       Re: Portfolio Optimization

• To: mathgroup at smc.vnet.net
• Subject: [mg119415] Re: Portfolio Optimization
• From: Oliver Ruebenkoenig <ruebenko at wolfram.com>
• Date: Thu, 2 Jun 2011 19:10:00 -0400 (EDT)

```On Thu, 2 Jun 2011, 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.

NMinimize[
Flatten[{weights.Covariants.Transpose[weights],
w1 + w2 + w3 == 1}], {w1, w2, w3}]
{0.00032759616739344176`, {w1 -> 0.3091024300341592`,
w2 -> 0.6596534907972391`, w3 -> 0.031244079168601693`}}

>
> Does anyone know why Mathematica is giving me the wrong answer? And, why is
> it saying the funcion value is not a number?

Because {{0.00408844}} is not a number, 0.00408844 is.

Hope this helps.

Oliver

>