Firm characteristics help estimate conditional factor loadings. Larger libraries contain new and
overlapping information. We use the cross-sectional distribution of firm characteristics as a ruler to
evaluate IPCA loading spaces. With factor counts fixed, expanding from 36 to 153 characteristics
can improve in-sample fit while representing momentum and size positions less fully. Reallocating
shared exposures changes attribution without changing joint fitted returns. With coefficients fixed,
exposure references alter holdings, trading, and subsequent risk at the same characteristic target.
Statistical factor models should be evaluated not only by return fit, but also by the exposures they
represent and the investment decisions they support.
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