Beta Calculation and Significance Testing in Portfolio Management | Exam Solution

Beta Calculation and Significance Testing

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Question

A portfolio manager has estimated the beta of a stock at 0.8, with a z-statistic of 1.7 in a sample size of 300 observations. At 5% significance level in a two-sided test the critical value is 1.96, therefore, the manager should conclude that:

Answers

A. the null hypothesis of beta = 0 cannot be rejected.

B. the null hypothesis of beta = 0 cannot be accepted.

C. the alternative hypothesis that beta is nonzero should be rejected.

D. the alternative hypothesis that beta is not zero should be accepted.

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Explanations

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A. B. C. D.

Since the z-statistic is less than the critical value of 1.96 in a two-sided test, the null hypothesis that beta = 0 cannot be rejected. Note, however, that this does not imply that beta equals zero. It just says that with the given observations, one cannot conclude that beta is statistically significantly different from zero. This is always the interpretation of the null hypothesis (that's the reason statisticians emphasize that "failing to reject the null hypothesis" is not the same as "accepting the null hypothesis." You should always remember this.) Also note that the nature of the alternative hypothesis is important. If the alternative had been onesided

(beta > 0), then the null would be rejected in this case at the 5% level.

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