FRM Part I · FRM Exam Part I · Linear Regression
An analyst regresses monthly fund excess returns on market excess returns using 60 observations. A plot of residuals shows their dispersion rising as market excess returns grow in magnitude. Which statement best describes the consequence for the OLS slope estimate?
Rising residual dispersion signals heteroskedasticity. OLS coefficient estimates remain unbiased and consistent if the errors have zero conditional mean, but the conventional standard errors are wrong, so hypothesis tests and confidence intervals are unreliable unless robust standard errors are used.
- AIt remains unbiased, but the usual standard errors are unreliableCorrect
- BIt becomes biased and inconsistent
- CIt remains unbiased and the usual standard errors remain valid
- DIt is no longer linear in Y
Explanation
The pattern indicates heteroskedasticity. Provided the zero conditional mean assumption holds, OLS coefficients stay unbiased and consistent. However, the conventional standard errors are incorrect, so t-tests and confidence intervals are unreliable. Robust standard errors would fix this.
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