  Firms having similar business activities are correlated. We analyze two
different cross-correlation matrices C constructed from (i) 30-min price
fluctuations of 1000 US stocks for the 2-year period 1994-95 and (ii) 1-day
price fluctuations of 422 US stocks for the 35-year period 1962-96. We find
that the eigenvectors of C corresponding to the largest eigenvalues allow us to
partition the set of all stocks into distinct subsets. These subsets are
similar to conventionally-identified business sectors, and are stable for
extended periods of time. Using a set of coupled stochastic differential
equations, we argue how correlations between stocks might arise. Finally, we
demonstrate that the sectors we identify are useful for the practical goal of
finding an investment which earns a given return without exposure to
unnecessary risk.
