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FRM Part I · FRM Exam Part I · Regression with Multiple Explanatory Variables

An analyst regresses monthly excess returns of a fund on three explanatory variables using 64 observations. The estimated coefficient on the value factor is 0.45 with a standard error of 0.15. Testing H0: coefficient = 0 against a two-sided alternative, what is the t-statistic and the degrees of freedom?

The t-statistic is the coefficient divided by its standard error, 0.45/0.15 = 3.00. With 64 observations and three slope coefficients plus an intercept, degrees of freedom are 64 - 3 - 1 = 60.

  1. At = 3.00 with 60 degrees of freedomCorrect
  2. Bt = 3.00 with 63 degrees of freedom
  3. Ct = 0.33 with 60 degrees of freedom
  4. Dt = 3.00 with 64 degrees of freedom

Explanation

t = 0.45/0.15 = 3.00. Degrees of freedom = n - k - 1 = 64 - 3 - 1 = 60 (three slopes plus an intercept). Using 63 or 64 ignores estimated parameters; 0.33 inverts the ratio.

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