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Asymmetry in Stock Comovements: An Entropy Approach

Published online by Cambridge University Press:  06 August 2018

Lei Jiang ,
Ke Wu  and
Guofu Zhou
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Abstract

We provide an entropy approach for measuring the asymmetric comovement between the return on a single asset and the market return. This approach yields a model-free test for stock return asymmetry, generalizing the correlation-based test proposed by Hong, Tu, and Zhou (2007). Based on this test, we find that asymmetry is much more pervasive than previously thought. Moreover, our approach also provides an entropy-based measure of downside asymmetric comovement. In the cross section of stock returns, we find an asymmetry premium: Higher downside asymmetric comovement with the market indicates higher expected returns.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 53 , Issue 4 , August 2018 , pp. 1479 - 1507
Copyright
Copyright © Michael G. Foster School of Business, University of Washington 2018 

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Footnotes

1

We are grateful to Vikas Agarwal, Doron Avramov, Jonathan Brogaard, Jeffrey Busse, Hui Chen, Tarun Chordia, Lauren Cohen, Philip Dybvig, Andrey Ermolov, Ping He, Zhiguo He, David Jacho-Chavez, Ying Jiang, Raymond Kan, Omesh Kini, Junghoon Lee, Tingjun Liu, Esfandiar Maasoumi, Michael Powers, Jun Tu, Aurelio Vasquez, Baozhong Yang, and seminar participants at Cornerstone Research, Case Western Reserve University, Emory University, Georgia State University, Harbin Institute of Technology, ITAM, Peking University, Washington University in St. Louis, the 2014 and 2015 Tsinghua Finance Workshops, the 2015 China Finance Review International Conference, the 2015 Five-Star Workshop in Finance, the 2015 China International Conference in Finance, and the 2017 Midwest Finance Association Annual Meeting for numerous helpful comments and especially to Jennifer Conrad (the editor) and Riccardo Colacito (the referee) for their many insightful and detailed comments that have substantially improved the article. Jiang gratefully acknowledges financial support from the AXA Research Fund, the Initiative Research Program supported by Tsinghua University (20151080398), the National Natural Science Foundation of China (71572091), and the Tsinghua National Laboratory for Information Science and Technology. The authors thank Jing Ding and Jinyu Liu for excellent research assistance.

References

Acharya, V. V., and Pedersen, L. H.. “Asset Pricing with Liquidity Risk.” Journal of Financial Economics, 77 (2005), 375–410.Google Scholar
Alcock, J., and Hatherley, A.. “Characterizing the Asymmetric Dependence Premium.” Review of Finance, 21 (2017), 1701–1737.Google Scholar
Amaya, D.; Christoffersen, P.; Jacobs, K.; and Vasquez, A.. “Does Realized Skewness Predict the Cross-Section of Equity Returns?” Journal of Financial Economics, 118 (2015), 135–167.Google Scholar
Ang, A.; Bekaert, G.; and Liu, J.. “Why Stocks May Disappoint.” Journal of Financial Economics, 76 (2005), 471–508.Google Scholar
Ang, A., and Chen, J.. “Asymmetric Correlations of Equity Portfolios.” Journal of Financial Economics, 63 (2002), 443–494.Google Scholar
Ang, A.; Chen, J.; and Xing, Y.. “Downside Risk.” Review of Financial Studies, 19 (2006), 1191–1239.Google Scholar
Backus, D.; Boyarchenko, N.; and Chernov, M.. “Term Structures of Asset Prices and Returns.” Journal of Financial Economics, 129 (2018), 1–23.Google Scholar
Backus, D.; Chernov, M.; and Zin, S.. “Sources of Entropy in Representative Agent Models.” Journal of Finance, 69 (2014), 51–99.Google Scholar
Bae, K.-H.; Karolyi, G. A.; and Stulz, R. M.. “A New Approach to Measuring Financial Contagion.” Review of Financial Studies, 16 (2003), 717–763.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. G.; Cakici, N.; and Whitelaw, R. F.. “Maxing Out: Stocks as Lotteries and the Cross-Section of Expected Returns.” Journal of Financial Economics, 99 (2011), 427–446.Google Scholar
Ball, R., and Kothari, S.. “Nonstationary Expected Returns: Implications for Tests of Market Efficiency and Serial Correlation in Returns.” Journal of Financial Economics, 25 (1989), 51–74.Google Scholar
Bekaert, G., and Engstrom, E.. “Asset Return Dynamics under Habits and Bad-Environment Good-Environment Fundamentals.” Journal of Political Economy, 125 (2017), 713–760.Google Scholar
Bekaert, G.; Engstrom, E.; and Ermolov, A.. “Bad Environments, Good Environments: A Non-Gaussian Asymmetric Volatility Model.” Journal of Econometrics, 186 (2015), 258–275.Google Scholar
Bekaert, G., and Wu, G.. “Asymmetric Volatility and Risk in Equity Markets.” Review of Financial Studies, 13 (2000), 1–42.Google Scholar
Cabrales, A.; Gossner, O.; and Serrano, R.. “Entropy and the Value of Information for Investors.” American Economic Review, 103 (2013), 360–377.Google Scholar
Carhart, M. M.“On Persistence in Mutual Fund Performance.” Journal of Finance, 52 (1997), 57–82.Google Scholar
Chabi-Yo, F., and Colacito, R.. “The Term Structures of Co-Entropy in International Financial Markets.” Available at https://ssrn.com/abstract=2341772 (2016).Google Scholar
Chabi-Yo, F.; Ruenzi, S.; and Weigert, F.. “Crash Sensitivity and the Cross Section of Expected Stock Returns.” Journal of Financial and Quantitative Analysis, 53 (2018), 1059–1100.Google Scholar
Cho, Y.-H., and Engle, R. F.. “Time-Varying Betas and Asymmetric Effect of News: Empirical Analysis of Blue Chip Stocks.” Technical Report, National Bureau of Economic Research (1999).Google Scholar
Colacito, R.; Ghysels, E.; Meng, J.; and Siwasarit, W.. “Skewness in Expected Macro Fundamentals and the Predictability of Equity Returns: Evidence and Theory.” Review of Financial Studies, 29 (2016), 2069–2109.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
Conrad, J.; Gultekin, M. N.; and Kaul, G.. “Asymmetric Predictability of Conditional Variances.” Review of Financial Studies, 4 (1991), 597–622.Google Scholar
Cont, R.“Empirical Properties of Asset Returns: Stylized Facts and Statistical Issues.” Quantitative Finance, 1 (2001), 223–236.Google Scholar
Dahlquist, M.; Farago, A.; and Tédongap, R.. “Asymmetries and Portfolio Choice.” Review of Financial Studies, 30 (2017), 667–702.Google Scholar
Duin, R. P.“On the Choice of Smoothing Parameters for Parzen Estimators of Probability Density Functions.” IEEE Transactions on Computers, C‐25 (1976).Google Scholar
Efron, B. The Jackknife, the Bootstrap, and Other Resampling Plans. CBMS-NSF Regional Conference Series in Applied Mathematics 38. Philadelphia, PA: Society for Industrial and Applied Mathematics (1982).Google Scholar
Fama, E. F., and French, K. R.. “The Cross-Section of Expected Stock Returns.” Journal of Finance, 47 (1992), 427–465.Google Scholar
Granger, C.; Maasoumi, E.; and Racine, J.. “A Dependence Metric for Possibly Nonlinear Processes.” Journal of Time Series Analysis, 25 (2004), 649–669.Google Scholar
Gul, F.“A Theory of Disappointment Aversion.” Econometrica, 59 (1991), 667–686.Google Scholar
Hall, P. The Bootstrap and Edgeworth Expansion (Springer Series in Statistics). New York, NY: Springer (1992).Google Scholar
Hansen, L. P., and Jagannathan, R.. “Implications of Security Market Data for Models of Dynamic Economies.” Journal of Political Economy, 99 (1991), 225–262.Google Scholar
Harvey, C. R., and Siddique, A.. “Conditional Skewness in Asset Pricing Tests.” Journal of Finance, 55 (2000), 1263–1295.Google Scholar
Hong, Y.; Tu, J.; and Zhou, G.. “Asymmetries in Stock Returns: Statistical Tests and Economic Evaluation.” Review of Financial Studies, 20 (2007), 1547–1581.Google Scholar
Hong, Y., and White, H.. “Asymptotic Distribution Theory for Nonparametric Entropy Measures of Serial Dependence.” Econometrica, 73 (2005), 837–901.Google Scholar
Horowitz, J. L.“The Bootstrap.” Handbook of Econometrics, 5 (2001), 3159–3228.Google Scholar
Jegadeesh, N., and Titman, S.. “Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency.” Journal of Finance, 48 (1993), 65–91.Google Scholar
Jiang, L.; Wu, K.; Zhou, G.; and Zhu, Y.. “Stock Return Asymmetry: Beyond Skewness.” Working Paper, Washington University in St. Louis (2018).Google Scholar
Kelly, B., and Jiang, H.. “Tail Risk and Asset Prices.” Review of Financial Studies, 27 (2014), 2841–2871.Google Scholar
Kroner, K., and Ng, V. K.. “Modeling Asymmetric Comovements of Asset Returns.” Review of Financial Studies, 11 (1998), 817–844.Google Scholar
Kullback, S., and Leibler, R.. “On Information and Sufficiency.” Annals of Mathematical Statistics, 22 (1951), 79–86.Google Scholar
Lettau, M.; Maggiori, M.; and Weber, M.. “Conditional Risk Premia in Currency Markets and Other Asset Classes.” Journal of Financial Economics, 114 (2014), 197–225.Google Scholar
Li, Q., and Racine, J. S.. Nonparametric Econometrics: Theory and Practice. Princeton, NJ: Princeton University Press (2007).Google Scholar
Maasoumi, E., and Racine, J.. “Entropy and Predictability of Stock Market Returns.” Journal of Econometrics, 107 (2002), 291–312.Google Scholar
Maasoumi, E., and Racine, J. S.. “A Robust Entropy-Based Test of Asymmetry for Discrete and Continuous Processes.” Econometric Reviews, 28 (2008), 246–261.Google Scholar
Parzen, E.“On Estimation of a Probability Density Function and Mode.” Annals of Mathematical Statistics, 33 (1962), 1065–1076.Google Scholar
Pástor, L., and Stambaugh, R. F.. “Liquidity Risk and Expected Stock Returns.” Journal of Political Economy, 111 (2003), 642–685.Google Scholar
Patton, A.; Politis, D. N.; and White, H.. “Correction to ‘Automatic Block-Length Selection for the Dependent Bootstrap’ by D. Politis and H. White.” Econometric Reviews, 28 (2009), 372–375.Google Scholar
Racine, J. S., and Maasoumi, E.. “A Versatile and Robust Metric Entropy Test of Time-Reversibility, and Other Hypotheses.” Journal of Econometrics, 138 (2007), 547–567.Google Scholar
Rosenblatt, M.“Remarks on Some Nonparametric Estimates of a Density Function.” Annals of Mathematical Statistics, 27 (1956), 832–837.Google Scholar
Schwert, G. W.“Why Does Stock Market Volatility Change over Time?” Journal of Finance, 44 (1989), 1115–1153.Google Scholar
Segal, G.; Shaliastovich, I.; and Yaron, A.. “Good and Bad Uncertainty: Macroeconomic and Financial Market Implications.” Journal of Financial Economics, 117 (2015), 369–397.Google Scholar
Shannon, C.“A Mathematical Theory of Communication.” Bell System Technical Journal, 27 (1948), 379–423.Google Scholar
Skaug, H. J., and Tjøstheim, D.. “A Nonparametric Test of Serial Independence Based on the Empirical Distribution Function.” Biometrika, 80 (1993), 591–602.Google Scholar
Tawn, J. A.“Bivariate Extreme Value Theory: Models and Estimation.” Biometrika, 75 (1988), 397–415.Google Scholar
Tjøstheim, D.“Measures of Dependence and Tests of Independence.” Statistics: A Journal of Theoretical and Applied Statistics, 28 (1996), 249–284.Google Scholar
Ullah, A.“Entropy, Divergence and Distance Measures with Econometric Applications.” Journal of Statistical Planning and Inference, 49 (1996), 137–162.Google Scholar
Zhou, G.“Asset-Pricing Tests under Alternative Distributions.” Journal of Finance, 48 (1993), 1927–1942.Google Scholar
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