Machine-Learning-Based Return Predictors and the Spanning Controversy in Macro-Finance

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.