FRM Part I · FRM Exam Part I · Regression Diagnostics
In a multiple regression of monthly fund excess returns on three risk factors, an analyst finds that two of the explanatory variables have a sample correlation of 0.97. Which of the following is the most likely consequence for the OLS estimates?
Near-perfect correlation between two regressors leaves OLS estimates unbiased but inflates their standard errors. Individual t-statistics become small and unreliable even though the overall fit, such as R-squared and the F-test, can remain strong. Multicollinearity does not cause bias or serial correlation.
- AThe OLS coefficient estimates become biased, though their standard errors stay unchanged
- BThe coefficient estimates remain unbiased but their standard errors are inflated, making individual t-statistics unreliableCorrect
- CThe residuals become serially correlated, invalidating the F-statistic
- DThe R-squared falls sharply because the regressors duplicate information
Explanation
High but imperfect multicollinearity leaves OLS unbiased and consistent, but it inflates the variance of the affected coefficients, so standard errors rise and t-statistics shrink. Option A is wrong because there is no bias. R-squared is not reduced by collinear regressors, and serial correlation is a separate problem.
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