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A Model-Free Measure of Aggregate Idiosyncratic Volatility and the Prediction of Market Returns

Published online by Cambridge University Press:  27 August 2014

René Garcia ,
Daniel Mantilla-García  and
Lionel Martellini
René Garcia
Affiliation:
rene.garcia@edhec.edu, EDHEC Business School, 393 Promenade des Anglais, BP 3116, Nice 06202, France and CIREQ and CIRANO
Daniel Mantilla-García
Affiliation:
daniel@optimalam.com, Research Department, Optimal Asset Management, 171 Main St # 298, Los Altos, CA 94022, and EDHEC-Risk Institute
Lionel Martellini
Affiliation:
lionel.martellini@edhec.edu, EDHEC Business School, 393 Promenade des Anglais, BP 3116, Nice 06202, France.
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Abstract

In this paper, we formally show that the cross-sectional variance of stock returns is a consistent and asymptotically efficient estimator for aggregate idiosyncratic volatility. This measure has two key advantages: It is model free and observable at any frequency. Previous approaches have used monthly model-based measures constructed from time series of daily returns. The newly proposed cross-sectional volatility measure is a strong predictor for future returns on the aggregate stock market at the daily frequency. Using the cross section of size and book-to-market portfolios, we show that the portfolios’ exposures to the aggregate idiosyncratic volatility risk predict the cross section of expected returns.

Type
Research Articles
Information
Journal of Financial and Quantitative Analysis , Volume 49 , Issue 5-6 , December 2014 , pp. 1133 - 1165
Copyright
Copyright © Michael G. Foster School of Business, University of Washington 2015 

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References

Allen, L., and Bali, T.. “Cyclicality in Catastrophic and Operational Risk Measurements.” Journal of Banking and Finance, 31 (2007), 1191–1235.CrossRefGoogle 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
Baker, M., and Wurgler, J.. “Investor Sentiment and the Cross-Section of Stock Returns.” Journal of Finance, 61 (2006), 1645–1680.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.CrossRefGoogle Scholar
Bali, T.; Cakici, N.; and Levy, H.. “A Model-Independent Measure of Aggregate Idiosyncratic Risk.” Journal of Empirical Finance, 15 (2008), 878–896.CrossRefGoogle Scholar
Bali, T.; Cakici, N.; and Whitelaw, R.. “Maxing Out: Stocks as Lotteries and the Cross-Section of Expected Returns.” Journal of Financial Economics, 99 (2011), 427–446.Google Scholar
Bali, T.; Cakici, N.; Yan, X.; and Zhang, Z.. “Does Idiosyncratic Risk Really Matter?” Journal of Finance, 60 (2005), 905–929.Google Scholar
Bansal, R., and Yaron, A.. “Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles.” Journal of Finance, 59 (2004), 1481–1509.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
Barberis, N.; Huang, M.; and Santos, T.. “Prospect Theory and Asset Prices.” Quarterly Journal of Economics, 116 (2001), 1–53.CrossRefGoogle Scholar
Bekaert, G.; Hodrick, R. J.; and Zhang, X.. “Aggregate Idiosyncratic Volatility.” Journal of Financial and Quantitative Analysis, 47 (2012), 1155–1185.Google Scholar
Black, F. “The Pricing of Commodity Contracts.” Journal of Financial Economics, 3 (1976), 167–179.Google Scholar
Bollerslev, T.; Tauchen, G.; and Zhou, H.. “Expected Stock Returns and Variance Risk Premia.” Review of Financial Studies, 22 (2009), 4463–4492.Google Scholar
Bowley, S. Elements of Statistics, Vol. 2, London, UK: P. S. King and Son (1920).Google Scholar
Brandt, M.; Brav, A.; Graham, J.; and Kumar, A.. “The Idiosyncratic Volatility Puzzle: Time Trend or Speculative Episodes.” Review of Financial Studies, 23 (2010), 863–899.Google Scholar
Brunnermeier, M. K.; Gollier, C.; and Parker, J. A.. “Optimal Beliefs, Asset Prices, and the Preference for Skewed Returns.” American Economic Review, 97 (2007), 159–165.Google Scholar
Campbell, J.; Lettau, M.; Malkiel, B.; and Xu, Y.. “Have Individual Stocks Become More Volatile? An Empirical Exploration of Idiosyncratic Risk.” Journal of Finance, 56 (2001), 1–43.CrossRefGoogle Scholar
Cuzick, J. “A Strong Law for Weighted Sums of I.I.D. Random Variables.” Journal of Theoretical Probability, 8 (1995), 625–641.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. F., and MacBeth, J. D.. “Risk, Return, and Equilibrium: Empirical Tests.” Journal of Political Economy, 81 (1973), 607–636.Google Scholar
French, K. R.; Schwert, G. W.; and Stambaugh, R. F.. “Expected Stock Returns and Volatility.” Journal of Financial Economics, 19 (1987), 3–29.CrossRefGoogle Scholar
Fu, F. “Idiosyncratic Risk and the Cross-Section of Expected Stock Returns.” Journal of Financial Economics, 91 (2009), 24–37.Google Scholar
Goyal, A., and Santa-Clara, P.. “Idiosyncratic Risk Matters!” Journal of Finance, 58 (2003), 975–1008.Google Scholar
Groeneveld, R., and Meeden, G.. “Measuring Skewness and Kurtosis.” Statistician, 33 (1984), 391–399.Google Scholar
Guo, H., and Savickas, R.. “Average Idiosyncratic Volatility in G7 Countries.” Review of Financial Studies, 21 (2008), 1259–1296.Google Scholar
Hinkley, D. “On Power Transformations to Symmetry.” Biometrika, 62 (1975), 101–111.Google Scholar
Huang, W.; Liu, Q.; Rhee, S.; and Zhang, L.. “Return Reversals, Idiosyncratic Risk, and Expected Returns.” Review of Financial Studies, 23 (2010), 147–168.Google Scholar
Kachman, S. D. “Distribution of Linear Transformations and Quadratic Forms.” Working Paper, University of Nebraska, Lincoln (1999).Google Scholar
Kapadia, N. “The Next Microsoft? Skewness, Idiosyncratic Volatility, and Expected Returns.” Working Paper, University of North Carolina at Chapel Hill (2009).Google Scholar
Kim, T., and White, H.. “On More Robust Estimation of Skewness and Kurtosis.” Finance Research Letters, 1 (2004), 56–73.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
Malkiel, B., and Xu, Y.. “Idiosyncratic Risk and Security Returns.” Working Paper, University of Texas at Dallas (2002).Google Scholar
Merton, R. “On the Pricing of Corporate Debt: The Risk Structure of Interest Rates.” Journal of Finance, 29 (1974), 449–470.Google Scholar
Merton, R. “A Simple Model of Capital Market Equilibrium with Incomplete Information.” Journal of Finance, 42 (1987), 483–510.Google Scholar
Mitton, T., and Vorkink, K.. “Equilibrium Underdiversification and the Preference for Skewness.” Review of Financial Studies, 20 (2007), 1255–1288.Google Scholar
Newey, W., and West, K.. “A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix.” Econometrica: Journal of the Econometric Society, 55 (1987), 703–708.CrossRefGoogle Scholar
Pontiff, J. “Costly Arbitrage and the Myth of Idiosyncratic Risk.” Journal of Accounting and Economics, 42 (2006), 35–52.Google Scholar
Ross, S. “The Arbitrage Theory of Capital Asset Pricing.” Journal of Economic Theory, 13 (1976), 341–360.Google Scholar
Sharpe, W. “A Simplified Model for Portfolio Analysis.” Management Science, 9 (1963), 277–293.Google Scholar
Sung, S. H. “Strong Laws for Weighted Sums of I.I.D. Random Variables.” Bulletin of the Korean Mathematical Society, 39 (2002), 607–615.Google Scholar
Tédongap, R. “Consumption Volatility and the Cross-Section of Stock Returns.” Review of Finance, forthcoming (2014).Google Scholar
Wei, S., and Zhang, C.. “Idiosyncratic Risk Does Not Matter: A Re-Examination of the Relationship between Average Returns and Average Volatilities.” Journal of Banking and Finance, 29 (2005), 603–621.Google Scholar
Welch, I., and Goyal, A.. “A Comprehensive Look at the Empirical Performance of Equity Premium Prediction.” Review of Financial Studies, 21 (2008), 1455–1508.CrossRefGoogle Scholar