Inflation Term‑Structure

Abstract

This note defines an inflation term‑structure signal using the breakeven curve slope and real yields. Inputs are the 5‑year breakeven (T5YIE), 10‑year breakeven (T10YIE), and the 10‑year TIPS yield (DFII10). Series are month‑end aligned. A robust z‑score standardisation (rolling median/MAD) is applied to each input, and a weighted blend (0.4 · z(T5YIE) + 0.3 · z(T10YIE) + 0.3 · z(−DFII10)) forms a continuous composite. The composite is discretised into regimes using fixed cut‑offs ±0.75.

1. Data Sources (Provenance, Construction, Caveats)

This signal uses market‑implied inflation compensation and real yields from U.S. Treasury markets, distributed via FRED. Each series is a constructed estimate (constant‑maturity / model‑based) rather than a raw trade print; the economic meaning is strongest when markets are liquid and functioning normally.

All inputs are resampled to month‑end and trimmed to a rolling history as required by the rolling window used in the robust z‑score (default win = 60 months, min\_win = 24 months).

2. Alignment & Transformations

1. Month‑end alignment: resample each series to month‑end and select the last observation.
2. Term spread: compute the slope of the breakeven curve
   \text{Term\_Spread}_t = T10YIE_t − T5YIE_t
   (The spread can be charted but is not directly used in the composite below.)
3. Robust standardisation: for any series X,
   z\_{rob}(X)_t = \dfrac{X_t − \mathrm{median}(X)_{t, w}}{1.4826 · \mathrm{MAD}(X)_{t, w}}

   with a rolling window w of up to 60 months (min 24). The 1.4826 factor scales MAD to σ under normality.

3. Composite Construction

1. Inputs: Z\_{T5} = z\_{rob}(T5YIE), Z\_{T10} = z\_{rob}(T10YIE), Z\_{mReal} = z\_{rob}(−DFII10) (lower real yields imply easier financial conditions, hence the sign inversion).
2. Weighted blend:
   \text{Infl\_Term\_Composite}_t = 0.4·Z\_{T5,t} + 0.3·Z\_{T10,t} + 0.3·Z\_{mReal,t}

4. Regime Mapping

Map the composite into discrete regimes using fixed thresholds:

5. Implementation Notes (Python)

import pandas as pd
import numpy as np

# ---- Robust z-score ----
def robust_z(s, win=60, min_win=24):
    x = pd.to_numeric(s, errors="coerce").astype(float)
    w = max(min_win, min(win, x.dropna().size))
    med = x.rolling(w, min_periods=min_win).median()
    mad = (x - med).abs().rolling(w, min_periods=min_win).median()
    return (x - med) / (1.4826 * mad.replace(0, np.nan))

# Assume df_infl_term with columns [Date, T5YIE, T10YIE, DFII10]
d = df_infl_term.copy()
d["Term_Spread"] = d["T10YIE"] - d["T5YIE"]

d["Z_T5"]    = robust_z(d["T5YIE"])      # 5y breakeven

d["Z_T10"]   = robust_z(d["T10YIE"])     # 10y breakeven

d["Z_mReal"] = robust_z(-d["DFII10"])    # inverted real yield

d["Infl_Term_Composite"] = 0.4*d["Z_T5"] + 0.3*d["Z_T10"] + 0.3*d["Z_mReal"]

# Discretise
hi, lo = 0.75, -0.75

def _regime(v):
    if pd.isna(v):
        return np.nan
    return "Reflation" if v > hi else ("Disinflation" if v < lo else "Neutral")

d["Infl_Term_Regime"] = d["Infl_Term_Composite"].apply(_regime)

df_sig_infl_term = d

Drop‑in compatible with existing pipelines: use df_sig_infl_term downstream for charts and dashboards.

6. Assumptions & Limitations

• Breakevens reflect inflation expectations plus liquidity/risk premia; structural shifts (QE/QT, balance‑sheet policy) can alter level and volatility.
• DFII10 availability gaps and revisions can affect recent z‑scores; robust scaling mitigates but does not eliminate this.
• Fixed weights (0.4/0.3/0.3) are heuristic; alternative weights may be tuned via cross‑validation for a target asset (e.g., breakeven curve, commodities, value vs growth).
• Monthly resampling smooths high‑frequency dynamics; use weekly views when trading shorter horizons.

7. Reproducibility

• Persist source IDs (T5YIE, T10YIE, DFII10), download timestamps, and code commit hash.
• Record window parameters (win, min_win) and regime thresholds (±0.75).
• Archive the final panel with Infl_Term_Composite and Infl_Term_Regime columns for auditability.

8. Applications

Useful as a conditioning variable for macro factor models, inflation‑sensitive tilts (commodities, breakevens, value/growth), and as a cross‑check against price‑based risk indicators (e.g., real‑yield shocks). Naturally pairs with liquidity and activity signals for broader regime classification.

9. Model Interpretation (How to Read the Signal)

10. References (Selected)

1. FRED: 5‑Year Breakeven Inflation Rate (T5YIE) — series description and construction.
2. FRED: 10‑Year TIPS Yield, Constant Maturity (DFII10) — series description.
3. D’Amico, Kim, and Wei (Fed, 2014): evidence that TIPS liquidity premia affect breakevens and interpretation.
4. Andreasen, Christensen, and Riddell (FRBSF, 2020): estimation and behavior of the TIPS liquidity premium.
5. Abrahams et al. (NY Fed, 2012): decomposition of real/nominal yield curves; discussion of TIPS liquidity and breakeven components.
6. Beauregard, Doppelt, and Zhu (FRBSF, 2021): breakeven inflation as expectations plus risk and liquidity premia.