FRM Part I · FRM Exam Part I · Linear Regression
An analyst regresses monthly fund returns on market returns. The residuals show variance that rises sharply when the market return is large in absolute value, but the residuals have zero mean and are uncorrelated with the market return. What is the consequence for the OLS slope estimate and its conventional standard error?
The slope remains unbiased because the errors are still uncorrelated with the regressor, but heteroskedasticity makes the conventional standard error unreliable. Hypothesis tests and confidence intervals would be misleading, so heteroskedasticity-robust standard errors should be used instead.
- AThe slope is biased, and the standard error is correct
- BThe slope is unbiased, but the conventional standard error is unreliableCorrect
- CThe slope is biased and the standard error is unreliable
- DThe slope is unbiased and the conventional standard error is still valid
Explanation
Heteroskedasticity with E[e|X]=0 leaves OLS unbiased and consistent. However, the usual standard error formula assumes constant variance, so t-tests and confidence intervals are unreliable; robust standard errors are needed. Option 0 wrongly attributes bias to heteroskedasticity.
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