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Re: Using a Correlation Matrix to reduce risk Options
*To*: mathgroup at smc.vnet.net
*Subject*: [mg114671] Re: Using a Correlation Matrix to reduce risk Options
*From*: Dana DeLouis <dana.del at gmail.com>
*Date*: Sun, 12 Dec 2010 05:45:55 -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.
Hi. This is not a solution to your portfolio question, as the =
correlations have negative values.
However, perhaps for your simple example:
m = {{1, 1, 0}, {1, 1, 0}, {0, 0, 1}};
Tr /@ PseudoInverse[m]
{1/2, 1/2, 1}
%/Tr[%]
{1/4, 1/4, 1/2}
Another example given in the thread:
m = {{1, 1, 1, 0}, {1, 1, 1, 0}, {1, 1, 1, 0}, {0, 0, 0, 1}};
Tr /@ PseudoInverse[m]
{1/3, 1/3, 1/3, 1}
%/Tr[%]
{1/6, 1/6, 1/6, 1/2}
= = = = = = = = = =
HTH : >)
Dana DeLouis
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