Re: Using a Correlation Matrix to reduce risk

*To*: mathgroup at smc.vnet.net*Subject*: [mg114408] Re: Using a Correlation Matrix to reduce risk*From*: Andreas <aagas at ix.netcom.com>*Date*: Fri, 3 Dec 2010 05:22:29 -0500 (EST)*References*: <id7t4n$l8c$1@smc.vnet.net>

More clarification than answer, but if I follow you, you've set up an interesting problem. It seems you want to always have positions in the same set of stocks, but adjust the size of the positions relative to correlation or concentration risk. Sort of efficient frontier without an assumption about future performance for the pieces. So, if you had a correlation matrix for 4 equities that looked like this: {{1,1,1,0},{1,1,1,0},{1,1,1,0},{0,0,0,1}} I think you'd want your portfolio to have the following proportions: {1/6, 1/6, 1/6, 1/2} This distributes half the value of the portfolio across the 3 things with correlations of 1 and 1/2 in the uncorrelated one. Does this idea describe what you want to do with your more complicated cMatrix? No time to think through a solution to this now, but maybe a couple of ideas can help put you or someone else on the right track. You might look at applying Factor Analysis to this problem or perhaps the related PrincipalComponents[] function from the MultiVariateStatistics package. It seems like you want to rank the absolute correlations (not exactly certain what that means) of the stocks. You may be able to apply Factor Analysis iteratively, finding first the 2 most correlated instruments than plugging those 2 as a single instrument and rerunning it, than doing it again and again to work through all the instruments to establish the rank. Someone with a better idea of MultiVariateStatistics probably has a more elegant way to do this. I'll think more about it.