Inflation risk premium

Definition

The inflation risk premium (IRP) is the component of a nominal bond yield that compensates the holder for bearing the risk that realized inflation differs from expected inflation. It is the wedge between the nominal yield and the sum of the expected real rate and expected inflation, i.e.

$IR{P}_n,t=y^{n}o{m}_n,t-E_t[avgrealrateovern]-E_t[avginflationovern]$.

Equivalently, it is the certainty-equivalent compensation a risk-averse investor demands for holding a nominal claim whose real payoff is uncertain because of inflation.

Intuition

A nominal bond promises a fixed nominal payoff. If inflation is volatile and positively correlated with the marginal-utility “bad times” of the representative investor, then nominal bonds are bad hedges against consumption risk and command a positive risk premium. The IRP captures exactly this: it is the sign-weighted price of inflation risk under the pricing kernel.

Formal notation

Under no arbitrage, the n-period nominal yield decomposes as

$y^{n}o{m}_n,t=(1/n)\Sigma E_t[r^{r}ea{l}_{t+i}]+(1/n)\Sigma E_t[{\pi }_{t+i}]+IR{P}_n,t+Jensen$

where the IRP equals the negative of the conditional covariance between the log pricing kernel and cumulative log inflation, scaled by horizon. In an affine model with state $x_t$ and prices of risk $\lambda$, the IRP is itself affine in $x_t$ and inherits any regime dependence through $\lambda (s_t)$.

Variants

• Constant IRP — assumed in early decompositions; counterfactually generates a flat decomposition over time.
• Time-varying IRP — IRP is affine in the latent state and the regime, as in ang-bekaert-wei-2008-real-rates-expected-inflation and most modern no-arbitrage decompositions.
• Sign-restricted IRP — IRP is required to be non-negative on average; a popular but model-dependent restriction.

Comparison

• vs. expected inflation: expected inflation is a physical-measure conditional expectation; IRP is a risk-neutral / pricing-kernel object. Confusing the two leads to systematic mis-attribution of yield-curve slope.
• vs. real-rate term premium: the real-rate term premium is the compensation for bearing real-rate risk on real (e.g. TIPS) bonds; IRP is specifically the additional compensation for inflation risk on nominal bonds.

When to use

• Decomposing the slope or level of the nominal yield curve into economic components.
• Interpreting break-even inflation (BEI = nominal − real) — BEI = expected inflation + IRP, so any movement in BEI must be allocated between the two.
• Studying how monetary policy or inflation regimes change the price (not just the quantity) of inflation risk.

Known limitations

• Direct observation is impossible; the IRP is always a model-implied residual.
• Identification typically requires either TIPS data, survey expectations of inflation, or strong dynamic restrictions on the inflation process.
• Estimates are sensitive to the assumed regime structure, the number of factors, and the price-of-risk specification.

Open problems

• How much of the empirical time variation in the IRP is real versus an artifact of misspecified inflation dynamics?
• Are IRP estimates from nominal-yield-only models reconcilable with TIPS- based estimates after correcting for the TIPS liquidity premium?
• Can the IRP be tied directly to identifiable monetary policy stance / policy uncertainty rather than purely latent regime variables?

Key papers

• ang-bekaert-wei-2008-real-rates-expected-inflation

My understanding

The Ang-Bekaert-Wei finding that the IRP — not expected real rates and not expected inflation — drives the slope of the US nominal yield curve is the empirical anchor for treating IRP as economically first-order. For this CRE asset pricing project, the equivalent statement is that any cap-rate decomposition must allow the price of inflation risk to vary across regimes; collapsing it to a constant will systematically mis-attribute curve dynamics to real fundamentals.