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Quant Project – PCA for Portfolio Risk

Goal: Apply Principal Component Analysis (PCA) to daily returns of 20 large-cap US equities to uncover hidden risk drivers, reduce dimensionality, and evaluate interpretability with Varimax rotation.

Data

  • Assets (20 US large-caps):
    • Technology/Communication: AAPL, MSFT, AMZN, GOOGL, META, NVDA, NFLX
    • Financials/Payments: JPM, GS, V, MA
    • Industrials/Energy: BA, GE, CAT, XOM, CVX
    • Consumer/Other: DIS, IBM, WMT, TSLA
  • Frequency: Daily adjusted closing prices
  • Period: January 2015 – January 2025 (~2,500 observations)
  • Transformations:
    • Returns computed as daily percentage changes
    • Returns standardized (z-scored) for PCA comparability

Methods

  • Correlation matrix (heatmap of return co-movements)
  • PCA extraction (eigenvalues, variance explained)
  • Scree plot + Kaiser criterion for component selection
  • Factor loadings:
    • Heatmap (PC1–PC5)
    • Scatterplot (PC1 vs PC2)
  • Factor returns (time series of PC scores)
  • Covariance reconstruction (Frobenius norm error vs k)
  • Varimax rotation (interpretability of first 3 PCs)

Key Results

  • PC1 (market factor): ~43% of variance → broad co-movement
  • PC2 (sector tilt): ~13% of variance → Tech vs. Industrials/Energy split
  • PC3 (idiosyncratic): ~9% of variance → Tesla & Nvidia dominance
  • Top 3 PCs explain ~65%, top 5 ~75–80%
  • Covariance reconstruction: 3–5 PCs approximate full risk matrix with minimal error
  • Varimax rotation: clarified sector-based groupings without reducing variance explained

Deliverables