[R-SIG-Finance] parma - How to optimize a long/short portfolio with sum( abs( weights )) = 1

[alexios ghalanos]

Dear Uwe,

1. DEoptim is a nonlinear global optimization solver. Global
optimization is usually reserved for hard to solve non-convex
problems with many local minima. There is no guarantee of
optimality not even for convex problems, nor any idea of
whether the answer you are getting is anything other than a local optimum.

2. The parma package was designed to solve linear and convex
optimization problems confidently (which is why all NLP problems use
analytic derivatives for the functions and contraints), and for problems
with non-smooth functionals or constraints, smooth equivalents with very
high accuracy were developed.

3. The fact that your covariance matrix is not positive definite (and we
already saw how highly correlated some of the data were previously)
points to a fundamental problem in your approach to solving the problem
and I very much fear that finding a way to force a solution this way
will only give you trouble going forward...but who knows? For some of
the time, in some of the cases you might get Garbage In->Magic Out.

Best,

Alexios

On 21/08/2014 22:49, u0055 at wolke7.net wrote:
> Dear R-SIGs,
> 
> I'm very happy of finding the package
> http://cran.r-project.org/web/packages/DEoptim
> for portfolio optimization.
> A very cool document is this:
> http://cran.r-project.org/web/packages/DEoptim/vignettes/DEoptimPortfolioOptimization.pdf
> 
> 
> For all my difficult input matrices of return values
> I got solutions with "DEoptim":
> - long/short portfolios
> - easy adding constraints, e.g:
>   sum( abs( weights )) = 1 and/or
>   sum( weights ) = 0
> - no problems with "positive definite"
> 
> The only disadvantage is maybe,
> that the solutions are only approximations.
> This is because of the different approach,
> as pointed out in the vignette documents ...
> 
> Best,
> Uwe
> 
>