What are the main applications of PCA in finance?

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AcadiFi · Accepted Answer

Principal Component Analysis (PCA) transforms correlated variables into a smaller set of uncorrelated linear combinations (components) ordered by variance explained. In finance, applications include:

1. Yield curve analysis: decompose daily yield changes across maturities. First three components (level, slope, curvature) typically explain 95%+ of variance. Lets risk managers track bond portfolio exposure along three intuitive axes rather than 30 individual yield points.

2. Equity factor models: decompose return covariance to identify dominant sector or style factors. Useful for building risk-balanced portfolios and estimating tracking error efficiently.

3. Stress testing: historical PCA reveals how assets co-move during crises. Simulating shocks to first few components generates realistic multi-asset scenarios.

4. VaR dimensionality reduction: risk systems with thousands of positions use PCA on correlation matrices to speed up full-revaluation VaR by simulating only principal components.

5. Credit spread modeling: CDS spreads across tenors decompose into market-wide and idiosyncratic components — useful for relative value trading.

6. Commodities: crude curve decomposition identifies front-month, term-structure, and seasonality factors separately.

Example: 10 yield maturities, covariance matrix 10×10. Eigen-decompose to get 10 eigenvectors and eigenvalues. Sort eigenvalues descending — λ₁/Σλᵢ = 78% (level), λ₂/Σλᵢ = 15% (slope), λ₃/Σλᵢ = 4% (curvature). Keep three components, discard 7 that collectively explain 3% of variance.

```mermaid
flowchart TD
    A[Original Data] --> B[Covariance Matrix]
    B --> C[Eigendecomposition]
    C --> D[Sort by Variance]
    D --> E[Keep Top K]
```

What are the main applications of PCA in finance?

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