Groups > comp.soft-sys.math.mathematica > #2895

Portfolio Optimization

From	Priyan Fernando <priyan.fernando@gmail.com>
Newsgroups	comp.soft-sys.math.mathematica
Subject	Portfolio Optimization
Date	2011-06-02 11:17 +0000
Organization	Steven M. Christensen and Associates, Inc and MathTensor, Inc.
Message-ID	<is7rfr$rhe$1@smc.vnet.net> (permalink)

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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?

Thanks for your all your comments,
Priyan.

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Portfolio Optimization Priyan Fernando <priyan.fernando@gmail.com> - 2011-06-02 11:17 +0000
  Re: Portfolio Optimization Albert Retey <awnl@gmx-topmail.de> - 2011-06-02 23:12 +0000

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