I am trying to test if the intercepts of two linear regression (CAPM) differ significantly or not. I have 2 fund's monthly return in the same period and regress them on the same market variable (MKT = Rm-Rf). The regression results seem pretty normal.
Now, I have 2 different intercepts. I want to test whether the intercepts differ significantly, so I create a time-series of differences between fund C and fund S (Rd = Rc - Rs) for each time period and then regress it against a market variable MKT. But the result of the regression seems strange.
The R-squared is only 0.0006 compared to the 0.8 - 0.9 of two funds above.
So, I wonder if the test method is correct and the result is reliable or not. If this method is wrong, could you recommend the right method and some related-paper for me to study?