How do I interpret factor loadings in practice?

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AcadiFi · Accepted Answer

A factor loading is the correlation between the observed variable and the latent factor. Magnitude above 0.70 is strong, 0.40 to 0.70 moderate...

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Reading rules:

1. Magnitude: |loading| > 0.70 is strong, 0.40-0.70 is moderate, < 0.30 is weak. Many practitioners use 0.40 as the floor for "meaningful loading."

2. Sign: positive means variable moves with factor; negative means opposite. A factor where tech loads +0.8 and utilities load −0.7 represents a growth-vs-defensive axis.

3. Simple structure: ideal factors have each variable loading on exactly one factor. Reality is messier; look for the dominant loading per variable.

Example interpretation (equity returns PCA, 3 rotated factors):

| Stock | F1 | F2 | F3 | Interpretation |
|-------|-----|-----|-----|---------------|
| TechCorp | 0.85 | 0.10 | 0.05 | Tech factor |
| MegaBank | 0.12 | 0.78 | 0.15 | Banking factor |
| UtilityPwr | 0.05 | 0.18 | 0.71 | Utility factor |
| EnergyCo | 0.15 | 0.45 | 0.35 | Mixed — ambiguous |

Naming factors: look for variables with strongest loadings, identify common economic theme. If F1 loads heavily on tech stocks, call it "Technology Growth."

Communality = sum of squared loadings across factors for each variable. Represents proportion of variable's variance explained by the factor model. TechCorp communality = 0.85² + 0.10² + 0.05² = 0.735 — 73.5% of its variance is systematic.

Uniqueness = 1 − communality = specific (idiosyncratic) variance. TechCorp uniqueness = 0.265.

For risk management, high-loading stocks move together — so they don't diversify factor exposure. Portfolio construction balances loadings across multiple factors.

How do I interpret factor loadings in practice?

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