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FRM Part I · FRM Exam Part I · Linear Regression

A regression of daily stock return (%) on market return M and a dummy D (1 for post-earnings days, 0 otherwise) over 200 observations gives a D coefficient of 0.45 with standard error 0.20. The critical t-value at 5% two-tailed is about 1.97. The analyst also states that the dummy coefficient shows post-earnings days have a 0.45% higher return than other days. Which conclusion is best?

The coefficient is significant at 5% because t = 0.45/0.20 = 2.25 exceeds 1.97. It means post-earnings days have an average return 0.45 percentage points higher than other days holding the market return fixed, not an unconditional return of 0.45%.

  1. AThe coefficient is insignificant because the t-statistic is 0.44, below 1.97
  2. BThe coefficient is significant at 5% (t = 2.25), and the 0.45% gap is the average difference in return at equal market returnCorrect
  3. CThe coefficient is significant at 5% (t = 2.25), and post-earnings days earn 0.45% regardless of the market return
  4. DThe coefficient is insignificant because the standard error is below 0.45

Explanation

t = 0.45/0.20 = 2.25, which exceeds 1.97, so reject the null of no difference. The coefficient is a ceteris paribus intercept shift, meaning the gap holds at a given market return, not an unconditional return of 0.45%. The 0.44 figure inverts the ratio.

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