>> Optimization with CVaR budgets in PortfolioAnalytics".
> >>>> If we use the default parameters for "mu" and "sigma", there is a
> >>>> match between
> >>>>
> >>>>> constrained_objective( w = rep(1/4,4) , R = indexes, portfolio =
> >>>>> ObjSpec)
> >>>>
> >>>> [,1]
> >>>> ES 0.1253199
> >>>>
> >>>> and
> >>>>
> >>>>> out<-ES(indexes, weights = rep(1/4,4),p=0.95,
> >>>
> >>> portfolio_method="component")
> >>>>>
> >>>>> out$MES
> >>>>
> >>>> [,1]
> >>>> [1,] 0.1253199
> >>>>
> >>>> as explained by the authors.
> >>>> If I insert a user-defined sigma matrix for the "sigma" parameter, the
> >>>> match is still there between this two exspressions. If I insert a
> >>>> user-defined vector for the "mu" parameter (for example "mu=rep(0.01,
> >>>
> >>> 4)",
> >>>>
> >>>> the result of the two exspressions is the same only for portafolio with
> >>>> risk objective function StdDev and VaR, not for CVaR.
> >>>>
> >>>> VaR case:
> >>>>>
> >>>>> ObjSpec = add.objective(portfolio=Wcons, type="risk", name="VaR",
> >>>>
> >>>> arguments=list(p=0.95, mu=rep(0.01,4)), enabled=TRUE)
> >>>>>
> >>>>> constrained_objective(w=rep(1/4,4), R=indexes, portfolio=ObjSpec)
> >>>>
> >>>> [,1]
> >>>> VaR 0.04638622
> >>>>
> >>>>> out<-VaR(indexes, weights=rep(1/4,4), p=0.95, mu=rep(0.01,4),
> >>>>
> >>>> portfolio_method="component")
> >>>>>
> >>>>> out
> >>>>
> >>>> $MVaR
> >>>> [,1]
> >>>> [1,] 0.04638622
> >>>>
> >>>>
> >>>> CVaR case:
> >>>>>
> >>>>> ObjSpec = add.objective(portfolio=Wcons, type="risk", name="CVaR",
> >>>>
> >>>> arguments=list(p=0.95, mu=rep(0.01,4)), enabled=TRUE)
> >>>>>
> >>>>> constrained_objective(w=rep(1/4,4), R=indexes, portfolio=ObjSpec)
> >>>>
> >>>> [,1]
> >>>> ES 0.1217594
> >>>>
> >>>>> out<-ES(indexes, weights=rep(1/4,4), p=0.95, mu=rep(0.01,4),
> >>>>
> >>>> portfolio_method="component")
> >>>>>
> >>>>> out
> >>>>
> >>>> $MES
> >>>> [,1]
> >>>> [1,] 0.1235878
> >>>>
> >>>> I can't find the explanation for this thing. Thanks a lot for your
> >>>> attention.
> >>>>
> >>>> Marco
> >>>>
> >>>> [[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.
> >>>
> >>
> >> [[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.
> >>
> >
> >
> > --
> > 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
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> > should go.
>
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