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Arbitrage Pricing, Weak Beta, Strong Beta: Identification-Robust and Simultaneous Inference

Author

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  • Marie-Claude Beaulieu
  • Jean-Marie Dufour
  • Lynda Khalaf
Abstract
Factor models based on Arbitrage Pricing Theory (APT) characterize key parameters jointly and nonlinearly, which complicates identification. We propose simultaneous inference methods which preserve equilibrium relations between all model parameters including ex-post sample-dependent ones, without assuming identification. Confidence sets based on inverting joint tests are derived, and tractable analytical solutions are supplied. These allow one to assess whether traded and nontraded factors are priced risk-drivers, and to take account of cross-sectional intercepts. A formal test for traded factor assumptions is proposed. Simulation and empirical analyses are conducted with Fama-French factors. Simulation results underscore the information content of cross-sectional intercept and traded factor restrictions. Three empirical results are especially noteworthy: (1) the Fama-French three factors are priced before 1970; thereafter, we find no evidence favoring any factor relative to the market; (2) heterogeneity is not sufficient to distinguish priced momentum from profitability or investment risk; (3) after the 1970s, factors are rejected or appear to be weak, depending on intercept restrictions or test portfolios.

Suggested Citation

  • Marie-Claude Beaulieu & Jean-Marie Dufour & Lynda Khalaf, 2020. "Arbitrage Pricing, Weak Beta, Strong Beta: Identification-Robust and Simultaneous Inference," CIRANO Working Papers 2020s-30, CIRANO.
    • Handle: RePEc:cir:cirwor:2020s-30
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    File URL: https://cirano.qc.ca/files/publications/2020s-30.pdf
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    References listed on IDEAS

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    More about this item

    Keywords

    Capital Asset Pricing Model; CAPM; Arbitrage Pricing Theory; Black; Fama-French Factors; Meanvariance Efficiency; Non-Normality; Weak Identification; Identification-Robust; Projection; Fieller; Multivariate Linear Regression; Uniform Linear Hypothesis; Exact Test; Monte Carlo Test; Bootstrap; Nuisance Parameters;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G1 - Financial Economics - - General Financial Markets
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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