Option-implied Value-at-Risk and the cross-section of stock returns

Abstract

Based on a novel rescaled option-implied Value-at-Risk (rVaR) measure, we show that option-implied information is priced differently depending on whether it is based on options with strikes close to the current price of the underlying or far-out-of-the-money options. If the rVaR is estimated from options close-to-the-money, i.e., the 50% rVaR, stocks with high risk outperform stocks with low risk by 0.60% per month, in line with downside risk-averse investors. In contrast, if rVaR is estimated from far-out-of-the-money options, i.e., the 90% rVaR, stocks with high risk underperform stocks with low risk by 0.42% per month, implying that stocks with low risk have higher returns in the cross-section of returns. Our results are consistent with investors who prefer reliable information over unreliable information and explain contradictory results of prior studies.

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References

  1. Aït-Sahalia, Y., & Lo, A. W. (1998). Nonparametric estimation of state-price densities implicit in financial asset prices. Journal of Finance, 53(2), 499–547.

    Article  Google Scholar 

  2. Amihud, Y. (2002). Illiquidity and stock returns: Cross-section and time-series effects. Journal of Financial Markets, 5(1), 31–56.

    Article  Google Scholar 

  3. An, B.-J., Ang, A., Bali, T. G., & Cakici, N. (2014). The joint cross section of stocks and options. Journal of Finance, 69(5), 2279–2337.

    Article  Google Scholar 

  4. Ang, A., Hodrick, R. J., Xing, Y., & Zhang, X. (2006). The cross-section of volatility and expected returns. Journal of Finance, 61(1), 259–299.

    Article  Google Scholar 

  5. Ang, A., Hodrick, R. J., Xing, Y., & Zhang, X. (2009). High idiosyncratic volatility and low returns: International and further U.S. evidence. Journal of Financial Economics, 91(1), 1–23.

    Article  Google Scholar 

  6. Augustin, P., Brenner, M., & Subrahmanyam, M. (2015). Informed options trading prior to M&A announcements: Insider trading? Working Paper.

  7. Bakshi, G., Kapadia, N., & Madan, D. (2003). Stock return characteristics, skew laws, and the differential pricing of individual equity options. Review of Financial Studies, 16(1), 101–143.

    Article  Google Scholar 

  8. Bali, T. G., & Murray, S. (2013). Does risk-neutral skewness predict the cross-section of equity option portfolio returns? Journal of Financial and Quantitative Analysis, 48(4), 1145–1171.

    Article  Google Scholar 

  9. Barberis, N., & Huang, M. (2008). Stocks as lotteries: The implications of probability weighting for security prices. American Economic Review, 98(5), 2066–2100.

    Article  Google Scholar 

  10. Barone Adesi, G. (2016). VaR and CVaR implied in option prices. Journal of Risk and Financial Management, 9(1), 2.

    Article  Google Scholar 

  11. Breeden, D. T., & Litzenberger, R. H. (1978). Prices of state-contingent claims implicit in option prices. Journal of Business, 51(4), 621–651.

    Article  Google Scholar 

  12. Cao, M., & Wei, J. (2010). Option market liquidity: Commonality and other characteristics. Journal of Financial Markets, 13(1), 20–48.

    Article  Google Scholar 

  13. Carr, P., & Wu, L. (2009). Variance risk premiums. Review of Financial Studies, 22(3), 1311–1341.

    Article  Google Scholar 

  14. Chakravarty, S., Gulen, H., & Mayhew, S. (2004). Informed trading in stock and option markets. Journal of Finance, 59(3), 1235–1257.

    Article  Google Scholar 

  15. Cleveland, W. S. (1979). Robust locally weighted regression and smoothing scatterplots. Journal of the American Statistical Association, 74(368), 829–836.

    Article  Google Scholar 

  16. Conrad, J., Dittmar, R. F., & Ghysels, E. (2013). Ex ante skewness and expected stock returns. Journal of Finance, 68(1), 85–124.

    Article  Google Scholar 

  17. Daniel, K., & Titman, S. (2006). Market reactions to tangible and intangible information. Journal of Finance, 61(4), 1605–1643.

    Article  Google Scholar 

  18. Easley, D., O’Hara, M., & Srinivas, P. S. (1998). Option volume and stock prices: Evidence on where informed traders trade. Journal of Finance, 53(2), 431–465.

    Article  Google Scholar 

  19. Fama, E. F., & French, K. R. (2016). Dissecting anomalies with a five-factor model. Review of Financial Studies, 29(1), 69–103.

    Article  Google Scholar 

  20. Frazzini, A., & Pedersen, L. H. (2014). Betting against beta. Journal of Financial Economics, 111(1), 1–25.

    Article  Google Scholar 

  21. Garleanu, N., Pedersen, L. H., & Poteshman, A. M. (2009). Demand-based option pricing. Review of Financial Studies, 22(10), 4259–4299.

    Article  Google Scholar 

  22. Gkionis, K., Kostakis, A., Skiadopoulos, G. S., & Stilger, P. S. (2018). Positive stock information in out-of-the-money option prices. Working Paper.

  23. Goncalves-Pinto, L., Grundy, B. D. , Hameed, A., van der Heijden, T., & Zhu, Y. (2016). Why do option prices predict stock returns? The role of price pressure in the stock market. Working Paper.

  24. Harvey, C. R., & Siddique, A. (2000). Conditional skewness in asset pricing tests. Journal of Finance, 55(3), 1263–1295.

    Article  Google Scholar 

  25. Jiang, G., Lee, C. M., & Zhang, Y. (2005). Information uncertainty and expected returns. Review of Accounting Studies, 10(2), 185–221.

    Article  Google Scholar 

  26. Jiang, G. J., & Tian, Y. S. (2007). Extracting model-free volatility from option prices: An examination of the VIX index. Journal of Derivatives, 14(3), 35–60.

    Article  Google Scholar 

  27. Jin, W., Livnat, J., & Zhang, Y. (2012). Option prices leading equity prices: Do option traders have an information advantage? Journal of Accounting Research, 50(2), 401–432.

    Article  Google Scholar 

  28. Kozhan, R., Neuberger, A., & Schneider, P. (2013). The skew risk premium in the equity index market. Review of Financial Studies, 26(9), 2174–2203.

    Article  Google Scholar 

  29. Kraus, A., & Litzenberger, R. H. (1976). Skewness preference and the valuation of risk assets. Journal of Finance, 31(4), 1085–1100.

    Google Scholar 

  30. Lettau, M., Maggiori, M., & Weber, M. (2014). Conditional risk premia in currency markets and other asset classes. Journal of Financial Economics, 114(2), 197–225.

    Article  Google Scholar 

  31. Li, Q., & Racine, J. (2004). Cross-validated local linear nonparametric regression. Statistica Sinica, 14(2), 485–512.

    Google Scholar 

  32. Lucca, D. O., & Moench, E. (2015). The pre-fomc announcement drift. The Journal of Finance, 70(1), 329–371.

    Article  Google Scholar 

  33. Newey, W. K., & West, K. D. (1987). A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica, 55(3), 703–708.

    Article  Google Scholar 

  34. Rehman, Z., & Vilkov, G. (2012). Risk-neutral skewness: Return predictability and its sources. Working Paper.

  35. Schneider, P., Wagner, C., & Zechner, J. (2018). Low risk anomalies? Working Paper.

  36. Shleifer, A., & Vishny, R. W. (1997). The limits of arbitrage. Journal of Finance, 52(1), 35–55.

    Article  Google Scholar 

  37. Stilger, P. S., Kostakis, A., & Poon, S.-H. (2016). What does risk-neutral skewness tell us about future stock returns? Management Science, 63(6), 1814–1834.

    Article  Google Scholar 

  38. Stone, C. J. (1977). Consistent nonparametric regression. Annals of Statistics, 5(4), 595–620.

    Article  Google Scholar 

  39. Tian, Y. S. (2011). Extracting risk-neutral density and its moments from American option prices. Journal of Derivatives, 18(3), 17–34.

    Article  Google Scholar 

  40. Xing, Y., Zhang, X., & Zhao, R. (2010). What does the individual option volatility smirk tell us about future equity returns? Journal of Financial and Quantitative Analysis, 45(3), 641–662.

    Article  Google Scholar 

  41. Zhang, X. (2006). Information uncertainty and stock returns. Journal of Finance, 61(1), 105–137.

    Article  Google Scholar 

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Correspondence to Alexander Feser.

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We thank Yakov Amihud, Fred Benth, Peter Carr, Magnus Dahlquist, Ralf Elsas, Joachim Grammig, Fabian Hollstein, Kjell Nyborg, Jens Jackwerth, Joël Peress, Marcel Prokopczuk, Stefan Ruenzi, Nic Schaub, Christian Schlag, David Schimko, Paul Söderlind, Erik Theissen, Grigory Vilkov, as well as the participants of the NYU Tandron Finance seminar, the annual conference of the Swiss Society for Financial Market Research 2017, of the 23rd annual meeting of the German Finance Association 2016, of the doctoral workshop at the 23rd annual meeting of the German Finance Association 2016, the Brown Bag Seminar of the University of St.Gallen, the 2016 joint seminar session of the University of St.Gallen and the University of Konstanz, and the 2015 Topics in Finance Seminar in Davos for helpful discussions and comments. All errors are our own.

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Ammann, M., Feser, A. Option-implied Value-at-Risk and the cross-section of stock returns. Rev Deriv Res 22, 449–474 (2019). https://doi.org/10.1007/s11147-019-09154-z

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Keywords

  • Option-implied moments
  • Option-implied skewness
  • Downside risk

JEL Classification

  • C14
  • G11
  • G12
  • G13
  • G14