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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