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FRM Part I · FRM Exam Part I · Linear Regression

In a simple linear regression of a fund's excess return on the market's excess return using 60 monthly observations, the estimated slope is 1.20 with a standard error of 0.40. Using the t-test at the 5% significance level (critical value approximately 2.00 for 58 degrees of freedom), what is the test of H0: slope = 0 and its conclusion?

The t-statistic is 1.20 divided by 0.40, which equals 3.00. Because this exceeds the critical value of about 2.00, the null hypothesis that the slope is zero is rejected at the 5% level, so the market return significantly explains the fund's return.

  1. At = 3.00; reject the nullCorrect
  2. Bt = 0.33; fail to reject the null
  3. Ct = 3.00; fail to reject the null
  4. Dt = 1.50; fail to reject the null

Explanation

t = (1.20 - 0)/0.40 = 3.00. This exceeds the critical value of 2.00, so the null is rejected. The value 0.33 comes from inverting the ratio (SE divided by estimate), and 1.50 comes from using 0.60 as if it were the standard error.

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