  Factor analysis is a statistical technique employed to evaluate how observed
variables correlate through common factors and unique variables. While it is
often used to analyze price movement in the unstable stock market, it does not
always yield easily interpretable results. In this study, we develop improved
factor models by explicitly incorporating sector information on our studied
stocks. We add eleven sectors of stocks as defined by the IBES, represented by
respective sector-specific factors, to non-specific market factors to revise
the factor model. We then develop an expectation maximization (EM) algorithm to
compute our revised model with 15 years' worth of S&P 500 stocks' daily close
prices. Our results in most sectors show that nearly all of these factor
components have the same sign, consistent with the intuitive idea that stocks
in the same sector tend to rise and fall in coordination over time. Results
obtained by the classic factor model, in contrast, had a homogeneous blend of
positive and negative components. We conclude that results produced by our
sector-based factor model are more interpretable than those produced by the
classic non-sector-based model for at least some stock sectors.
