To test whether small-cap stocks perform worse than large stocks under the Fama-French three-factor model, you set up the following hypothesis:
Ho: Expected excess returns of small stocks = 0
H1: Expected excess returns of small stocks < 0
The excess returns are returns adjusted for risk using the Fama-French three-factor model. In this setup, which of the following is/are true?
I. You must employ a right-tailed test.
II. The rejection region for the z-statistic on the excess return extends from negative infinity to the critical value associated with the significance level.
III. It is harder to reject the null than in the case where the alternative is specified as H1: Excess returns are non-zero.
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A. B. C. D. E.A
Since the rejection region for the null is to the left of the maintained null value of zero, you must employ a left-tailed test. In that case, the rejection region for the z- statistic on the excess return extends from negative infinity to the critical value associated with the significance level. Also note that it is harder to reject the null under a two-tailed test than under a one-tailed test since the critical value for any given significance level is higher (in magnitude) for a two-tailed test.