FRM Part I · FRM Exam Part I · Machine Learning and Prediction
A bank uses the first three principal components of 12 equity factor returns as regressors in a model to predict portfolio losses (principal components regression). Which is the main drawback of this approach?
The main drawback is that components are selected by how much variance they explain, not by how well they predict the target. A discarded low-variance component could therefore contain useful predictive information for portfolio losses.
- AThe components are correlated with each other, which creates severe multicollinearity
- BThe components are chosen without regard to the target, so a low-variance component that predicts losses well may be discardedCorrect
- CThe approach cannot be used when the original variables are correlated
- DThe regression must include all 12 components or the coefficients are biased
Explanation
PCA is unsupervised: components are ranked by variance explained, not predictive power, so an omitted low-variance component might carry predictive information. Components are uncorrelated by construction, so multicollinearity is not the issue. PCA works best when variables are correlated, and using fewer components is the purpose of the method.
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