25 return streams built from a market factor + 5 unequal sector factors + noise. PCA reads the structure back out: the market is the spike, the sectors are the next bumps, the rest is sea.
Cumulative return paths
colored by sector · thick line = equal-weight index (realized market factor)
Eigenvalue spectrum
each bar = a PCA factor · height = variance it carries
Loading map & correlation
left: each asset by PC1/PC2 loading · right: correlation, grouped by sector