US Treasury Yield Curve — PCA Factor Decomposition

The heatmap (left) shows each maturity's yield level month by month — red = high rates, blue = low rates. Read across a row to see how one maturity evolved over time; read down a column to see the shape of the curve at a point in time. The snapshot (right) compares the current yield curve shape against 1M, 3M, and 1Y ago — an upward-sloping curve (normal) vs a flat/inverted curve (potential recession signal).

PCA decomposes every yield curve change into three independent drivers. PC1 (blue) = Level — rises when all yields rise together (parallel shift); fell during QE (2009–2021) and spiked during the 2022–2023 hiking cycle. PC2 (orange) = Slope — positive when the curve is steep (long rates > short rates); turns negative when the curve inverts. PC3 (green) = Curvature — measures the belly of the curve relative to the ends; typically the smallest and noisiest factor. Together these three components explain nearly all yield curve variation.

Each PC score is plotted against a closely-related yield or spread, both re-scaled to mean=0, std=1 so they can be compared on the same axis regardless of units. A tight co-movement confirms the economic interpretation of that factor. Divergences are informative: when the PC and its spread decouple, other forces are at work (e.g. central bank intervention, flight to safety).

Pearson correlation between each monthly PC score and various yield levels / computed spreads over the full history. Red = strong positive, Blue = strong negative. PC1 (Level) should show near-1.0 correlation with all yield levels — it IS the parallel shift. PC2 (Slope) should show strong correlation with spread measures (10Y-2Y, 30Y-5Y) and weaker/opposite correlation with short-end yields. PC3 (Curvature) typically shows the weakest correlations — it captures residual curve shape, often driven by term-premium or convexity effects.

Loadings show how much each maturity contributes to each factor. PC1 loadings should all be positive and similar in magnitude (parallel shift). PC2 loadings should be positive at the long end and negative at the short end (slope). PC3 loadings should be positive at the ends and negative in the belly (curvature / "hump"). The variance bar shows how much of total yield curve variation each PC explains.