Unspanned Macro Risk in the Yield Curve

Most textbook models of the yield curve claim that three or four numbers — level, slope, curvature — summarize everything you need to know about future interest rates. If that were literally true, then any macro variable useful for forecasting bond returns, like an inflation gauge or a measure of economic slack, should already be recoverable just by looking hard enough at today's curve shape. In practice it isn't. There are macro signals that genuinely predict how bond risk premia move, yet leave almost no fingerprint on the curve today. That gap is what "unspanned macro risk" means.

Why "spanned" was ever the assumption

Standard affine term-structure models assume a small number of curve factors (level, slope, curvature) drive both today's yields and the risk premia embedded in them. If those factors are all that matters, then knowing the curve today tells you everything relevant about expected future returns — macro data would be redundant, since any macro-relevant information would already be priced into curve shape. Researchers tested this directly: they built curve-only models, then asked whether adding macro variables (inflation surveys, output gap measures, ISM survey diffusion indices) improved forecasts of future bond returns. It did, quite a lot on some variables, even after fully accounting for the current level, slope, and curvature. That result is inconsistent with pure spanning.

What is actually going on

The resolution is that curve factors capture the expected path of short rates plus the average term premium, but a macro variable can shift the variance or risk-aversion component of the term premium — the part investors charge for uncertainty — while the level of yields stays put because other forces offset it. Inflation uncertainty is the textbook case: two economies can have the same 10-year yield today, but one has inflation anchored and predictable while the other has inflation drifting and hard to forecast. The curve looks identical; the compensation bondholders will demand going forward does not.

Worked example

Suppose a strategist runs two return forecasting regressions using five years of monthly data on 10-year Treasury excess returns over the next 12 months. Regression 1 uses only the three curve principal components (level, slope, curvature) as predictors and gets an out-of-sample R² of 8%. Regression 2 adds a survey-based measure of inflation disagreement (the spread between the 75th and 25th percentile forecasters in a survey of professional forecasters) and the R² rises to 15%. The inflation-disagreement coefficient is statistically significant even after controlling for the three curve factors. Because that variable improves forecasts beyond what the curve factors already capture, and because it does not itself load heavily on the current curve shape (it's nearly uncorrelated with today's level, slope, curvature), it is behaving as an unspanned risk: it changes expected returns without changing today's curve.

What this means in practice

A rates desk that only watches curve shape for cues about carry and roll can miss a real, priced source of return variation. Before FOMC meetings or CPI releases, dispersion in economists' forecasts often widens without today's curve shifting at all — yet realized volatility and term premium behavior around those events tends to track that dispersion. Risk managers who model bond portfolios purely off curve factors will systematically underestimate risk in periods where unspanned macro uncertainty is elevated, because their model has no variable to represent it.