Affine Term Structure Perturbations and Cross-Asset Discounting Regimes

Annotation on the propagation of small perturbations in affine term-structure factors through cross-asset discounting. We isolate the conditions under which a level shift in the short rate maps approximately linearly into equity discount-rate revisions versus the conditions under which the mapping becomes regime-dependent and nonlinear.

Short rate r_t = a + b·X_t with X_t an affine factor process. Equity discount sensitivity is examined through projection of equity ERP onto Δr_t conditional on regime indicators.

In low-volatility regimes the mapping is well-approximated by a constant duration. Outside those regimes, equity ERP exhibits convex sensitivity that violates the linear approximation in the direction of larger downside.

Memos that touch interest-rate sensitivity should explicitly flag the regime classification used and avoid implicit constant-duration assumptions.

Regime identification is itself a model choice; we report results under multiple identification schemes.