Modeling real (inflation-adjusted) corporate bond returns with IID residuals

Develop a regression-based annual time-series model for inflation-adjusted (real) U.S. investment‑grade corporate bond total returns (e.g., the BofA ICE U.S. Corporate Bonds Total Return Index) whose regression residuals are independent and identically distributed, analogous in structure to the paper’s nominal-return specification that regresses bond log returns on the lagged BAA rate level and contemporaneous rate changes.

Background

The simulator currently operates in nominal terms because the authors could not obtain a satisfactory real (inflation-adjusted) bond model producing IID residuals, even though they could do so for equities. This limitation prevents a fully real (inflation-adjusted) simulation framework including bonds.

A successful model would parallel the nominal specification that captures carry (via the lagged BAA rate) and duration (via contemporaneous rate changes), but in real terms, while ensuring independent, identically distributed innovations.