       Re: Portfolio Optimization

• To: mathgroup at smc.vnet.net
• Subject: [mg119432] Re: Portfolio Optimization
• From: Albert Retey <awnl at gmx-topmail.de>
• Date: Thu, 2 Jun 2011 19:13:04 -0400 (EDT)
• References: <is7rfr\$rhe\$1@smc.vnet.net>

```Am 02.06.2011 13:17, schrieb Priyan Fernando:
> 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?

NMinimize wants an expression that evaluates to a number, yours does
evaluate to a List of a List, which represents an 1x1 Matrix. This does
work and yields the expected results:

NMinimize[{(weights.Covariants.Transpose[weights])[[1, 1]],
w1 + w2 + w3 == 1}, {w1, w2, w3}]

hth,

albert

```

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