Instantaneous covariance rank in a one-factor rate model
= Instantaneous covariance rank in a one-factor rate model
If all traded <zero-coupon bonds> depend on one scalar rate driven by one <Brownian motion>, their diffusion exposures form one vector $v_i=\eta P_{i,r}$. Their instantaneous <covariance matrix> is $vv^T$, of rank at most one. Nondegenerate maturity changes are therefore instantaneously perfectly correlated, with correlation $+1$ or $-1$, though finite-horizon bond-return correlations need not be one.