       Re: Portfolio Optimization

• To: mathgroup at smc.vnet.net
• Subject: [mg119447] Re: Portfolio Optimization
• From: Gregory Lypny <gregory.lypny at videotron.ca>
• Date: Sat, 4 Jun 2011 06:20:36 -0400 (EDT)

```Hi Priyan,

You don't need to do numerical optimization because there is an exact analytical solution.  Let me know if you'd like the script.

Gregory

> 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?
>