Re: Portfolio Optimization

*To*: mathgroup at smc.vnet.net*Subject*: [mg119422] Re: Portfolio Optimization*From*: Priyan Fernando <priyan.fernando at gmail.com>*Date*: Thu, 2 Jun 2011 19:11:16 -0400 (EDT)

Many thanks for all your comments! On 2 June 2011 22:25, Heike Gramberg <heike.gramberg at gmail.com> wrote: > 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. > > > > > > -- Thanks and Regards, Priyan Fernando Mob. +94 772 622 368