Portfolio Optimization

• To: mathgroup at smc.vnet.net
• Subject: [mg119414] Portfolio Optimization
• From: Priyan Fernando <priyan.fernando at gmail.com>
• Date: Thu, 2 Jun 2011 07:17:22 -0400 (EDT)

```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?