10-Year TIPS: Fair Value Model

Regression Statistics

OLS regression: DFII10 = α + β₁·R* + β₂·TP + ε  |  N = 240 monthly observations

*** p<0.01   ** p<0.05   * p<0.10.   OLS standard errors are not HAC-adjusted; given the autocorrelated nature of macro time series, t-statistics are indicative rather than exact.

Model Methodology

This model estimates the fair value of the 10-year TIPS yield (DFII10) via OLS regression on two theoretically motivated inputs:

Regression: DFII10 = α + β₁·R* + β₂·TP + ε

OLS coefficients are estimated over the full available sample. Fair value at each date is the in-sample fitted value. Unlike a calibrated mean-zero intercept, regression-estimated coefficients allow the data to determine how much each factor loads onto the real yield — which may deviate from 1:1 due to inflation risk premium, liquidity effects, and other wedges between nominal and real term premia.

Residual = Actual DFII10 − Fair Value

• Residual > 0: Real yield trades above fair value → market is cheap / undervalued
• Residual < 0: Real yield trades below fair value → market is rich / overvalued

ADF test on residuals: Stationarity of ε confirms the regression is not spurious (cointegrating relationship between DFII10, R*, and TP).

Notes & Caveats

• Sample is constrained by DFII10 availability (from April 2006 onwards).
• R* is the Laubach-Williams two-sided (smoothed) estimate; it is revised retrospectively each quarter. Real-time r* is subject to significant uncertainty and revision.
• THREEFYTP10 is the ACM nominal term premium; it reflects both real term risk and inflation risk premium. The regression intercept and β₂ absorb these wedges relative to the TIPS market.
• Daily series (DFII10, THREEFYTP10) are averaged to monthly; quarterly r* is forward-filled to monthly.
• This is an in-sample fit. The model is not estimated on a rolling or expanding basis — residuals should not be used as a standalone trading signal without out-of-sample validation.

Sources: Federal Reserve Bank of New York (Laubach-Williams r* estimates), Federal Reserve Bank of New York via FRED (ACM Term Premium, THREEFYTP10), Federal Reserve H.15 via FRED (DFII10). DFII10 is the 10-Year Treasury Inflation-Indexed Constant Maturity yield.