Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-15T08:57:10.707Z Has data issue: false hasContentIssue false
  • English
  • Français

Unknown Unknowns: Uncertainty About Risk and Stock Returns

Published online by Cambridge University Press:  18 July 2018

Guido Baltussen ,
Sjoerd van Bekkum  and
Bart van der Grient
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Stocks with high uncertainty about risk, as measured by the volatility of expected volatility (vol-of-vol), robustly underperform stocks with low uncertainty about risk by 8% per year. This vol-of-vol effect is distinct from (combinations of) at least 20 previously documented return predictors, survives many robustness checks, and holds in the United States and across European stock markets. We empirically explore the pricing mechanism behind the vol-of-vol effect. The evidence points toward preference-based explanations and away from alternative explanations. Collectively, our results show that uncertainty about risk is highly relevant for stock prices.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 53 , Issue 4 , August 2018 , pp. 1615 - 1651
Copyright
Copyright © Michael G. Foster School of Business, University of Washington 2018 

Footnotes

1

This paper has benefited greatly from extensive discussions with Jules van Binsbergen, Menachem Brenner, Stephen Brown, George Constantinides, Zhi Da, Wayne Ferson, Mark Grinblatt, Arthur Korteweg, Tyler Shumway, Aurelio Vasquez, Peter Wakker, Robert Whitelaw, Jeffrey Wurgler, and Hao Zhou. We also thank Nusret Cakici (the referee), Paul Malatesta (the editor), and conference participants and discussants at the 2012 Eastern Finance Association Meeting, the 2012 European Finance Association Meeting, the 2013 American Finance Association Meeting, and the 2013 Luxembourg Asset Management Summit. Baltussen and van Bekkum gratefully acknowledge financial support from the Tinbergen Institute, the Erasmus Research Institute of Management, and the Erasmus Trustfonds. van Bekkum also gratefully acknowledges financial support from the Niels Stensen Foundation. Part of this research project was completed when either Baltussen or van Bekkum was at New York University.

References

Abdellaoui, M.; Baillon, A.; Placido, L.; and Wakker, P.. “The Rich Domain of Uncertainty: Source Functions and Their Experimental Implementation.” American Economic Review, 101 (2011), 695–723.Google Scholar
Ahn, D.; Choi, S.; Gale, D.; and Kariv, S.. “Estimating Ambiguity Aversion in a Portfolio Choice Experiment.” Quantitative Economics, 5 (2014), 195–223.Google Scholar
Ali, A.; Hwang, L.; and Trombley, M.. “Arbitrage Risk and the Book-to-Market Anomaly.” Journal of Financial Economics, 69 (2003), 355–373.Google Scholar
Amihud, Y.“Illiquidity and Stock Returns: Cross-Section and Time-Series Effects.” Journal of Financial Markets, 5 (2002), 31–56.Google Scholar
Amihud, Y., and Mendelson, H.. “Asset Pricing and the Bid–Ask Spread.” Journal of Financial Economics, 17 (1986), 223–249.Google Scholar
An, B.-J.; Ang, A.; Bali, T.; and Cakici, N.. “The Joint Cross Section of Stocks and Options.” Journal of Finance, 69 (2014), 2279–2337.Google Scholar
Andrews, D.“Tests for Parameter Instability and Structural Change with Unknown Change Point.” Econometrica, 61 (1993), 821–856.Google Scholar
Ang, A.; Chen, J.; and Xing, Y.. “Downside Risk.” Review of Financial Studies, 19 (2006), 1191–1239.Google Scholar
Ang, A.; Hodrick, R.; 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.; 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
Bai, J., and Perron, P.. “Estimating and Testing Linear Models with Multiple Structural Changes.” Econometrica, 66 (1998), 47–78.Google Scholar
Bakshi, G., and Kapadia, N.. “Delta-Hedged Gains and the Negative Market Volatility Risk Premium.” Review of Financial Studies, 16 (2003), 527–566.Google Scholar
Bali, T., 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., and Hovakimian, A.. “Volatility Spreads and Expected Stock Returns.” Management Science, 55 (2009), 1797–1812.Google Scholar
Ball, R., and Brown, P.. “An Empirical Evaluation of Accounting Income Numbers.” Journal of Accounting Research, 6 (1968), 159–178.Google Scholar
Baltussen, G., and Post, G. T.. “Irrational Diversification: An Examination of Individual Portfolio Choice.” Journal of Financial and Quantitative Analysis, 46 (2011), 1463–1491.Google Scholar
Barberis, N., and Huang, M.. “Mental Accounting, Loss Aversion, and Individual Stock Returns.” Journal of Finance, 56 (2001), 1247–1292.Google Scholar
Barberis, N., and Huang, M.. “Stocks as Lotteries: The Implications of Probability Weighting for Security Prices.” American Economic Review, 98 (2008), 2066–2100.Google Scholar
Battalio, R., and Schultz, P.. “Options and the Bubble.” Journal of Finance, 61 (2006), 2071–2102.Google Scholar
Beber, A.; Driessen, J.; and Tuijp, P.. “Pricing Liquidity Risk with Heterogeneous Investment Horizons.” Discussion Paper, Centre for Economic Policy Research (2011).Google Scholar
Bossaerts, P.; Ghirardato, P.; Guarnaschelli, S.; and Zame, W.. “Ambiguity in Asset Markets: Theory and Experiment.” Review of Financial Studies, 23 (2010), 1325–1359.Google Scholar
Brenner, M., and Izhakian, Y.. “Asset Pricing and Ambiguity: Empirical Evidence.” Working Paper, New York University (2012).Google Scholar
Campbell, J.“Intertemporal Asset Pricing without Consumption Data.” American Economic Review, 83 (1993), 487–512.Google Scholar
Campbell, J.“Understanding Risk and Return.” Journal of Political Economy, 104 (1996), 298–345.Google Scholar
Cao, H.; Wang, T.; and Zhang, H.. “Model Uncertainty, Limited Market Participation, and Asset Prices.” Review of Financial Studies, 18 (2005), 1219–1251.Google Scholar
Carhart, M.“On Persistence in Mutual Fund Performance.” Journal of Finance, 52 (1997), 57–82.Google Scholar
Chapman, D., and Polkovnichenko, V.. “First-Order Risk Aversion, Heterogeneity, and Asset Market Outcomes.” Journal of Finance, 64 (2009), 1863–1887.Google Scholar
Chen, J.; Hong, H.; and Stein, J.. “Forecasting Crashes: Trading Volume, Past Returns, and Conditional Skewness in Stock Prices.” Journal of Financial Economics, 61 (2001), 345–381.Google Scholar
Chen, Y.; Katuscak, P.; and Ozdenoren, E.. “Sealed Bid Auctions with Ambiguity: Theory and Experiments.” Journal of Economic Theory, 136 (2007), 513–535.Google Scholar
Conte, A., and Hey, J. D.. “Assessing Multiple Prior Models of Behaviour under Ambiguity.” Journal of Risk and Uncertainty, 46 (2013), 113–132.Google Scholar
Cremers, M.; Halling, M.; and Weinbaum, D.. “Aggregate Jump and Volatility Risk in the Cross-Section of Stock Returns.” Journal of Finance, 70 (2015), 577–614.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
Cubitt, R.; van de Kuilen, G.; and Mukerji, S.. “Sensitivity towards Ambiguity: A Qualitative Test and a Measurement.” Working Paper, University of Oxford (2012).Google Scholar
Daniel, K., and Titman, S.. “Evidence on the Characteristics of Cross Sectional Variation in Stock Returns.” Journal of Finance, 52 (1997), 1–33.Google Scholar
Daniel, K.; Titman, S.; and Wei, K.. “Explaining the Cross-Section of Stock Returns in Japan: Factors or Characteristics?” Journal of Finance, 56 (2001), 743–766.Google Scholar
Davis, J.; Fama, E.; and French, K.. “Characteristics, Covariances, and Average Returns: 1929 to 1997.” Journal of Finance, 55 (2000), 389–406.Google Scholar
D’Avolio, G.“The Market for Borrowing Stock.” Journal of Financial Economics, 66 (2002), 271–306.Google Scholar
De Long, J.; Shleifer, A.; Summers, L. H.; and Waldmann, R. J.. “Noise Trader Risk in Financial Markets.” Journal of Political Economy, 98 (1990), 703–738.Google Scholar
Diether, K.; Malloy, C.; and Scherbina, A.. “Differences of Opinion and the Cross Section of Stock Returns.” Journal of Finance, 57 (2002), 2113–2141.Google Scholar
Dimmock, S. G.; Kouwenberg, R.; Mitchell, O. S.; and Peijnenburg, K.. “Ambiguity Attitudes and Economic Behavior.” Working Paper No. 18743, National Bureau of Economic Research (2013).Google Scholar
Dimson, E.“Risk Measurement When Shares Are Subject to Infrequent Trading.” Journal of Financial Economics, 7 (1979), 197–226.Google Scholar
Dittmar, R.“Nonlinear Pricing Kernels, Kurtosis Preference, and Evidence from the Cross Section of Equity Returns.” Journal of Finance, 57 (2002), 369–403.Google Scholar
Dow, J., and Werlang, S.. “Uncertainty Aversion, Risk Aversion, and the Optimal Choice of Portfolio.” Econometrica, 60 (1992), 197–204.Google Scholar
Drechsler, I., and Yaron, A.. “What’s Vol Got To Do with It.” Review of Financial Studies, 24 (2011), 1–45.Google Scholar
Duarte, J.; Lou, X.; and Sadka, R.. “Option-Based Hedging of Liquidity Costs in Short Selling.” Working Paper, University of Washington (2005).Google Scholar
Easley, D., and O’Hara, M.. “Ambiguity and Nonparticipation: The Role of Regulation.” Review of Financial Studies, 22 (2009), 1817–1843.Google Scholar
Ellsberg, D.“Risk, Ambiguity, and the Savage Axioms.” Quarterly Journal of Economics, 75 (1961), 643–669.Google Scholar
Ergin, H., and Gul, F.. “A Theory of Subjective Compound Lotteries.” Journal of Economic Theory, 144 (2009), 899–929.Google Scholar
Fama, E., and French, K.. “Common Risk Factors in the Returns on Stocks and Bonds.” Journal of Financial Economics, 33 (1993), 3–56.Google Scholar
Fama, E., and MacBeth, J.. “Risk, Return, and Equilibrium: Empirical Tests.” Journal of Political Economy, 81 (1973), 607–636.Google Scholar
Frazzini, A., and Lamont, O.. “The Earnings Announcement Premium and Trading Volume.” Working Paper No. 13090, National Bureau of Economic Research (2007).Google Scholar
Frazzini, A., and Pedersen, L. H.. “Betting against Beta.” Journal of Financial Economics, 111 (2014), 1–25.Google Scholar
Goetzmann, W. N., and Kumar, A.. “Why Do Individual Investors Hold Under-Diversified Portfolios?” Working Paper, Yale School of Management (2005).Google Scholar
Halevy, Y.“Ellsberg Revisited: An Experimental Study.” Econometrica, 75 (2007), 503–536.Google Scholar
Harvey, C., and Siddique, A.. “Conditional Skewness in Asset Pricing Tests.” Journal of Finance, 55 (2000), 1263–1295.Google Scholar
Heath, C., and Tversky, A.. “Preference and Belief: Ambiguity and Competence in Choice under Uncertainty.” Journal of Risk and Uncertainty, 4 (1991), 5–28.Google Scholar
Hong, H., and Sraer, D.. “Speculative Betas.” Working Paper No. 18548, National Bureau of Economic Research (2012).Google Scholar
Klibanoff, P.; Marinacci, M.; and Mukerji, S.. “A Smooth Model of Decision Making under Ambiguity.” Econometrica, 73 (2005), 1849–1892.Google Scholar
Levy, H.“Equilibrium in an Imperfect Market: A Constraint on the Number of Securities in the Portfolio.” American Economic Review, 68 (1978), 643–658.Google Scholar
Lintner, J.“The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets.” Review of Economics and Statistics, 47 (1965), 13–37.Google Scholar
Livnat, J., and Mendenhall, R. R.. “Comparing the Post–Earnings Announcement Drift for Surprises Calculated from Analyst and Time Series Forecasts.” Journal of Accounting Research, 44 (2006), 177–205.Google Scholar
Mashruwala, C.; Rajgopal, S.; and Shevlin, T.. “Why Is the Accrual Anomaly Not Arbitraged Away? The Role of Idiosyncratic Risk and Transaction Costs.” Journal of Accounting and Economics, 42 (2006), 3–33.Google Scholar
McNichols, M., and O’Brien, P.. “Self-Selection and Analyst Coverage.” Journal of Accounting Research, 35 (1997), 167–199.Google Scholar
Mendenhall, R.“Arbitrage Risk and Post-Earnings-Announcement Drift.” Journal of Business, 77 (2004), 875–894.Google Scholar
Merton, R. C.“A Simple Model of Capital Market Equilibrium with Incomplete Information.” Journal of Finance, 42 (1987), 483–510.Google Scholar
Miller, E.“Risk, Uncertainty, and Divergence of Opinion.” Journal of Finance, 32 (1977), 1151–1168.Google Scholar
Nagel, S.“Short Sales, Institutional Investors and the Cross-Section of Stock Returns.” Journal of Financial Economics, 78 (2005), 277–309.Google Scholar
Nau, R.“A Generalization of Pratt-Arrow Measure to Nonexpected-Utility Preferences and Inseparable Probability and Utility.” Management Science, 49 (2003), 1089–1104.Google Scholar
Nau, R.“Uncertainty Aversion with Second-Order Utilities and Probabilities.” Management Science, 52 (2006), 136–145.Google Scholar
Neilson, W. S.“A Simplified Axiomatic Approach to Ambiguity Aversion.” Journal of Risk and Uncertainty, 41 (2010), 113–124.Google Scholar
Newey, W., and West, K.. “A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix.” Econometrica, 55 (1987), 703–708.Google Scholar
Polkovnichenko, V.“Household Portfolio Diversification: A Case for Rank-Dependent Preferences.” Review of Financial Studies, 18 (2005), 1467–1502.Google Scholar
Pontiff, J.“Costly Arbitrage and the Myth of Idiosyncratic Risk.” Journal of Accounting and Economics, 42 (2006), 35–52.Google Scholar
Post, T., and Levy, H.. “Does Risk Seeking Drive Stock Prices? A Stochastic Dominance Analysis of Aggregate Investor Preferences and Beliefs.” Review of Financial Studies, 18 (2005), 925–953.Google Scholar
Ross, S.“The Arbitrage Theory of Capital Asset Pricing.” Journal of Economic Theory, 13 (1976), 341–360.Google Scholar
Segal, U.“The Ellsberg Paradox and Risk Aversion: An Anticipated Utility Approach.” International Economic Review, 28 (1987), 175–202.Google Scholar
Segal, U.“Two-Stage Lotteries Without the Reduction Axiom.” Econometrica, 58 (1990), 349–377.Google Scholar
Seo, K.“Ambiguity and Second-Order Belief.” Econometrica, 77 (2009), 1575–1605.Google Scholar
Sharpe, W.“Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk.” Journal of Finance, 19 (1964), 425–442.Google Scholar
Shleifer, A., and Vishny, R.. “The Limits of Arbitrage.” Journal of Finance, 52 (1997), 35–55.Google Scholar
Uppal, R., and Wang, T.. “Model Misspecification and Underdiversification.” Journal of Finance, 58 (2003), 2465–2486.Google Scholar
Wakker, P.; Timmermans, D.; and Machielse, I.. “The Effects of Statistical Information on Risk and Ambiguity Attitudes, and on Rational Insurance Decisions.” Management Science, 53 (2007), 1770–1784.Google Scholar
Yan, S.“Jump Risk, Stock Returns, and Slope of Implied Volatility Smile.” Journal of Financial Economics, 99 (2011), 216–233.Google Scholar
Zhang, X.“Information Uncertainty and Stock Returns.” Journal of Finance, 61 (2006), 105–137.Google Scholar
Supplementary material: File

Baltussen et al. supplementary material

Baltussen et al. supplementary material 1

Download Baltussen et al. supplementary material(File)
File 357.2 KB