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

Patrick Burns patrick at burns-stat.com
Tue Sep 22 20:59:36 CEST 2015

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.


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
twitter: @burnsstat @portfolioprobe

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