Re: Portfolio Optimization

• To: mathgroup at smc.vnet.net
• Subject: [mg119425] Re: Portfolio Optimization
• From: "Sjoerd C. de Vries" <sjoerd.c.devries at gmail.com>
• Date: Thu, 2 Jun 2011 19:11:48 -0400 (EDT)

```There is no difference between row and column vectors in Mathematica, so you don't need to do a Transpose in order to do  a matrix multiplication. The following works:

In[86]:= (*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 = {w1, w2, w3}

(*Optimize Portfolio Variance*)
NMinimize[{weights.Covariants.weights, w1 + w2 + w3 == 1}, {w1, w2,
w3}]

Out[86]= {{0.000572843, 0.000223023, 0.000109176}, {0.000223023,
0.000387437, 0.0000987402}, {0.000109176, 0.0000987402, 0.00732028}}

Out[87]= {w1, w2, w3}

Out[88]= {0.000327596, {w1 -> 0.309102, w2 -> 0.659653,
w3 -> 0.0312441}}

BTW the NMinimize call could have been written more nicely as:

NMinimize[{weights.Covariants.weights, Total[weights] == 1}, weights]

Cheers-- Sjoerd

```

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