CFA Level II ExamQuantitative MethodsMedium
A researcher is using a simple linear regression to model stock returns (dependent variable) based on the market risk premium (independent variable). The estimated regression equation is given by: Return = 0.005 + 1.2 * Market Risk Premium. The researcher suspects that there might be heteroskedasticity in the model's error terms. Which of the following statements about the consequences of heteroskedasticity is most accurate?
- AThe standard errors of the coefficients will be unreliable, affecting hypothesis tests.
- BThe R-squared value will be artificially inflated.
- CThe estimated slope coefficient (1.2) will be biased.
- DThe model will exhibit perfect multicollinearity.
Show answer & explanationAnswer & explanation
Correct answer: A. The standard errors of the coefficients will be unreliable, affecting hypothesis tests.
Heteroskedasticity means the variance of the error terms is not constant across observations. While it does not bias the OLS coefficient estimates themselves, it makes their standard errors incorrect, which in turn invalidates hypothesis tests (t-tests) and confidence intervals. The estimated coefficients are still unbiased and consistent, but inefficient.
Why the other options are wrong
- B. Heteroskedasticity does not directly inflate the R-squared value. R-squared is a measure of model fit and is not fundamentally altered by non-constant error variance.
- C. Heteroskedasticity does not cause the OLS coefficient estimates to be biased. They remain unbiased and consistent, though inefficient.
- D. Heteroskedasticity is unrelated to multicollinearity. Multicollinearity refers to high correlation among independent variables, while heteroskedasticity refers to the non-constant variance of the error terms.
Consequences of Heteroskedasticity
Heteroskedasticity (non-constant error variance) in linear regression primarily affects the reliability of hypothesis tests and confidence intervals because it leads to incorrect standard errors of the estimated coefficients.
- OLS coefficient estimates remain unbiased and consistent.
- OLS coefficient estimates become inefficient (not minimum variance).
- Standard errors are biased, invalidating t-tests and F-tests.
- R-squared is not directly affected, but predictions can be less precise.
Memory trick: Uneven errors make your tests unreliable.