Definition
A no-arbitrage decomposition of the n-period nominal Treasury yield into three economically distinct components:
- The expected average real short rate over the next n periods,
- Expected average inflation over the next n periods, and
- The inflation risk premium (and any residual Jensen / convexity term).
The decomposition operationalizes the Fisher identity in a model where the joint dynamics of real rates, inflation, and the pricing kernel determine each piece.
Intuition
A nominal yield is “what you earn”; the decomposition asks “why you earn it.” Two yields can be equal at a given date for very different economic reasons: high expected real rates, high expected inflation, or large compensation for bearing inflation risk. Without a structural decomposition, the nominal yield curve is a black box; with one, every basis point of slope and level can be attributed.
Formal notation
For a no-arbitrage model with state , regime , and inflation process ,
y^nom_n$,t = (1/n) E_t[\Sigma_{i=0}^{n-1} r^r$eal_{t+i}] $+ (1/n) E_t[\Sigma_{i=0}^{n-1} \pi_{t+i}]$ + IRP_n,t + (Jensen)
where each component is recovered by an analytical or numerical projection of the model. In an affine ATSM, all three pieces are themselves affine in , so the decomposition is closed-form.
Variants
- Static / Fisher decomposition — assumes constant real rate and constant IRP; useful only as a benchmark.
- Survey-based decomposition — uses observed survey forecasts of inflation to identify expected inflation directly, leaving IRP as a residual.
- No-arbitrage model-based decomposition — jointly estimates a regime- switching ATSM on nominal yields (and optionally surveys / TIPS) and reads off the three components from the model. This is the approach in ang-bekaert-wei-2008-real-rates-expected-inflation.
- TIPS-based decomposition — uses TIPS yields to pin down the real curve directly, leaving expected inflation + IRP to be split using surveys or dynamic restrictions.
Comparison
- vs. break-even inflation (BEI): BEI = nominal − real, which lumps expected inflation and IRP together. The decomposition splits BEI into its two pieces, which can move in opposite directions.
- vs. VAR-based decomposition: a VAR decomposition does not impose no arbitrage and so can produce internally inconsistent forecasts at long horizons. The no-arbitrage decomposition guarantees consistency between the cross-section of yields and the time series of factors.
When to use
- Attributing nominal-yield-curve dynamics to monetary policy versus inflation expectations versus risk compensation.
- Reading the “real signal” in long-maturity nominal yields, particularly in pre-TIPS samples or other regimes without a directly observable real curve.
- Constructing an exogenous real-rate process for a downstream asset-pricing model.
Known limitations
- The decomposition is model-dependent: different no-arbitrage specifications can produce noticeably different splits, especially for the IRP.
- Identification of expected inflation versus IRP is empirically delicate without survey or TIPS information.
- Regime structure, number of factors, and price-of-risk specification all affect the answers.
Open problems
- How much variation across published decompositions reflects true model uncertainty versus differences in identifying assumptions?
- How can the decomposition be extended to multi-country settings without introducing new identification problems via FX risk?
- Joint decomposition of nominal and corporate / municipal yields under a common pricing kernel.
Key papers
My understanding
This decomposition is the empirical engine that turned “term structure of nominal yields” into “term structure of real rates + expected inflation + inflation risk premium.” For the CRE asset pricing project it is the template for how to decompose a yield-like object (cap rates) into rent-growth expectations, real-rate expectations, and risk premia under a regime- switching no-arbitrage pricing kernel.