Minimizing tracking error with restricted number of stocks

Alec,

I do not believe that there is a closed form optimization solution for
what you are trying to do.  In other words, I am agreeing with Coleman
et. al.

That is not the same thing as saying that you can't solve it with
PortfolioAnalytics.

First, add a position_limit constraint setting the number of non-zero
positions that you want in the portfolio

Second, add a tracking error objective as described in Ross'
presentation.

(along with adding any other objectives or constraints you need in your
portfolio specification)

Third, utilize one of the global numerical solvers, e.g. DEoptim,
random portfolios, genSA, or pso.

The numerical solvers will not search the entire feasible space, but
rather search a subset of the feasible space stochastically.  You
should get acceptably close to the global optimum portfolio using these
methods in finite time.

Regards,

- Brian

On Thu, 2018-03-08 at 16:04 +0000, Alec Schmidt wrote:
> This is a very handy doc indeed. I'm not sure though that examples on
> #29 - #31 address the problem I'm looking into. Namely, I need
> minimum tracking error with explicit constraint on the number of
> stocks that is lower than in the benchmark portfolio. Coleman, Li,
> and Henniger (2004) state that it's NP-hard problem and review a few
> heuristic methods. Is there one implemented in PortfolioAnalytics?
> Thanks much! Alec
> ________________________________________
> From: R-SIG-Finance <r-sig-finance-bounces at r-project.org> on behalf
> of Jason Hart <jasonhart4 at icloud.com>
> Sent: Thursday, March 8, 2018 9:46 AM
> To: Brian G. Peterson
> Cc: R-SIG-Finance
> Subject: Re: [R-SIG-Finance]  Minimizing tracking error with
> restricted number of stocks
>
> Great presentation, thanks for sharing the link
>
> Sent from my iPad
>
> > On Mar 7, 2018, at 10:00 PM, Brian G. Peterson <brian at braverock.com
> > > wrote:
> >
> > > On 03/07/2018 08:39 PM, Alec Schmidt wrote:
> > > Thank you Brian. I searched PortfolioAnalytics.pdf for 'tracking'
> > > but didn't find one. Are there any implementation examples?
> >
> > See Ross Bennett's tutorial from R/Finance 2017:
> >
> > https://rossb34.github.io/PortfolioAnalyticsPresentation2017/#1
> >
> > Tracking Error example starts on slide 29, though you should find
> > the rest of the tutorial useful.
> >
> > - Brian
> >
> > > ________________________________________
> > > From: R-SIG-Finance <r-sig-finance-bounces at r-project.org> on
> > > behalf of Brian G. Peterson <brian at braverock.com>
> > > Sent: Wednesday, March 7, 2018 9:14 PM
> > > To: r-sig-finance at r-project.org
> > > Subject: Re: [R-SIG-Finance]  Minimizing tracking error with
> > > restricted number of stocks
> > > > On 03/07/2018 07:55 PM, Alec Schmidt wrote:
> > > > Say I have a portfolio of 100 stocks and want to find a subset
> > > > of 20 stocks with minimum tracking error in respect to the
> > > > original portfolio. I wonder if a solver to this problem is
> > > > implemented in some R-based library.
> > >
> > > PortfolioAnalytics can do this.
> > >
> >
> > _______________________________________________
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