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

An analyst regresses a fund's monthly excess return on the market excess return (Model A). She then recognizes that a size factor, which is positively correlated with the market factor, also drives the fund's returns and has a true positive coefficient, but she leaves it out. What is the most likely effect on the estimated market beta in Model A?

The market beta is biased upward. Omitting a relevant variable creates bias equal to its true coefficient times its relationship with the included regressor. With both positive, the bias is positive, so the market beta picks up part of the size factor's effect.

  1. AIt is biased upward, because the omitted variable has a positive coefficient and is positively correlated with the included regressorCorrect
  2. BIt is biased downward, because the omitted variable has a positive coefficient and is positively correlated with the included regressor
  3. CIt is unbiased but has a larger standard error
  4. DIt is unbiased and has a smaller standard error

Explanation

Omitted variable bias in the included coefficient equals the omitted variable's true coefficient times the slope from regressing the omitted variable on the included one. Both are positive here, so the bias is positive. The market beta absorbs part of the size effect. Option C describes heteroskedasticity-type inefficiency, not omitted variable bias.

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