A factor model can explain a fund's returns convincingly while being unable to say whether its exposure came from value, quality, or a correlated sector tilt. When factor columns move together, OLS has little variation with which to separate their individual effects. This note turns that ambiguity into a quantitative diagnosis: distinguish exact from near multicollinearity, derive the variance inflation factor (VIF), and read the resulting wide confidence intervals without mistaking them for evidence that the factors have no joint explanatory power.
The practical payoff is a disciplined response. Near multicollinearity inflates but does not, by itself, bias OLS or necessarily damage in-sample prediction. A high VIF is a warning about the estimand and the available design, not an instruction to remove whichever factor has the least flattering -statistic. The next diagnostic question is whether the research objective is interpretable factor attribution, a joint hypothesis, or stable prediction.
Learning objectives. By the end of this note you should be able to:
- distinguish perfect from near multicollinearity and state what each does to OLS;
- derive the VIF form of from an auxiliary regression;
- calculate and interpret VIFs and a condition number as complementary diagnostics;
- explain why insignificant individual factors can coexist with a significant factor model and useful predictions;
- choose a response based on the economic estimand rather than by chasing individual significance.
In this lesson
- Collinearity is a lack of independent variation
- Why coefficient variance inflates
- Diagnosing a correlated factor set
- Inference, prediction, and the wrong fixes
Before you start
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