Sparse Macro Factors

Abstract

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.