Probability weighting and default risk: a possible explanation for distressed stock puzzles

Abstract

This paper suggests incorporating investor probability weighting and the default risk of individual firms into a consumption-based asset pricing model. The extended model provides a unified explanation for several anomalous patterns observed in financial markets. The analysis addresses not only widely recognized asset pricing puzzles, such as the equity premium puzzle, but also less-studied anomalies on financially distressed stocks. The simulation, under which the model is calibrated according to U.S. historical data, shows that a combination of mild overweighting of probability on tail events and nonlinearity of equity values caused by default risk has the potential to resolve these patterns.

Keywords:

• Asset pricing puzzles
• Consumption-based asset pricing
• Distressed stock
• Probability weighting function
• Default risk
• Business time

Acknowledgments

I thank Daisuke Yoshikawa, Hideyuki Takamizawa, Koichiro Takaoka, and the participants in Finance Workshop at Hitotsubashi University for their helpful comments and suggestions. I am especially grateful for the detailed feedback of the two anonymous referees, whose comments have dramatically improved the paper.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1 See Appendix A.2 for fundamental properties of subordinated Brownian motions.

2 The simulation results in VG with calibrated parameter $\omega =-0.0919$ are available upon request.

3 S&P Global Ratings issuer credit rating states that an obligor rated ‘CC’ is currently highly vulnerable. The ‘CC’ rating is used when a default has not yet occurred but S&P Global Ratings expects default to be a virtual certainty, regardless of the anticipated time to default. See https://www.standardandpoors.com/en_US/web/guest/article/-/view/sourceId/504352.

4 In Appendices 1, 3, and 4, I omit superscripts on functions and operators denoting probability measures, because these appendices provides mathematically general discussions. The results derived below are held under suitable probability measures.

5 A standard choice for control parameter q is $T{\psi }_R\left(1\right)$, which is the mean value of $R_T$. See Chapter 11.1.3 in Cont and Tankov (2004) and Appendix 1 in Yamazaki (2018) for example.

Additional information

Funding

This study was financially supported by JSPS KAKENHI Grant Number 26380402 and the Research Institute for Innovation Management at Hosei University.