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? > > Thanks for your all your comments, > Priyan. > >