Statement
In a no-arbitrage regime-switching dynamic term structure model fitted to US Treasury yields, the price of regime-shift risk is statistically and economically distinct from the within-regime price of factor risk, and the regime-shift component of the term premium is large at long maturities — comparable to or larger than the factor-risk component, and large enough that the conventional assumption of a zero regime-shift risk premium materially understates compensation for regime uncertainty in long-maturity Treasury yields.
Evidence summary
DSY 2007 derive a closed-form decomposition of the expected excess holding-period
return on an n-period Treasury bond into a within-regime factor-risk component
and a regime-shift component, the latter governed by a Radon–Nikodym density
ξ_{ij}(X_t) with log ξ_{ij} affine in the factors. They estimate the
parameters of ξ jointly with the rest of the model on monthly US Treasury
yields and report that:
- The estimated regime-shift price-of-risk parameters are statistically different from zero;
- The implied regime-shift component of the term premium is economically large at long maturities — comparable to or larger than the within-regime factor-risk component;
- Imposing
ξ_{ij} ≡ 1(the standard earlier-literature zero-regime-premium assumption) materially distorts the estimated term premium, especially around the Volcker transition window where regime uncertainty is highest; - The regime-shift component is highly time-varying and tracks economically interpretable proxies for regime uncertainty.
Conditions and scope
Established for:
- Monthly US Treasury zero-coupon yields, sample bracketing the Volcker episode;
- Gaussian-affine factor dynamics, two regimes;
- State-dependent Π(X_t) (multinomial-logit / logistic);
- Affine
log ξ_{ij}(X_t)parametrization of the regime-shift market price of risk; - Standard maturity range (3m–10y zero-coupon).
Not established for:
- Maturities beyond 10y (the structure should generalize but identification becomes thinner);
- Compound regime structures (multiple independent binary Markov sub-chains);
- Non-Gaussian factor dynamics;
- Non-Treasury asset classes (corporate bonds, mortgages, commercial real estate cap rates);
- Particle-filter / RBPF settings where the regime path is sampled rather than smoothed in closed form.
Counter-evidence
None recorded yet. Earlier regime-switching DTSMs that imposed zero regime-shift risk premium (Bansal–Zhou 2002 in some specifications, etc.) do not contradict this claim — they simply do not test it. A future model that allows priced regime-shift risk on the same data and finds the premium statistically zero would be direct counter-evidence.
Linked ideas
(none yet)
Open questions
- Is the magnitude of the regime-shift risk premium robust to the log-linear
approximation of
log Π^Q(X_t)used to keep bond prices affine? - Does the same decomposition apply to commercial real estate prices, where hold periods are much longer than 10 years and regime-shift risk should be even more important?
- Under a compound (multi-sub-chain) Markov structure, does the regime-shift premium decompose cleanly into one component per sub-chain, or are cross-chain interaction terms identified?
- How does the regime-shift risk premium interact with the no-bubble / determinacy constraints in forward-looking RE models that price assets via Riccati recursions on exponential-quadratic factors?