📊 Principal Component Analysis — Multi-Asset ETFs
SPY, QQQ, TLT, GLD, TIP, DBA, DBC, USO | Weekly returns | 5 Years (262 obs)
Correlation Matrix
| SPY | QQQ | TLT | GLD | TIP | DBA | DBC | USO |
|---|
| SPY | 1.00 | 0.94 | 0.11 | 0.15 | 0.29 | 0.16 | 0.17 | 0.11 |
| QQQ | 0.94 | 1.00 | 0.13 | 0.11 | 0.23 | 0.12 | 0.11 | 0.05 |
| TLT | 0.11 | 0.13 | 1.00 | 0.12 | 0.68 | -0.11 | -0.18 | -0.23 |
| GLD | 0.15 | 0.11 | 0.12 | 1.00 | 0.28 | 0.16 | 0.32 | 0.15 |
| TIP | 0.29 | 0.23 | 0.68 | 0.28 | 1.00 | 0.09 | 0.19 | 0.12 |
| DBA | 0.16 | 0.12 | -0.11 | 0.16 | 0.09 | 1.00 | 0.43 | 0.24 |
| DBC | 0.17 | 0.11 | -0.18 | 0.32 | 0.19 | 0.43 | 1.00 | 0.88 |
| USO | 0.11 | 0.05 | -0.23 | 0.15 | 0.12 | 0.24 | 0.88 | 1.00 |
PC Loadings (first 4 components — 91.99% of variance)
Interpretation:
PC1 (53.1%): Oil/Commodities factor — USO (0.87), DBC (0.45), DBA (0.13) dominate. This is the energy/real assets dimension.
PC2 (22.3%): Equity risk factor — QQQ (0.77), SPY (0.58). Pure equity beta.
PC3 (9.2%): Gold/inflation hedge — GLD (0.81), TLT (0.37), DBA (0.27). Real asset + duration.
PC4 (7.4%): Duration/rates — TLT (0.61), DBA (-0.73). Long bonds vs agriculture (inflation regime switch).
PC Scores Over Time
PC scores show the market's exposure to each factor at each point in time. Large moves = factor shock.
PC1 vs PC2 — Factor Space (each dot = 1 week)
X = oil/commodities factor, Y = equity factor. Quadrants: top-right = risk-on + oil up, bottom-left = risk-off + oil down.
PCA on weekly return covariance matrix. Source: Yahoo Finance | Chart: Marshall 🔶