       Re: Portfolio Optimization

• To: mathgroup at smc.vnet.net
• Subject: [mg119421] Re: Portfolio Optimization
• From: Heike Gramberg <heike.gramberg at gmail.com>
• Date: Thu, 2 Jun 2011 19:11:05 -0400 (EDT)

```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 answer you can do 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?
>