[R-SIG-Finance] Genetic Algorithms & Portfolio Optimization

ArdiaD david.ardia at unifr.ch
Sun Jan 23 23:32:40 CET 2011

This might be of interest:

On 01/23/2011 11:23 PM, Ulrich Staudinger wrote:
> Lui,
> you can also have a look at
> http://aqr.activequant.org/index.php/2010/08/genetically-optimizing-a-trading-system/for
> inspiration on how to genetically optimize a trading system, whether
> it's quadratic or not. It's just some snipplet but exemplifies it pretty
> well ...
> Regards,
> Ulrich
> On Sun, Jan 23, 2011 at 11:15 PM, Guillaume Yziquel <
> guillaume.yziquel at citycable.ch> wrote:
>> Le Sunday 23 Jan 2011 à 15:56:40 (-0600), Brian G. Peterson a écrit :
>>> On Saturday, January 22, 2011 04:33:09 pm Lui ## wrote:
>>>> Dear group,
>>>> I was just wondering whether some of you have some experience with the
>>>> package "rgenoud" which does provide genetic algorithms for complex
>>>> optimization problems.
>>> <...>
>>>> What is your general experience? Did you ever try solving the
>>>> Markowitz portfolio with the rgenoud package?
>>>> I know that there are good solvers around for the qudratic programming
>>>> problem of the markowitz portfolio, but I want to go into a different
>>>> direction which translates into a quadratic problem with quadratic
>>>> constraints (and I havent found a good solver for that...).
>>>> I am interested in your replies! Have a good weekend!
>>> As others have already said, for a quadtratic problem with quadratic
>>> constraints, there is an exact analytical solution.
>> I wouldn't qualify dual interior point methods as an "exact" solution, but,
>> yes, that's the basic idea: they're better suited for that.
>>> In these cases, you will be much better off both from a performance and
>>> accuracy perspective in using a quadratic solver (quadprog is most often
>>> applied in R, see list archives and many packages for examples).
>> Is quadprog a second-order cone programming solver? If that is the case,
>> yes, it probably solves quadratic objective function with quadratic
>> constraints faster and with more accuracy than a full-fledged SDP
>> solver.
>>> Other portfolio problems may be stated in terms of linear solvers, which
>> will
>>> likewise be faster than a global optimizer for finding an exact
>> analytical
>>> solution.
>>> If, however, your portfolio problem is non-convex and non-smooth, then a
>>> genetic algorithm, a migration algorithm, grid search, or random
>> portfolios
>>> may be a good option for finding a near-optimal portfolio.  If this is
>> your
>>> true goal, perhaps you can say a little more about your actual
>> constraints and
>>> objectives (and use assets that are outside of your true area of
>> interest,
>>> such as the S&P sector indices).
>> Yes, the problem structure often gives good insight as to which method
>> to apply. It may be noted, however, that quite a lot of non-convex
>> problems may be transformed into convex ones. And using some relaxation
>> methods, you can often use SDPs to optimise multivariate polynomial
>> objective under multivariate polynomial constraints, without too many
>> convexity hypothesis.
>> SDPs are not always easy to manipulate, but they do solve a broad range
>> of optimisation problems.
>>> Regards,
>>>   - Brian
>> Best regards,
>> --
>>     Guillaume Yziquel
>> http://yziquel.homelinux.org
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