Hi All, i'm testing the FF Three Factor model in the italian stock market. In my regressions i found that 3 out of 16 portfolios have alphas statistically different from 0 but at the same time the GRS test has a p-value of 0.17 not rejecting the null hypothesis that all alphas are jointly equal to 0. HOW IS IT POSSIBLE? MAYBE THIS IS DUE TO THE SMALL SAMPLE SIZE (96 OBS) ? ANY HINT OR PAPER ON THIS ARGUMENT ?
Thank You in advance
Hi Nstale Muriana
I expecte that the sample size is quite but I thought there are some problemes in your model suc as multiculanertiy and non homogeniaty that effecting badly in estimation of good equation of your model.
Hi Nstale Muriana
I expecte that the sample size is quite but I thought there are some problemes in your model suc as multiculanertiy and non homogeniaty that effecting badly in estimation of good equation of your model.
I am not sure to understand your problem. If you mean that individual tests for testing alpha_i = 0 (i = 1,...,13) lead to 3 rejections out of 13 of the null hypotheses whereas the global test that the same alpha_i are all equal to 0 (i = 1, ..., 13) leads to acceptance of the null hypothesis (at the same probability level, I suppose), this is not at all surprising. The contrary would be surprising. If an event has probability 0.17 to occur, on 13 independent trials, you would have on average 13 x 0.17 = 2.21occurences of the event. Of course that reasoning assumes that the samples (the portfolios in your case) are independent, which is very approximative.
Thank You Abbas Lafta Kneehr ...i have problems with normality of error terms and a bit of heteroskedasticity.. but i used also the GMM method and my results didn't differ significantly.
Thank You Guy Mélard , Yes that's exactly what i meant. Anyway the other stranger thing is that adj R-squared is about 67%...do you think is this compatible with the results of grs test?
Thank You in advance
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