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.