When do characteristics-sorted factors mechanically explain returns?

► Sorting and differencing create a mechanical regression fit. ► Characteristic-sorted factors fit well the portfolios sorted on that characteristic. ► Size and value factors do not fit well the portfolios not sorted on size and value. This paper demonstrates that the factors based on typical procedures that employ sorting by characteristics (including size and book-to-market, among others) can create a good mechanical fit in the regressions of portfolio returns. Such factors are approximately linear functions of the sorted portfolios, and including them into regressions adds linear restrictions on the intercepts. These restrictions mechanically reduce significance of the time-series regression intercepts, increase the regression R2, and lead to a good fit in the cross-sectional regressions. Our simulation evidence confirms these propositions. Moreover, we show that popular size and value factors do not “work” in the sets of asset portfolios, which they are not mechanically related to. These results cast doubt on the interpretation of characteristics-sorted factors as the true risk factors.