We find a novel correlation structure in the residual noise of stock market
returns that is remarkably linked to the composition and stability of the top
few significant factors driving the returns, and moreover indicates that the
noise band is composed of multiple subbands that do not fully mix. Our findings
allow us to construct effective generalized random matrix theory market models
that are closely related to correlation and eigenvector clustering. We show how
to use these models in a simulation that incorporates heavy tails.