Sparse Macro Factors
49 Pages Posted: 25 Oct 2018 Last revised: 2 Feb 2019
Date Written: January 31, 2019
We use machine learning to estimate sparse principal components (PCs) for 120 monthly macro variables spanning 1960:02 to 2018:06 from the FRED-MD database. For comparison, we also extract the ﬁrst ten conventional PCs from the macro variables. Each of the conventional PCs is a linear combination of all the underlying macro variables, making them difficult to interpret. In contrast, each of the sparse PCs is a sparse linear combination, whose active weights allow for intuitive economic interpretations of the sparse PCs. The ﬁrst ten sparse PCs can be interpreted as yields, inﬂation, production, housing, employment, yield spreads, wages, optimism, money, and credit. Innovations to the conventional (sparse) PCs constitute a set of conventional (sparse) macro factors. Robust tests indicate that only one of the conventional macro factors earns a signﬁcant risk premium. In contrast, three of sparse macro factors — corresponding to yields, housing, and optimism — earn signﬁcant risk premia. Compared to leading risk factors from the literature, mimicking portfolios for the yields, housing, and optimism factors deliver sizable Sharpe ratios. A four-factor model comprised of the market factor and mimicking portfolio returns for the yields, housing, and optimism factors performs on par with or better than leading multi-factor models from the literature in accounting for numerous anomalies in cross-sectional stock returns.
Keywords: Sparse Principal Component Aanalysis, FRED-MD, Risk Premia, Factor Mimicking Portfolio, Three-Pass Regression, Multifactor Models
JEL Classification: C38, C58, G12
Suggested Citation: Suggested Citation