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FRM Part I · FRM Exam Part I · Hypothesis Testing

In a simple linear regression of a stock's excess returns on market excess returns using 32 observations, the estimated slope is 0.85 with a standard error of 0.30. A risk manager tests H0: beta = 1 against a two-sided alternative at the 5% level (critical t with 30 degrees of freedom is 2.042). Which statement is correct?

The t-statistic is -0.50, calculated as (0.85 - 1)/0.30. Its absolute value is below the critical value of 2.042 with 30 degrees of freedom, so the null hypothesis that beta equals 1 is not rejected at the 5% level.

  1. At = -0.50; do not reject H0 because |t| is below 2.042Correct
  2. Bt = 2.83; reject H0 because |t| exceeds 2.042
  3. Ct = -0.50; reject H0 because the t-statistic is negative
  4. Dt = -0.15; do not reject H0 because the slope is below 1

Explanation

The statistic is (0.85 - 1)/0.30 = -0.50. Its absolute value is well below 2.042, so H0 is not rejected. The value 2.83 (0.85/0.30) tests beta = 0, not beta = 1. The sign of t does not determine rejection in a two-sided test.

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