Re: Portfolio Optimization
- To: mathgroup at smc.vnet.net
- Subject: [mg119432] Re: Portfolio Optimization
- From: Albert Retey <awnl at gmx-topmail.de>
- Date: Thu, 2 Jun 2011 19:13:04 -0400 (EDT)
- References: <is7rfr$rhe$1@smc.vnet.net>
Am 02.06.2011 13:17, schrieb Priyan Fernando: > 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? NMinimize wants an expression that evaluates to a number, yours does evaluate to a List of a List, which represents an 1x1 Matrix. This does work and yields the expected results: NMinimize[{(weights.Covariants.Transpose[weights])[[1, 1]], w1 + w2 + w3 == 1}, {w1, w2, w3}] hth, albert