FRM Part I · FRM Exam Part I · Regression Diagnostics
An analyst regresses a fund's returns on two highly correlated factors. The standard error of the coefficient on factor 1 is 0.30 when factor 2 is included. If the two factors were uncorrelated, the VIF would be 1. Given that the actual VIF for factor 1 is 16, what would the standard error be, all else equal, with uncorrelated factors?
The standard error would be 0.075. Variance is inflated by the VIF, so the standard error is inflated by its square root. With a VIF of 16 the inflation factor is 4, so removing the collinearity gives 0.30 divided by 4, equal to 0.075.
- A0.019
- B0.075Correct
- C0.300
- D4.800
Explanation
Variance scales with VIF, so standard error scales with the square root of VIF. sqrt(16) = 4, so the standard error would be 0.30/4 = 0.075. Dividing by 16 gives 0.019, which wrongly treats VIF as scaling the standard error directly. 4.8 multiplies instead of dividing.
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