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

[Alec Schmidt]

Brian, 
My goals are still very fluid. As you certainly know, Markowitz theory does not guarantee good diversification, and its out of sample performance is less than perfect. So I just started thinking about other formulations, leaving for now  the same Markowitz constraints: sum of weights is unity, mean portfolio return is given; also all weights are positive. Does this make sense?

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 9:00 PM
To: r-sig-finance at r-project.org
Subject: Re: [R-SIG-Finance] Solver for a generic optimal portfolio

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

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