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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 the market excess return and a dummy variable D that equals 1 for months in which the VIX is above 25 and 0 otherwise. The model is R = a + b*Mkt + c*D + e, with estimates a = 0.20%, b = 0.90, c = -0.50%. What is the expected fund excess return when the market excess return is 2.0% and VIX is above 25?

The expected excess return is 1.50%. In the high-VIX regime the intercept shifts by the dummy coefficient, so the prediction is 0.20% plus 0.90 times 2.0% minus 0.50%, which equals 1.50%. The slope on the market is unchanged.

  1. A1.50%Correct
  2. B1.80%
  3. C1.50% only if the slope also changes
  4. D2.00%

Explanation

With D = 1: expected return = 0.20 + 0.90*2.0 - 0.50 = 0.20 + 1.80 - 0.50 = 1.50%. The 1.80% option omits the dummy coefficient, and the intercept-only shift means the slope does not change in this model, so the third option is wrong. 2.00% ignores the beta and the dummy.

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