For my thesis I am evaluating two mutual fund portfolios in order to check for differences in manager performance. My hypothesis is that there will be no differences in performance (in terms of alpha) between the two portfolios. Unfortunately even though one group seems to outperform the other all alphas are statistically insignificant. Do I reject the hypothesis (because one outperforms the other) or accept the hypothesis (because none of the alphas are signficant)? Thanks in advance
Given that you're correctly measuring Alpha, the difference lies in the Beta exposures of the two managers. You may not be capturing certain tilts, which would show up in your error or incorrectly categorized as Beta. Consider the simple case where you have returns grouped into just technology vs. Energy for instance.
$R_p$ = $B_0$ + $B_t$$R_m$ + $B_e$$R_m$+ $e$
If there isn't a distinction for cap size, you could have large cap energy firms significantly outperform small cap energy, but wouldn't know it from the regression. Make sure you're correctly benchmarking returns before concluding insignificant alpha.