Annals of Finance

, Volume 12, Issue 1, pp 95–133 | Cite as

The skewness risk premium in equilibrium and stock return predictability

  • Hiroshi Sasaki
Research Article


In this study, we investigate the skewness risk premium in the financial market under a general equilibrium setting. Extending the long-run risks (LRR) model proposed by Bansal and Yaron (J Financ 59:1481–1509, 2004) by introducing a stochastic jump intensity for jumps in the LRR factor and the variance of consumption growth rate, we provide an explicit representation for the skewness risk premium, as well as the volatility risk premium, in equilibrium. On the basis of the representation for the skewness risk premium, we propose a possible reason for the empirical facts of time-varying and negative risk-neutral skewness. Moreover, we also provide an equity risk premium representation of a linear factor pricing model with the variance and skewness risk premiums. The empirical results imply that the skewness risk premium, as well as the variance risk premium, has superior predictive power for future aggregate stock market index returns, which are consistent with the theoretical implication derived by our model. Compared with the variance risk premium, the results show that the skewness risk premium plays an independent and essential role for predicting the market index returns.


Long-run risks model Epstein–Zin preferences Variance risk premium Skewness risk premium Stock return predictability Stochastic volatility Volatility of volatility Jump intensity 

JEL Classification


  1. Aït-Sahalia, Y., Lo, A.: Nonparametric estimation of state-price-densities implicit in financial asset prices. J Financ 53, 499–547 (1998)CrossRefGoogle Scholar
  2. Aït-Sahalia, Y., Wang, W., Yared, F.: Do option markets correctly price the probabilities of movement of the underlying asset? J Econ 102, 67–110 (2001)CrossRefGoogle Scholar
  3. Bakshi, G., Kapadia, N., Madan, D.: Stock return characteristics, skew laws, and the differential pricing of individual equity options. Rev Financ Stud 16, 101–143 (2003)CrossRefGoogle Scholar
  4. Bali, T., Hovakimian, A.: Volatility spread and expected stock returns. Manage Sci 55, 1797–1812 (2009)CrossRefGoogle Scholar
  5. Bansal, R., Yaron, A.: Risks for the long run: a potential resolution of asset-pricing puzzles. J Financ 59, 1481–1509 (2004)CrossRefGoogle Scholar
  6. Black, F.: Studies of stock market volatility changes. In: Proceedings of the American Statistical Association, Business and Economic Statistics Section, pp. 177–181, (1976)Google Scholar
  7. Bollerslev, T., Sizova, N., Tauchen, G.: Volatility in equilibrium: asymmetries and dynamic dependencies. Rev Financ 16, 31–80 (2012)CrossRefGoogle Scholar
  8. Bollerslev, T., Tauchen, G., Zhou, H.: Expected stock returns and variance risk premia. Rev Financ Stud 22, 4463–4492 (2009)CrossRefGoogle Scholar
  9. Campbell, J., Shiller, R.J.: The dividend-price ratio and expectations of future dividends and discount factors. Rev Financ Stud 1, 195–227 (1988)CrossRefGoogle Scholar
  10. Chan, W., Maheu, J.M.: Conditional jump dynamics in stock market returns. J Bus Econ Stat 20, 377–389 (2002)CrossRefGoogle Scholar
  11. Chang, B., Christoffersen, Y.P., Jacobs, K.: Market skewness risk and the cross section of stock returns. J Financ Econ 107, 46–68 (2013)CrossRefGoogle Scholar
  12. Christoffersen, P., Jacobs, K., Ornthanalai, C.: Dynamic jump intensities and risk premiums: evidence from S&P500 returns and options. J Financ Econ 106, 447–472 (2012)CrossRefGoogle Scholar
  13. Cont, R., Tankov, P.: Financial Modeling with Jump Processes. London: Chapman & Hall (2004)Google Scholar
  14. Demeterfi, K., Derman, E., Kamal, M., Zou, J.: A guide to volatility and variance swaps. J Deriv 6, 9–32 (1999)CrossRefGoogle Scholar
  15. Drechsler, I., Yaron, A.: What’s vol got to do with it? Rev Financ Stud 24, 1–45 (2011)CrossRefGoogle Scholar
  16. Driessen, J., Lin, T., Lu, X.: Why do option prices predict stock returns? Working paper (2012)Google Scholar
  17. Epstein, L., Zin, S.: Substitution, risk aversion and the temporal behavior of consumption and asset returns: a theoretical framework. Econometrica 57, 937–969 (1989)CrossRefGoogle Scholar
  18. Eraker, B.: The volatility premium. Working paper, Department of Finance, University of Wisconsin (2008)Google Scholar
  19. Lettau, M., Ludvigson, S.: Consumption, and expected stock returns. J Financ 56, 815–849 (2001)CrossRefGoogle Scholar
  20. Neuberger, A.: Realized skewness. Rev Financ Stud 26, 2174–2203 (2012)Google Scholar
  21. Rehman, Z., Vilkov, G.: Risk-neutral skewness: return predictability and its sources. Working paper (2012)Google Scholar
  22. Yan, S.: Jump risk, stock returns, and slope of implied volatility smile. J Financ Econ 99, 216–233 (2011)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Mizuho-DL Financial Technology Co., Ltd.TokyoJapan

Personalised recommendations