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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


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