Re: Portfolio Optimization

*To*: mathgroup at smc.vnet.net*Subject*: [mg119416] Re: Portfolio Optimization*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Thu, 2 Jun 2011 19:10:10 -0400 (EDT)

Covariants = { {0.000572843, 0.000223023, 0.000109176}, {0.000223023, 0.000387437, 0.0000987402}, {0.000109176, 0.0000987402, 0.007320276}}; weights = Transpose[{{w1}, {w2}, {w3}}]; {{w1, w2, w3}} As the error message stated, weights.Covariants.Transpose[weights] is not a number weights.Covariants.Transpose[weights] {{w2 (0.000223023 w1 + 0.000387437 w2 + 0.0000987402 w3) + w1 (0.000572843 w1 + 0.000223023 w2 + 0.000109176 w3) + (0.000109176 w1 + 0.0000987402 w2 + 0.00732028 w3) w3}} Use Part NMinimize[{ (weights.Covariants.Transpose[weights])[[1, 1]], w1 + w2 + w3 == 1}, {w1, w2, w3}] {0.000327596, {w1 -> 0.309102, w2 -> 0.659653, w3 -> 0.0312441}} Bob Hanlon ---- Priyan Fernando <priyan.fernando at gmail.com> 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.