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