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Higher-Order Asset Pricing Factors via Forward Selection Fama-MacBeth Regression

Nicola Borri, Denis Chetverikov, Yukun Liu, Aleh Tsyvinski

Abstract

We show that the higher-order terms and interactions of the common sparse linear factors are significantly priced in the cross-section of equity returns. A higher-order model with only a small number of selected higher-order terms from six widely used factors outperforms traditional benchmarks both in-sample and out-of-sample. It also substantially reduces the alphas of the extensive factor zoo, suggesting that the pricing power of many zoo factors is attributable to their exposure to higher-order terms of common linear factors. We identify and rank the most relevant higher-order terms by developing a forward selection Fama-MacBeth procedure.

Higher-Order Asset Pricing Factors via Forward Selection Fama-MacBeth Regression

Abstract

We show that the higher-order terms and interactions of the common sparse linear factors are significantly priced in the cross-section of equity returns. A higher-order model with only a small number of selected higher-order terms from six widely used factors outperforms traditional benchmarks both in-sample and out-of-sample. It also substantially reduces the alphas of the extensive factor zoo, suggesting that the pricing power of many zoo factors is attributable to their exposure to higher-order terms of common linear factors. We identify and rank the most relevant higher-order terms by developing a forward selection Fama-MacBeth procedure.

Paper Structure

This paper contains 27 sections, 16 theorems, 94 equations, 7 figures, 14 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Methodology
  3. Model
  4. Estimation
  5. Debiased Estimation
  6. Asymptotic Theory
  7. Empirical Analysis
  8. Data
  9. Selected Factors by Forward Selection Fama-MacBeth Regressions
  10. Out-of-Sample
  11. Asset space
  12. Time periods
  13. Factor Zoo
  14. Cross-sectional method
  15. Time-series method
  16. ...and 12 more sections

Key Result

Theorem 1

Suppose that Assumptions as: ulln -- as: growth conditions are satisfied. Then

Figures (7)

  • Figure 1: Actual vs. Predicted Returns
  • Figure 2: Reducing the Factor Zoo in the Cross-Section
  • Figure 3: Reducing the Factor Zoo in the Time-Series
  • Figure 4: Sampling Distribution of R-squareds
  • Figure 5: Reducing Alternative Zoo Factors in the Cross-Section
  • ...and 2 more figures

Theorems & Definitions (40)

  • Remark 1: Equivalent Form of Estimator $\widehat{\psi}$
  • Remark 2: Equivalent Forms of Forward Selection Fama-MacBeth Procedure
  • Remark 3: Relation to Literature
  • Remark 4: Relation to Literature
  • Theorem 1: Convergence Rate
  • Remark 5: Consistency of $\widehat{\psi}$
  • Theorem 2: Asymptotic Normality
  • Remark 6: Comparison of $\widehat{\psi}$ and $\widehat{\psi}_D$
  • Remark 7: Estimating $\sigma_{\psi,j}^2$
  • Remark 8: Relation to Literature
  • ...and 30 more