Nonparametric Specification Testing of Conditional Asset Pricing Models

Abstract

This article presents an adaptive omnibus specification test of asset pricing models where the stochastic discount factor is conditionally affine in the pricing factors. These models provide constraints that conditional moments of returns and pricing factors must satisfy, but most of them do not provide information on the functional form of those moments. Our test is robust to functional form misspecification, and also detects any relationship between pricing errors and conditioning variables. We give special emphasis to the test implementation and calibration, and extensive simulation studies prove the functioning in practice. Our empirical applications show a conditional counterpart of a well-known problem of unconditional models. The lack of rejection of consumption based conditional models seems to be due to a poor conditional correlation between consumption and stock returns.

Keywords:

• Adaptive testing
• Bootstrap methods
• Conditional asset pricing model
• Specification test

Supplementary Material

The appendices are available online. Appendix A shows the proofs of Theorems 1–5. Appendix B reviews previous approaches to testing asset pricing models with nonparametric prices of risk. Appendix C develops the centered SDF variant and its relationship with the uncentered SDF variant. Appendix D describes the Monte Carlo design in detail. Finally, Appendix E studies the special case of an SDF that is conditionally uncorrelated with excess returns, and also the SDF implications of a riskless asset.

Acknowledgments

We thank participants at the 10th Conference on Computational and Financial Econometrics (Sevilla), the New Methods for the Empirical Analysis of Financial Markets (Comillas), the 26th Finance Forum (Santander), the 88th Meeting of the Southern Finance Association (Washington DC), the 68th Meeting of the Midwest Finance Association (Chicago), the CUNY Macroeconomics and Finance Colloquium (New York), the 12th Society for Financial Econometrics Conference (Shanghai), and specially Yacine Ait-Sahalia, Stefanos Delikouras, and Nikolay Gospodinov, for helpful comments and suggestions. The comments from Christian Hansen (the editor), an associate editor, and two anonymous referees have also led to a substantially improved article.

Additional information

Funding

The authors gratefully acknowledge financial support from the Research Projects APIE 1/2015-17: “New methods for the empirical analysis of financial markets” of the Santander Financial Institute (SANFI) of UCEIF Foundation resolved by the University of Cantabria and funded with sponsorship from Banco Santander; and PID2019-105986GB-C22: “Dependent risks: modeling and application” funded by the Spanish M. de Ciencia e Innovación.