Using a Correlation Matrix to reduce risk

*To*: mathgroup at smc.vnet.net*Subject*: [mg114366] Using a Correlation Matrix to reduce risk*From*: Garapata <warsaw95826 at mypacks.net>*Date*: Thu, 2 Dec 2010 05:39:56 -0500 (EST)

I have a problem for school and hoped someone could assist me. I have price data on 5 stocks and calculate a correlation matrix: cMatrix = Correlation[data] {{1.,0.635562,0.698852,0.404792,-0.32746}, {0.635562,1.,0.410075,0.314375,-0.0636438}, {0.698852,0.410075,1.,0.374416,-0.260137}, {0.404792,0.314375,0.374416,1.,0.293135}, {-0.32746,-0.0636438,-0.260137,0.293135,1.}} cMatrix //TableForm 1.000000 0.635562 0.698852 0.404792 -0.32746 0.635562 1.000000 0.410075 0.314375 -0.0636438 0.698852 0.410075 1.000000 0.374416 -0.260137 0.404792 0.314375 0.374416 1.000000 0.293135 -0.32746 -0.0636438 -0.260137 0.293135 1.000000 Now I want to construct a portfolio of the 5 stocks that minimizes its correlation or concentration risk. It's easy to understand this if for instance I had just 3 stocks, with 2 of them having correlations of 1 (100%) and the third at 0, I think it's matrix would look like this: {{1,1,0},{1,1,0},{0,0,1}} Than it would make sense to put 25% in each of the 2 correlated stocks and 50% in the uncorrelated one. This offsets the risk of concentrating in correlated instruments. But I can not think of how to use the correlation matrix to do this (especially for the 5 instruments). I keep searching for a solution on the internet and at the library but can not find a specific discussion on this. I hope someone can help or point me in the right direction. Thank you. G