[R-SIG-Finance] Solver for a generic optimal portfolio

[Brian G. Peterson]

The diversification return is a side effect of rebalancing.

To 'optimize' for diversification return, you'll still need some other 
objectives and constraints.

In any complex feasible space for optimization with a non-trivial number 
of assets, you can often find multiple portfolios with similar base 
properties (like return and variance).  You could, in theory, maximize 
diversification return by finding neighboring 'near-optimal' portfolios 
on your other objectives and constraints and then choosing among them 
with a preference for higher turnover.

This, of course, will incur significant rebalancing costs. These 
associated costs are why a continuously rebalanced portfolio is 
unrealistic, and why most portfolio construction methodologies try to 
minimize turnover. (There are other reasons for minimizing turnover too, 
but those are the ones most often discussed).

We still don't know enough about what the other objectives and 
constraints you have for your portfolio to recommend a specific solver.

Regards,

Brian


On 03/12/2016 07:47 PM, Alec Schmidt wrote:
> Brian/Mark/Patrick,
> Thanks for answering my curiosity on Saturday night. I just come across the Willenbrock's paper http://arxiv.org/abs/1109.1256
> and wonder if it makes sense to optimize so-called diversification return (eq 13) and, if yes, what tool you might suggest.
> Best, Alec
>
> ________________________________________
> From: R-SIG-Finance <r-sig-finance-bounces at r-project.org> on behalf of Brian G. Peterson <brian at braverock.com>
> Sent: Saturday, March 12, 2016 8:38 PM
> To: r-sig-finance at r-project.org
> Subject: Re: [R-SIG-Finance] Solver for a generic optimal portfolio
>
> On 03/12/2016 07:30 PM, Alec Schmidt wrote:
>> I'd like to estimate weights of an optimal portfolio other than min
>> variance portfolio by replacing covariance matrix with something
>> else. Is there an R package that can do this (my understanding is
>> that solve.QP is not helpful for this task).
>
> Alec,
>
> You'll need to be a little more specific about what your target
> objectives and constraints are if someone is going to be able to help you.
>
> For some objectives and constraints, quadratic, linear, or conical
> solvers can be used.  For other objective and constraint combinations,
> you'll need a global stochastic solver.
>
> Without understanding precisely what you're trying to do, no one can
> give you an answer about which package(s) will be best for your problem.
>
> I can say that I think of any portfolio formulation I can come up with
> may be solved with R.
>
> Regards,
>
> Brian
>
> --
> Brian G. Peterson
> http://braverock.com/brian/
> Ph: 773-459-4973
> IM: bgpbraverock
>
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-- 
Brian G. Peterson
http://braverock.com/brian/
Ph: 773-459-4973
IM: bgpbraverock