Before revision:  As an application of the random factor model , we analyze reproduction of correlation coefficients in the well-diversified Russell 3,000 equity index using the random factor model. Comparison with the principal component analysis (PCA) shows that the random factor model requires significantly fewer factors to provide an equally accurate reproduction of correlation coefficients. This occurs despite the finding that PCA reproduces single equity return time-series more faithfully than the random factor model. Accuracy of a random factor model is not very sensitive to which particular set of randomly-chosen factors is used. A more general kind of universality of random factor models is also present: it does not much matter which particular method is used to construct the random factor model, accuracy of the resulting factor model is almost identical .
After revision:  As an application of the random factor model , we analyze reproduction of correlation coefficients in the well-diversified Russell 3,000 equity index .