6. Factor spanning regressions

Factor spanning regressions are a means to test if an explanatory factor can be explained by a combination of other explanatory factors. Spanning tests are performed by regressing returns of one factor against the returns of all other factors and analysing the intercepts from that regression.

Table 4 shows regressions for the 5F-FF model's explanatory variables, where four factors explain returns on the fifth. In the RM-Rf regressions, the intercept is not statistically significant (t = 0.55). Regressions to explain HML, RMW and CMA factors are strongly positive. However, regressions to explain SMB show insignificant intercept, with intercept of 0.27% (t = 1.34). These results suggest that removing either the RM-Rf or SMB factor would not hurt the mean-variance-efficient tangency portfolio produced by combining the remaining four factors.


RM-Rf is the equal-weighted return on BIST-100 Index minus the 3-month Tryribor rate. SMB is the size factor, HML is the value factor, RMW is the profitability factor, and CMA is the investment factor. The factors are constructed using individual sorts of stocks into two size groups and three B/M groups, three OP groups or three Inv groups. Bolded and shaded t-statistics indicate the significance at the 5% level.

Table 4. Factor spanning regressions on five factors: spanning regressions using four factors to explain average returns on the fifth (June 2000–May 2017, 204 months).
