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FRM Part I · FRM Exam Part I · Hypothesis Testing

In a simple regression of a portfolio's excess returns on market excess returns using 62 observations, the estimated beta is 1.15 with a standard error of 0.10. Testing H0: beta = 1 against a two-sided alternative, the test statistic and conclusion at the 5% level are closest to (critical t with 60 df is about 2.00):

The t statistic is 1.50, found as (1.15 minus 1.00) divided by 0.10. Because it is below the critical value of about 2.00 at the 5% level, the analyst fails to reject that beta equals 1. Using a null of zero would wrongly give 11.5.

  1. At = 1.50; fail to reject H0Correct
  2. Bt = 11.5; reject H0
  3. Ct = 1.50; reject H0
  4. Dt = 0.15; fail to reject H0

Explanation

The null value is 1, not 0, so t = (1.15 - 1)/0.10 = 1.50. This is below the critical value of about 2.00, so H0 is not rejected. The 11.5 figure tests beta = 0, the wrong null.

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