[R-SIG-Finance] CVaR and Penalty Augmented objective function

[Marco Mastrangeli]

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

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