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FRM Part I · FRM Exam Part I · Regression Diagnostics

An analyst regresses monthly excess returns of a fund on market excess returns and finds that the residual variance is clearly larger in months when market volatility is high. Which statement best describes the consequence for ordinary least squares (OLS) estimates?

Non-constant residual variance is heteroskedasticity. OLS coefficients remain unbiased and consistent, but the conventional standard errors are wrong, so t-statistics and confidence intervals can mislead. Using heteroskedasticity-robust standard errors fixes the inference problem without changing the coefficient estimates.

  1. ACoefficient estimates are biased and inconsistent, but the standard errors are correct
  2. BCoefficient estimates remain unbiased, but the usual standard errors are unreliable, so t-tests may be misleadingCorrect
  3. CCoefficient estimates remain unbiased and the usual standard errors remain valid, so no correction is needed
  4. DThe R-squared becomes negative and the model cannot be interpreted

Explanation

Residual variance that changes with the level of a regressor is heteroskedasticity. It does not violate the zero conditional mean assumption, so OLS coefficients stay unbiased and consistent. The usual standard error formula assumes constant variance, so it is unreliable and t-tests can mislead. Robust (White) standard errors address this.

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