[R-SIG-Finance] Failure of solve.QP in portfolio modeling

[Alexandre Shannon]

Hello Alec

Package "corpcor" has a useful function called "make.positive.definite",
which might help in your particular case.

Alex
On Tue, Sep 22, 2015 at 16:03 Patrick Burns <patrick at burns-stat.com> wrote:

> One correction and another comment.
>
> I should have said that a trade optimizer
> not caring about positive definiteness is
> usually a bad thing -- it has its uses
> but giving the optimizer a shot at a
> portfolio with negative variance is asking
> for trouble (because it will do its best
> to get there).
>
> The estimates of the variance with only a
> few observations are going to be extremely
> noisy.  I think the length of history to
> be used to estimate the variance should
> depend on what length gives the best variance
> estimate and should be independent of the
> rebalancing schedule.  (Though perhaps I
> have misinterpreted the original post.)
>
> Pat
>
> On 22/09/2015 19:59, Patrick Burns wrote:
> > You can use a factor model or shrinkage
> > to get a positive definite variance matrix.
> > There is a function for each in the
> > BurStFin package on CRAN.
> >
> > The optimizer in Portfolio Probe doesn't
> > care about positive definiteness (though
> > that is not always a good thing).  It is
> > free for academic use.
> >
> > Pat
> >
> > On 22/09/2015 14:37, aschmid1 wrote:
> >> Hi everyone,
> >> I'm trying to estimate optimal Markowitz portfolio weights for a list of
> >> stocks chosen upon some criterion using solve.QP from quadprog library.
> >> When the number of stocks N reaches some limit, I get a message "matrix
> >> D in quadratic function is not positive definite." For example, if I
> >> rebalance every 6 weeks (which implies that variance is calculated for
> >> 6-week interval prior to the period for which I calculate portfolio
> >> weights), I can get solution for 25>=N<50. For 12-week interval,
> >> solution exists for 50>=N<100, and for 24-week interval, I can get
> >> solution for N=100. My attempt to remedy this problem with Higham's
> >> method doesn't help. I'll greatly appreciate you input: first, why this
> >> may happen (can there be lack of local minimum?), and second, whether
> >> there are R solvers that may need only semi positive definite matrix.
> >>
> >> Thanks! Alec
> >>
> >> _______________________________________________
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> >
>
> --
> Patrick Burns
> patrick at burns-stat.com
> http://www.burns-stat.com
> http://www.portfolioprobe.com/blog
> twitter: @burnsstat @portfolioprobe
>
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