Country versus sector factors in equity returns: The roles of non-unit exposures

In this paper we disentangle, analytically and empirically, the roles of the unit-exposure restriction in Heston and Rouwenhorst (1994). We show that if the purpose is to construct factors, the unit-exposure variance-analysis model can be viewed as just an algorithm that does not really assume a return-generating process; and in practice the effect of relaxing the restriction is immaterial. The restriction is more important if one wants to estimate whether, for a typical stock, the country factor generates more variance than the sector factor: exposure estimation becomes more important (i) the further the average exposures are from unity; or (ii) the higher the dispersion of the exposures. With respect to (i), the more important the corrections for sector (or geographical) structure in country (or sector) factors are, the more the average exposure falls below unity. Thus, the average exposure provides an alternative indicator of the importance of country versus sector effects. We empirically find that the average sector exposure is low (0.3) compared to the average country exposure (0.9). With respect to (ii) we correct the dispersion of exposures for estimation error in the exposures. We find that in our sample these estimation error corrections are more important for sector factors than for country factors, and that country factors are generating far more variance, in a typical stock's return, than do sector factors.