Factor Covariance in Yield-Curve Risk Forecasts: Evidence from U.S. Treasury Yields

Abstract

Yield-curve risk is often assembled in two steps: estimate separate volatilities for Nelson–Siegel factors, then map those volatilities back to individual maturities. The convenient diagonal map silently treats level, slope, and curvature innovations as conditionally uncorrelated. We show that this is not a harmless simplification for U.S. Treasury yields. Negative level–slope comovement makes diagonal forecasts too large at the front end, with a much smaller effect at long maturities. In a strictly out-of-sample exercise from 2008 to 2026, rolling CCC- and DCC-GARCH forecasts that retain factor covariance reduce QLIKE loss relative to diagonal GARCH at horizons of one, five, and twenty trading days. At two years, DCC lowers mean QLIKE by 0.77, 0.82, and 0.72, respectively, and reduces mean-squared error by 35–60 percent. The advantage narrows sharply with maturity. Two-sided interval exceedances provide the same diagnosis: the diagonal model covers too often because its intervals are excessively wide, whereas covariance-aware forecasts are much closer to nominal coverage. The improvement is not universal—it weakens at longer maturities and reverses for some twenty-day forecasts during the 2022–2023 tightening—but its maturity pattern follows directly from the Nelson–Siegel loadings. Factor covariance is therefore part of the forecast object, not a dispensable refinement to marginal volatility.

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