Sparse Macro Factors

49 Pages Posted: 25 Oct 2018 Last revised: 2 Feb 2019

See all articles by David Rapach

David Rapach

Saint Louis University; Washington University in St. Louis

Guofu Zhou

Washington University in St. Louis - John M. Olin Business School; China Academy of Financial Research (CAFR)

Date Written: January 31, 2019

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.

Keywords: Sparse Principal Component Aanalysis, FRED-MD, Risk Premia, Factor Mimicking Portfolio, Three-Pass Regression, Multifactor Models

JEL Classification: C38, C58, G12

Suggested Citation

Rapach, David and Zhou, Guofu, Sparse Macro Factors (January 31, 2019). Available at SSRN: https://ssrn.com/abstract=3259447 or http://dx.doi.org/10.2139/ssrn.3259447

David Rapach

Saint Louis University ( email )

3674 Lindell Blvd
St. Louis, MO 63108-3397
United States

HOME PAGE: http://https://sites.google.com/slu.edu/daverapach

Washington University in St. Louis

One Brookings Drive
Campus Box 1133
St. Louis, MO 63130-4899
United States

HOME PAGE: http://https://sites.google.com/slu.edu/daverapach

Guofu Zhou (Contact Author)

Washington University in St. Louis - John M. Olin Business School ( email )

Washington University
Campus Box 1133
St. Louis, MO 63130-4899
United States
314-935-6384 (Phone)
314-658-6359 (Fax)

HOME PAGE: http://apps.olin.wustl.edu/faculty/zhou/

China Academy of Financial Research (CAFR)

Shanghai Advanced Institute of Finance
Shanghai P.R.China, 200030
China

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