FRM Part I · FRM Exam Part I · Regression Diagnostics
An analyst regresses monthly fund returns on the market excess return but leaves out a size factor that is positively correlated with the market excess return. The true coefficient on the size factor is positive. Which statement best describes the likely effect on the estimated market beta?
The market beta is biased upward. The omitted size factor has a positive true effect and is positively correlated with the market excess return, so the included market variable absorbs part of that effect and its coefficient is overstated.
- AIt is biased upward, because the market variable picks up part of the size factor's effectCorrect
- BIt is biased downward, because the omitted factor adds noise to the residuals
- CIt is unbiased, because the omitted factor only affects the intercept
- DIt is unbiased but its standard error is understated
Explanation
Omitted variable bias in the included coefficient has the sign of (true coefficient on the omitted variable) times (correlation between omitted and included variables). Both are positive, so the bias is positive. Option B confuses bias with added noise, which would affect variance rather than the direction of bias.
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