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Unknown Unknowns: Uncertainty About Risk and Stock Returns

  • Guido Baltussen, Sjoerd van Bekkum and Bart van der Grient

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.

Corresponding author
*Baltussen,, van Bekkum (corresponding author),, Erasmus University Rotterdam Erasmus School of Economics; and van der Grient,, Robeco Asset Management.
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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.

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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), 695723.
Ahn, D.; Choi, S.; Gale, D.; and Kariv, S.. “Estimating Ambiguity Aversion in a Portfolio Choice Experiment.” Quantitative Economics, 5 (2014), 195223.
Ali, A.; Hwang, L.; and Trombley, M.. “Arbitrage Risk and the Book-to-Market Anomaly.” Journal of Financial Economics, 69 (2003), 355373.
Amihud, Y.Illiquidity and Stock Returns: Cross-Section and Time-Series Effects.” Journal of Financial Markets, 5 (2002), 3156.
Amihud, Y., and Mendelson, H.. “Asset Pricing and the Bid–Ask Spread.” Journal of Financial Economics, 17 (1986), 223249.
An, B.-J.; Ang, A.; Bali, T.; and Cakici, N.. “The Joint Cross Section of Stocks and Options.” Journal of Finance, 69 (2014), 22792337.
Andrews, D.Tests for Parameter Instability and Structural Change with Unknown Change Point.” Econometrica, 61 (1993), 821856.
Ang, A.; Chen, J.; and Xing, Y.. “Downside Risk.” Review of Financial Studies, 19 (2006), 11911239.
Ang, A.; Hodrick, R.; Xing, Y.; and Zhang, X.. “The Cross-Section of Volatility and Expected Returns.” Journal of Finance, 61 (2006), 259299.
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), 123.
Bai, J., and Perron, P.. “Estimating and Testing Linear Models with Multiple Structural Changes.” Econometrica, 66 (1998), 4778.
Bakshi, G., and Kapadia, N.. “Delta-Hedged Gains and the Negative Market Volatility Risk Premium.” Review of Financial Studies, 16 (2003), 527566.
Bali, T., and Cakici, N.. “Idiosyncratic Volatility and the Cross Section of Expected Returns.” Journal of Financial and Quantitative Analysis, 43 (2008), 2958.
Bali, T., and Hovakimian, A.. “Volatility Spreads and Expected Stock Returns.” Management Science, 55 (2009), 17971812.
Ball, R., and Brown, P.. “An Empirical Evaluation of Accounting Income Numbers.” Journal of Accounting Research, 6 (1968), 159178.
Baltussen, G., and Post, G. T.. “Irrational Diversification: An Examination of Individual Portfolio Choice.” Journal of Financial and Quantitative Analysis, 46 (2011), 14631491.
Barberis, N., and Huang, M.. “Mental Accounting, Loss Aversion, and Individual Stock Returns.” Journal of Finance, 56 (2001), 12471292.
Barberis, N., and Huang, M.. “Stocks as Lotteries: The Implications of Probability Weighting for Security Prices.” American Economic Review, 98 (2008), 20662100.
Battalio, R., and Schultz, P.. “Options and the Bubble.” Journal of Finance, 61 (2006), 20712102.
Beber, A.; Driessen, J.; and Tuijp, P.. “Pricing Liquidity Risk with Heterogeneous Investment Horizons.” Discussion Paper, Centre for Economic Policy Research (2011).
Bossaerts, P.; Ghirardato, P.; Guarnaschelli, S.; and Zame, W.. “Ambiguity in Asset Markets: Theory and Experiment.” Review of Financial Studies, 23 (2010), 13251359.
Brenner, M., and Izhakian, Y.. “Asset Pricing and Ambiguity: Empirical Evidence.” Working Paper, New York University (2012).
Campbell, J.Intertemporal Asset Pricing without Consumption Data.” American Economic Review, 83 (1993), 487512.
Campbell, J.Understanding Risk and Return.” Journal of Political Economy, 104 (1996), 298345.
Cao, H.; Wang, T.; and Zhang, H.. “Model Uncertainty, Limited Market Participation, and Asset Prices.” Review of Financial Studies, 18 (2005), 12191251.
Carhart, M.On Persistence in Mutual Fund Performance.” Journal of Finance, 52 (1997), 5782.
Chapman, D., and Polkovnichenko, V.. “First-Order Risk Aversion, Heterogeneity, and Asset Market Outcomes.” Journal of Finance, 64 (2009), 18631887.
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), 345381.
Chen, Y.; Katuscak, P.; and Ozdenoren, E.. “Sealed Bid Auctions with Ambiguity: Theory and Experiments.” Journal of Economic Theory, 136 (2007), 513535.
Conte, A., and Hey, J. D.. “Assessing Multiple Prior Models of Behaviour under Ambiguity.” Journal of Risk and Uncertainty, 46 (2013), 113132.
Cremers, M.; Halling, M.; and Weinbaum, D.. “Aggregate Jump and Volatility Risk in the Cross-Section of Stock Returns.” Journal of Finance, 70 (2015), 577614.
Cremers, M., and Weinbaum, D.. “Deviations from Put-Call Parity and Stock Return Predictability.” Journal of Financial and Quantitative Analysis, 45 (2010), 335367.
Cubitt, R.; van de Kuilen, G.; and Mukerji, S.. “Sensitivity towards Ambiguity: A Qualitative Test and a Measurement.” Working Paper, University of Oxford (2012).
Daniel, K., and Titman, S.. “Evidence on the Characteristics of Cross Sectional Variation in Stock Returns.” Journal of Finance, 52 (1997), 133.
Daniel, K.; Titman, S.; and Wei, K.. “Explaining the Cross-Section of Stock Returns in Japan: Factors or Characteristics?Journal of Finance, 56 (2001), 743766.
Davis, J.; Fama, E.; and French, K.. “Characteristics, Covariances, and Average Returns: 1929 to 1997.” Journal of Finance, 55 (2000), 389406.
D’Avolio, G.The Market for Borrowing Stock.” Journal of Financial Economics, 66 (2002), 271306.
De Long, J.; Shleifer, A.; Summers, L. H.; and Waldmann, R. J.. “Noise Trader Risk in Financial Markets.” Journal of Political Economy, 98 (1990), 703738.
Diether, K.; Malloy, C.; and Scherbina, A.. “Differences of Opinion and the Cross Section of Stock Returns.” Journal of Finance, 57 (2002), 21132141.
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).
Dimson, E.Risk Measurement When Shares Are Subject to Infrequent Trading.” Journal of Financial Economics, 7 (1979), 197226.
Dittmar, R.Nonlinear Pricing Kernels, Kurtosis Preference, and Evidence from the Cross Section of Equity Returns.” Journal of Finance, 57 (2002), 369403.
Dow, J., and Werlang, S.. “Uncertainty Aversion, Risk Aversion, and the Optimal Choice of Portfolio.” Econometrica, 60 (1992), 197204.
Drechsler, I., and Yaron, A.. “What’s Vol Got To Do with It.” Review of Financial Studies, 24 (2011), 145.
Duarte, J.; Lou, X.; and Sadka, R.. “Option-Based Hedging of Liquidity Costs in Short Selling.” Working Paper, University of Washington (2005).
Easley, D., and O’Hara, M.. “Ambiguity and Nonparticipation: The Role of Regulation.” Review of Financial Studies, 22 (2009), 18171843.
Ellsberg, D.Risk, Ambiguity, and the Savage Axioms.” Quarterly Journal of Economics, 75 (1961), 643669.
Ergin, H., and Gul, F.. “A Theory of Subjective Compound Lotteries.” Journal of Economic Theory, 144 (2009), 899929.
Fama, E., and French, K.. “Common Risk Factors in the Returns on Stocks and Bonds.” Journal of Financial Economics, 33 (1993), 356.
Fama, E., and MacBeth, J.. “Risk, Return, and Equilibrium: Empirical Tests.” Journal of Political Economy, 81 (1973), 607636.
Frazzini, A., and Lamont, O.. “The Earnings Announcement Premium and Trading Volume.” Working Paper No. 13090, National Bureau of Economic Research (2007).
Frazzini, A., and Pedersen, L. H.. “Betting against Beta.” Journal of Financial Economics, 111 (2014), 125.
Goetzmann, W. N., and Kumar, A.. “Why Do Individual Investors Hold Under-Diversified Portfolios?” Working Paper, Yale School of Management (2005).
Halevy, Y.Ellsberg Revisited: An Experimental Study.” Econometrica, 75 (2007), 503536.
Harvey, C., and Siddique, A.. “Conditional Skewness in Asset Pricing Tests.” Journal of Finance, 55 (2000), 12631295.
Heath, C., and Tversky, A.. “Preference and Belief: Ambiguity and Competence in Choice under Uncertainty.” Journal of Risk and Uncertainty, 4 (1991), 528.
Hong, H., and Sraer, D.. “Speculative Betas.” Working Paper No. 18548, National Bureau of Economic Research (2012).
Klibanoff, P.; Marinacci, M.; and Mukerji, S.. “A Smooth Model of Decision Making under Ambiguity.” Econometrica, 73 (2005), 18491892.
Levy, H.Equilibrium in an Imperfect Market: A Constraint on the Number of Securities in the Portfolio.” American Economic Review, 68 (1978), 643658.
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), 1337.
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), 177205.
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), 333.
McNichols, M., and O’Brien, P.. “Self-Selection and Analyst Coverage.” Journal of Accounting Research, 35 (1997), 167199.
Mendenhall, R.Arbitrage Risk and Post-Earnings-Announcement Drift.” Journal of Business, 77 (2004), 875894.
Merton, R. C.A Simple Model of Capital Market Equilibrium with Incomplete Information.” Journal of Finance, 42 (1987), 483510.
Miller, E.Risk, Uncertainty, and Divergence of Opinion.” Journal of Finance, 32 (1977), 11511168.
Nagel, S.Short Sales, Institutional Investors and the Cross-Section of Stock Returns.” Journal of Financial Economics, 78 (2005), 277309.
Nau, R.A Generalization of Pratt-Arrow Measure to Nonexpected-Utility Preferences and Inseparable Probability and Utility.” Management Science, 49 (2003), 10891104.
Nau, R.Uncertainty Aversion with Second-Order Utilities and Probabilities.” Management Science, 52 (2006), 136145.
Neilson, W. S.A Simplified Axiomatic Approach to Ambiguity Aversion.” Journal of Risk and Uncertainty, 41 (2010), 113124.
Newey, W., and West, K.. “A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix.” Econometrica, 55 (1987), 703708.
Polkovnichenko, V.Household Portfolio Diversification: A Case for Rank-Dependent Preferences.” Review of Financial Studies, 18 (2005), 14671502.
Pontiff, J.Costly Arbitrage and the Myth of Idiosyncratic Risk.” Journal of Accounting and Economics, 42 (2006), 3552.
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), 925953.
Ross, S.The Arbitrage Theory of Capital Asset Pricing.” Journal of Economic Theory, 13 (1976), 341360.
Segal, U.The Ellsberg Paradox and Risk Aversion: An Anticipated Utility Approach.” International Economic Review, 28 (1987), 175202.
Segal, U.Two-Stage Lotteries Without the Reduction Axiom.” Econometrica, 58 (1990), 349377.
Seo, K.Ambiguity and Second-Order Belief.” Econometrica, 77 (2009), 15751605.
Sharpe, W.Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk.” Journal of Finance, 19 (1964), 425442.
Shleifer, A., and Vishny, R.. “The Limits of Arbitrage.” Journal of Finance, 52 (1997), 3555.
Uppal, R., and Wang, T.. “Model Misspecification and Underdiversification.” Journal of Finance, 58 (2003), 24652486.
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), 17701784.
Yan, S.Jump Risk, Stock Returns, and Slope of Implied Volatility Smile.” Journal of Financial Economics, 99 (2011), 216233.
Zhang, X.Information Uncertainty and Stock Returns.” Journal of Finance, 61 (2006), 105137.
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