Bread-basket of stocks as proxy for index

[Paul <paltman@xxxxxxxxxxx>]

Folks:

I need to understand what logical reasoning is used to concoct a bread
basket of stocks as a proxy for an stock index.

Let's suppose that I have an index of 100 stocks, but no convenient
derivatives are traded on it.

I want to create a bread basket of 8 stocks that optimally correlate with
the index, and then to trade those 8 stocks.  How is this done?    IOW, how
do I choose the stocks from a known universe of potential candidates (some
of which may not even be in the index), and choose weightings such that
I've optimally represented the daily moves of the index?

I'll guess that there's an elegant stats solution to this, other than an
ugly brute force one like having a computer crunch out a zillion random
weightings and taking the best one.

BTW, is it possible that some of the candidates with the worst
correlations, will take on magical properties when properly combined with
other poor performers?  I.e., is it even theoretically possible to get
great correlation with the index from a mix of candidates that, by
themselves, may have terrible correlation?

Hope I've phrased the question precisely enough.  I'm pretty fuzzy about
where to get started with this, though I'll bet it's done all the time by
the big brokerage firms in their program trading and index arbitrage.

Thanks for any help.

	-Paul