Right tail information and asset pricing

Abstract

The right tail of the distribution of financial variables provides important information to investors and decision-makers. In this paper, we study the role of the right tail distributional information in finance. First, we propose semiparametric estimators for the right tail mean (RTM) and right tail variance (RTV). The proposed estimators use parsimonious parametric models to capture the dynamics of the data, and also allow for nonparametric flexibility in the distribution. These estimators can be estimated at the rate of root-T and are asymptotically normal. We then conduct a comparative study on the dynamics and empirical feature of the RTM and RTV in two international equity markets: The US and The Chinese stock markets. Third, we study the effect of right tail measures in the cross-sectional pricing of stock returns. Our empirical investigation indicates that the right tail information plays a significant role in explaining the cross-section pricing of stock returns. In addition, the RTV and left tail variance (LTV) have opposite impacts on asset prices. Finally, we use simulation based analysis to examine the impact of RTM on the optimal investment strategy. Our results have important implications for portfolio management in financial market.

Keywords:

• Asset pricing
• quantile
• right tail mean
• right tail variance
• tail information

JEL CLASSIFICATION:

• C13
• C58
• G12

Acknowledgments

We thank Essie Maasoumi, Tong Li, two anonymous referees, and conference participants in the 3rd Economics and Business Forum in honor of Cheng Hsiao at Beihang University for very helpful comments on early versions of this paper.

Notes

1 Arditti (1967) shows the close link between the investment return and its distributional skewness. Kraus and Litzenberger (1976) incorporate this idea in a three-moment CAPM and demonstrate that expected security returns can be determined by systematic sknewness. Scott and Horvath (1980) discuss other higher moments of return distribution and their crucial roles in pricing issues of financial assets, e.g. higher even moments such as kurtosis etc.

2 Lai (1991) and Chunhachinda et al. (1997) use the polynomial goal programming to address the problem of portfolio selection with skewness. Athayde and Flores (2004) solve an optimization problem of efficient portfolio by defining moments as tensors.

3 Berkelaar and Kouwenberg (2000) give a clear definition on downside risk measures and use the mean-ES criterion in their new approach. Alexander and Baptista (2004) address a portfolio optimization problem by introducing additional constraint on the downside risk of portfolio.

4 We thank the referee for the comments and suggestion.

5 See, e.g. Barberis, Huang and Santos (2001, QJE), Barberis and Huang (2001, JF) for applications of using such utility functions in capturing investor’s propspect-type behavior.

Additional information

Funding

This material is financially supported by the National Natural Science Foundation of China (Grant No. 11901233) and the Empirical Research of CAPM Between China and Japan (Grant No. 2019XXJD14, Jilin University).