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