       Re: Portfolio Optimization

• To: mathgroup at smc.vnet.net
• Subject: [mg119422] Re: Portfolio Optimization
• From: Priyan Fernando <priyan.fernando at gmail.com>
• Date: Thu, 2 Jun 2011 19:11:16 -0400 (EDT)

```Many thanks for all your comments!

On 2 June 2011 22:25, Heike Gramberg <heike.gramberg at gmail.com> wrote:

> Mathematica is complaining because the function you are trying to minimize
> returns a
> 1x1 matrix instead of a number. In Mathematica both row vectors and column
> vectors are
> represented as lists, not as 1xn or nx1 matrices, so to get the right
> something like
>
> weights = {w1, w2, w3};
> NMinimize[{weights.Covariants.weights, w1 + w2 + w3 == 1}, {w1, w2, w3}]
>
> which has as output
>
> {0.000327596, {w1 -> 0.309102, w2 -> 0.659653, w3 -> 0.0312441}}
>
> Heike.
>
> On 2 Jun 2011, at 12:17, Priyan Fernando wrote:
>
> > Hi!
> >
> > I am trying to run a portfolio optimizer in Mathematica. That is,
> minimising
> > the variance of a portfolio of assets.
> >
> > (* Variance Covariance Matrix *)
> > Covariants = {{0.000572843, 0.000223023, 0.000109176}, {0.000223023,
> >   0.000387437, 0.0000987402}, {0.000109176, 0.0000987402,
> >   0.007320276}}
> >
> > (* Asset Weights Vector*)
> > weights = Transpose[{{w1}, {w2}, {w3}}]
> >
> > (* Optimize Portfolio Variance*)
> > NMinimize[{weights.Covariants.Transpose[weights],
> >  w1 + w2 + w3 == 1}, {w1, w2, w3}]
> >
> > The output Mathematica throws is as follows:
> > *NMinimize::nnum: "The function value {{0.00408844}} is not a number at
> > {w1,w2,w3} = {-0.63531,0.918621,0.716689}. "*
> >
> > However if I program the same optimization in Excel (using Solver to find
> > optimal weights) I see the weights should be {0.309102831, 0.659653054,
> > 0.031244115} as this gives a lower portoflio variance of 0.0003276.
> >
> > Does anyone know why Mathematica is giving me the wrong answer? And, why
> is
> > it saying the funcion value is not a number?
> >
> > Priyan.
> >
> >
>
>

--
Thanks and Regards,
Priyan Fernando

Mob. +94 772 622 368

```

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