This article estimates inflation risk premia using data on prices of Treasury Inflation-Protected Securities (TIPS) from 2000 to 2008. The estimation approach is arbitrage-free, largely model-free, and easy to implement. It also distinguishes between TIPS yields and real yields by explicitly taking into account the three-month indexation lag of TIPS in the analysis. In addition, we consider three measures of TIPS liquidity, including one new measure based on TIPS prices only. We estimate the liquidity premium to be around 13 basis points over the full sample but substantially higher in the first subperiod. We find that the inflation risk premium is time-varying and, on average, considerably lower than suggested by various structural models. Depending on the proxy used for expected inflation, the unconditional 10-year inflation risk premium ranges from –9 basis points to 4 basis points over the full sample, and between 1 basis point and 6 basis points over the 2004–2008 subperiod.

Credit risk is also the subject of this article by Huang and Kong. There are numerous credit risk models in which the relevant stochastic variables for pricing a risky bond are obtained from the term structure of interest rates, and perhaps from firm-level capital structure data. In this article, the authors look at option-adjusted spreads on corporate bond indexes for different credit ratings classes. They find that term structure variables alone are limited in their ability to explain yield spreads, but adding macroeconomic variables, like an index of leading economic indicators, and equity market variables, including the return on the Russell 2000 index and the Fama-French “high minus low” factor, can contribute significant explanatory power, especially for lower rated bonds.

We propose a two-step machine learning algorithm—the Supervised Adaptive Group LASSO (SAGLasso) method—that is suitable for constructing parsimonious return predictors from a large set of macro variables. We apply this method to government bonds and a set of 917 macro variables and construct a new, transparent, and easy-to-interpret macro variable with significant out-of-sample predictive power for excess bond returns. This new macro factor, termed the SAGLasso factor, is a linear combination of merely 30 selected macro variables out of 917. Furthermore, it can be decomposed into three sublevel factors: a novel housing factor, an employment factor, and an inflation factor. Importantly, the predictive power of the SAGLasso factor is robust to bond yields, namely, the SAGLasso factor is not spanned by bond yields. Moreover, we show that the unspanned variation of the SAGLasso factor cannot be attributed to yield measurement error or macro measurement error. The SAGLasso factor therefore provides a potential resolution to the spanning controversy in the macro-finance literature.This paper was accepted by Haoxiang Zhu, finance.Funding: This work was supported by a grant from the Penn State Institute for Real Estate Studies.Supplemental Material: Data and the internet appendices are available at https://doi.org/10.1287/mnsc.2022.4386 .