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.

fund1 fund2

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.

Regression of return differences between two funds

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?



1 Answer 1


No, that's right!

One fund has a beta of 81.6% and the other 82.4%, each with a ~90% R^2 to market.

Therefore, it makes total sense that the spread between the two should have almost no correlation to the market (which is your very low mkt co-efficient value, and your very low R^2).

The >90% P-value on the intercept (of the spread) co-efficients does suggest very little confidence either fund would be biased to outperform (in a flat market). That test is fair - you just have to be mindful of what you're testing here.

The very low regressiokn R^2 just says that the market does very little to explain the difference in the two fund's performance. The intercept t/p-tests suggest that neither is reliably better or worse than the other. So what differences you do see between the two are just random noise. Or possibly some weird convoluted non-linear distribution (for which a whole different set of suites exist, but are probably not relevant if these are vanilla funds).

  • $\begingroup$ I am working on a dissertation to see whether the return of socially responsible funds differ from conventional funds. :-) Btw, I also did the Carhart's 4-factor regression which give me a little bit more r-squared (0.0146). This means that adding factors could help improve the ability to explain the difference between two funds (even though no factor is significant)? This is the link to the said result: [link]drive.google.com/file/d/12zEUxIQMEBcaZfO2EzWHjEPEh0IwcwT8/… Thank you in advance! $\endgroup$
    – Fuuka
    Oct 26, 2019 at 17:34

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