Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-08T07:30:02.188Z Has data issue: false hasContentIssue false
  • English
  • Français

Volatility and Expected Option Returns

Published online by Cambridge University Press:  17 April 2019

Guanglian Hu  and
Kris Jacobs
Guanglian Hu
Affiliation:
Hu, [email protected], University of Sydney Business School Discipline of Finance
Kris Jacobs*
Affiliation:
Jacobs, [email protected], University of Houston Bauer College of Business
*
Jacobs (corresponding author), [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We analyze the relation between expected option returns and the volatility of the underlying securities. The expected return from holding a call (put) option is a decreasing (increasing) function of the volatility of the underlying. These predictions are supported by the data. In the cross section of equity option returns, returns on call (put) option portfolios decrease (increase) with underlying stock volatility. This finding is not due to cross-sectional variation in expected stock returns. It holds in various option samples with different maturities and moneyness, and is robust to alternative measures of underlying volatility and different weighting methods.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 55 , Issue 3 , May 2020 , pp. 1025 - 1060
Copyright
Copyright © Michael G. Foster School of Business, University of Washington 2019

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

We thank Torben Andersen, Michael Anderson, David Bates, Jay Cao, Hui Chen, Peter Christoffersen, Stefano Della Corta, Christian Dorion, Hitesh Doshi, Bjorn Eraker, Jan Ericsson, J.-S. Fontaine, Mathieu Fournier, Amit Goyal, Bing Han, Markus Huggenberger, Travis Johnson, Matthew Linn, Rui Liu, Dmitriy Muravyev, Benno Nguyen, Neil Pearson, Alessio Saretto, Gustavo Schwenkler, Viktor Todorov, Aurelio Vasquez, Liuren Wu, Chu Zhang, seminar participants at UMass, the 2016 China International Conference on Finance, the 2015 SFS Cavalcade, the 2016 IFSID Derivatives, 2016 MFA and 2017 FMA International Conferences, the 2016 Johns Hopkins Carey Business School Conference on the role of Derivatives in Asset Pricing, and especially Gurdip Bakshi, Scott Murray, Bruno Feunou, and Nikunj Kapadia for helpful comments.

References

Adrian, T., and Rosenberg, J.. “Stock Returns and Volatility: Pricing the Short-Run and Long-Run Components of Market Risk.” Journal of Finance, 63 (2008), 2997–3030.Google Scholar
An, B. J.; Ang, A.; Bali, T. G.; and Cakici, N.. “The Joint Cross Section of Stocks and Options.” Journal of Finance, 69 (2014), 2279–2337.Google Scholar
Ang, A.; Hodrick, R. J.; Xing, Y.; and Zhang, X.. “The Cross-Section of Volatility and Expected Returns.” Journal of Finance, 61 (2006), 259–299.Google Scholar
Ang, A.; Hodrick, R. J.; Xing, Y.; and Zhang, X.. “High Idiosyncratic Volatility and Low Returns: International and Further U.S. Evidence.” Journal of Financial Economics, 91 (2009), 1–23.Google Scholar
Bakshi, G.; Cao, C.; and Chen, Z.. “Empirical Performance of Alternative Option Pricing Models.” Journal of Finance, 52 (1997), 2003–2049.Google Scholar
Bakshi, G.; Cao, C.; and Zhong, Z.. “Assessing Models of Individual Equity Option Prices.” Working Paper, University of Maryland (2012).Google Scholar
Bakshi, G., and Kapadia, N.. “Delta-Hedged Gains and the Negative Market Volatility Risk Premium.” Review of Financial Studies, 16 (2003a), 527–566.Google Scholar
Bakshi, G., and Kapadia, N.. “Volatility Risk Premiums Embedded in Individual Equity Options: Some New Insights.” Journal of Derivatives, 11 (2003b), 45–54.Google Scholar
Bakshi, G.; Madan, D.; and Panayotov, G.. “Returns of Claims on the Upside and the Viability of U-Shaped Pricing Kernels.” Journal of Financial Economics, 97 (2010), 130–154.Google Scholar
Bali, T. G.“The Intertemporal Relation between Expected Returns and Risk.” Journal of Financial Economics, 87 (2008), 101–131.Google Scholar
Bali, T. G., and Cakici, N.. “Idiosyncratic Volatility and the Cross Section of Expected Returns.” Journal of Financial and Quantitative Analysis, 43 (2008), 29–58.Google Scholar
Bali, T. G.; Cakici, N.; Yan, X.; and Zhang, Z.. “Does Idiosyncratic Risk Really Matter?” Journal of Finance, 60 (2005), 905–929.Google Scholar
Bali, T. G., and Hovakimian, A.. “Volatility Spreads and Expected Stock Returns.” Management Science, 55 (2009), 1797–1812.Google Scholar
Barraclough, K., and Whaley, R. E.. “Early Exercise of Put Options on Stocks.” Journal of Finance, 67 (2012), 1423–1456.Google Scholar
Bates, D. S.“Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options.” Review of Financial Studies, 9 (1996), 69–107.Google Scholar
Bates, D. S.“Empirical Option Pricing: A Retrospection.” Journal of Econometrics, 116 (2003), 387–404.Google Scholar
Black, F., and Scholes, M.. “The Valuation of Option Contracts and a Test of Market Efficiency.” Journal of Finance, 27 (1972), 399–417.Google Scholar
Black, F., and Scholes, M.. “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy, 81 (1973), 637–654.Google Scholar
Bollen, N. P., and Whaley, R. E.. “Does Net Buying Pressure Affect the Shape of Implied Volatility Functions?” Journal of Finance, 59 (2004), 711–753.Google Scholar
Bollerslev, T.“Generalized Autoregressive Conditional Heteroskedasticity.” Journal of Econometrics, 31 (1986), 307–327.Google Scholar
Boyer, B. H., and Vorkink, K.. “Stock Options as Lotteries.” Journal of Finance, 69 (2014), 1485–1527.Google Scholar
Branger, N., and Schlag, C.. “Can Tests Based on Option Hedging Errors Correctly Identify Volatility Risk Premia?” Journal of Financial and Quantitative Analysis, 43 (2008), 1055–1090.Google Scholar
Broadie, M.; Chernov, M.; and Johannes, M.. “Model Specification and Risk Premia: Evidence from Futures Options.” Journal of Finance, 62 (2007), 1453–1490.Google Scholar
Broadie, M.; Chernov, M.; and Johannes, M.. “Understanding Index Option Returns.” Review of Financial Studies, 22 (2009), 4493–4529.Google Scholar
Byun, S. J., and Kim, D. H.. “Gambling Preference and Individual Equity Option Returns.” Journal of Financial Economics, 122 (2016), 155–174.Google Scholar
Campbell, J., and Hentschel, L.. “No News Is Good News: An Asymmetric Model of Changing Volatility in Stock Returns.” Journal of Financial Economics, 31 (1992), 281–318.Google Scholar
Cao, J., and Han, B.. “Cross Section of Option Returns and Idiosyncratic Stock Volatility.” Journal of Financial Economics, 108 (2013), 231–249.Google Scholar
Carr, P., and Wu, L.. “Variance Risk Premiums.” Review of Financial Studies, 22 (2009), 1311–1341.Google Scholar
Chang, B. Y.; Christoffersen, P.; and Jacobs, K.. “Market Skewness Risk and the Cross Section of Stock Returns.” Journal of Financial Economics, 107 (2013), 46–68.Google Scholar
Chaudhuri, R., and Schroder, M.. “Monotonicity of the Stochastic Discount Factor and Expected Option Returns.” Review of Financial Studies, 22 (2015), 1981–2006.Google Scholar
Chen, Z., and Petkova, R.. “Does Idiosyncratic Volatility Proxy for Risk Exposure?” Review of Financial Studies, 25 (2012), 2745–2787.Google Scholar
Chernov, M., and Ghysels, E.. “A Study towards a Unified Approach to the Joint Estimation of Objective and Risk Neutral Measures for the Purpose of Option Valuation.” Journal of Financial Economics, 56 (2000), 407–458.Google Scholar
Christoffersen, P.; Heston, S.; and Jacobs, K.. “Capturing Option Anomalies with a Variance-Dependent Pricing Kernel.” Review of Financial Studies, 26 (2013), 1963–2006.Google Scholar
Conrad, J.; Dittmar, R. F.; and Ghysels, E.. “Ex Ante Skewness and Expected Stock Returns.” Journal of Finance, 68 (2013), 85–124.Google Scholar
Coval, J. D., and Shumway, T.. “Expected Option Returns.” Journal of Finance, 56 (2001), 983–1009.Google Scholar
Cremers, M., and Weinbaum, D.. “Deviations from Put-Call Parity and Stock Return Predictability.” Journal of Financial and Quantitative Analysis, 45 (2010), 335–367.Google Scholar
Cuzick, J.“A Wilcoxon-Type Test for Trend.” Statistics in Medicine, 4 (1985), 543–547.Google Scholar
Driessen, J.; Maenhout, P. J.; and Vilkov, G.. “The Price of Correlation Risk: Evidence from Equity Options.” Journal of Finance, 64 (2009), 1377–1406.Google Scholar
Duan, J. C., and Wei, J.. “Systematic Risk and the Price Structure of Individual Equity Options.” Review of Financial Studies, 22 (2009), 1981–2006.Google Scholar
Duarte, J., and Jones, C. S.. “The Price of Market Volatility Risk.” Working Paper, University of Southern California (2007).Google Scholar
Engle, R. F.“Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation.” Econometrica, 50 (1982), 987–1007.Google Scholar
Engle, R. F., and Ng, V.. “Measuring and Testing the Impact of News on Volatility.” Journal of Finance, 48 (1993), 1749–1778.Google Scholar
Eraker, B.“Do Stock Prices and Volatility Jump? Reconciling Evidence from Spot and Option Prices.” Journal of Finance, 59 (2004), 1367–1403.Google Scholar
Fama, E. F., and MacBeth, J. D.. “Risk, Return, and Equilibrium: Empirical Tests.” Journal of Political Economy, 81 (1973), 607–636.Google Scholar
French, K.; Schwert, G.; and Stambaugh, R.. “Expected Stock Returns and Volatility.” Journal of Financial Economics, 19 (1987), 3–30.Google Scholar
Fu, F.“Idiosyncratic Risk and the Cross-Section of Expected Stock Returns.” Journal of Financial Economics, 91 (2009), 24–37.Google Scholar
Galai, D., and Masulis, R. W.. “The Option Pricing Model and the Risk Factor of Stock.” Journal of Financial Economics, 3 (1976), 53–81.Google Scholar
Garcia, R.; Ghysels, E.; and Renault, E.. “The Econometrics of Option Pricing.” Handbook of Financial Econometrics, 1 (2010), 479–552.Google Scholar
Garleanu, N.; Pedersen, L.; and Poteshman, A.. “Demand-Based Option Pricing.” Review of Financial Studies, 22 (2009), 4259–4299.Google Scholar
Ghysels, E.; Santa-Clara, P.; and Valkanov, R.. “There Is a Risk-Return Trade-Off After All.” Journal of Financial Economics, 76 (2005), 509–548.Google Scholar
Glosten, L. R.; Jagannathan, R.; and Runkle, D. E.. “On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks.” Journal of Finance, 48 (1993), 1779–1801.Google Scholar
Goodman, Theodore; Neamtiu, M.; and Zhang, X. F.. “Fundamental Analysis and Option Returns.” Journal of Accounting, Auditing and Finance, 33 (2018), 72–97.Google Scholar
Gourier, E.“Pricing of Idiosyncratic Equity and Variance Risks.” Working Paper, Queen Mary University of London (2015).Google Scholar
Goyal, A., and Santa-Clara, P.. “Idiosyncratic Risk Matters!.” Journal of Finance, 58 (2003), 975–1008.Google Scholar
Goyal, A., and Saretto, A.. “Cross-Section of Option Returns and Volatility.” Journal of Financial Economics, 94 (2009), 310–326.Google Scholar
Heston, S. L.“A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options.” Review of Financial Studies, 6 (1993), 327–343.Google Scholar
Huang, W.; Liu, Q.; Rhee, S. G.; and Zhang, L.. “Return Reversals, Idiosyncratic Risk, and Expected Returns.” Review of Financial Studies, 23 (2009), 147–168.Google Scholar
Johnson, T. C.“Forecast Dispersion and the Cross Section of Expected Returns.” Journal of Finance, 59 (2004), 1957–1978.Google Scholar
Jones, C.“The Dynamics of Stochastic Volatility: Evidence from Underlying and Options Markets.” Journal of Econometrics, 116 (2003), 181–224.Google Scholar
Karakaya, M.“Characteristics and Expected Returns in Individual Equity Options.” Working Paper, University of Chicago (2014).Google Scholar
Linn, M.“Risk and Return in Equity and Options Markets.” Working Paper, University of Michigan (2014).Google Scholar
Lyle, M. R.“How Does Information Quality Affect Option and Stock Returns?” Working Paper, Northwestern University (2014).Google Scholar
Merton, R. C.“Theory of Rational Option Pricing.” Bell Journal of Economics and Management Science, 4 (1973), 141–183.Google Scholar
Muravyev, D.“Order Flow and Expected Option Returns.” Journal of Finance, 71 (2016), 673–708.Google Scholar
Nelson, D. B.“Conditional Heteroskedasticity in Asset Returns: A New Approach.” Econometrica, 59 (1991), 347–370.Google Scholar
Newey, W. K., and West, K. D.. “A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix.” Econometrica, 55 (1987), 703–708.Google Scholar
Ni, S. X.; Pearson, N.; and Poteshman, A.. “Stock Price Clustering on Option Expiration Dates.” Journal of Financial Economics, 78 (2005), 49–87.Google Scholar
Pan, J.“The Jump-Risk Premia Implicit in Options: Evidence from an Integrated Time-Series Study.” Journal of Financial Economics, 63 (2002), 3–50.Google Scholar
Patton, A. J., and Timmermann, A.. “Monotonicity in Asset Returns: New Tests with Applications to the Term Structure, the CAPM, and Portfolio Sorts.” Journal of Financial Economics, 98 (2010), 605–625.Google Scholar
Rubinstein, M.“A Simple Formula for the Expected Rate of Return of an Option over a Finite Holding Period.” Journal of Finance, 39 (1984), 1503–1509.Google Scholar
Schaefer, S., and Strebulaev, I.. “Structural Models of Credit Risk Are Useful: Evidence from Hedge Ratios on Corporate Bonds.” Journal of Financial Economics, 90 (2008), 1–19.Google Scholar
Stambaugh, R. F.; Yu, J.; and Yuan, Y.. “Arbitrage Asymmetry and the Idiosyncratic Volatility Puzzle.” Journal of Finance, 70 (2015), 1903–1948.Google Scholar
Vasquez, A.“Equity Volatility Term Structures and the Cross Section of Option Returns.” Journal of Financial and Quantitative Analysis, 52 (2017), 2727–2754.Google Scholar
Xing, Y.; Zhang, X.; and Zhao, R.. “What Does the Individual Option Volatility Smirk Tell Us about Future Equity Returns?” Journal of Financial and Quantitative Analysis, 45 (2010), 641–662.Google Scholar
Supplementary material: File

Hu and Jacobs supplementary material

Hu and Jacobs supplementary material

Download Hu and Jacobs supplementary material(File)
File 159.8 KB