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A Question of Theory



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If one were to try to take a group of stocks and correlate that group of
stocks to an index, mathematically how would you do it?  I know how to
correlate one stock to an index but how do you correlate a bunch of stocks
to an index? I am assuming that you would have to create an pseudo-index out
of the stocks  then correlate that result  to the existing index to see if
you have a match.  Is there any mathematical way to accomplish the same task
so as to avoid minimize the trial and error process?
I know the simple theory would be to just look at the stocks in the existing
index but my goal is to look for a combination of more volatile stocks which
correlate to a given index

TIA
Chris