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Nonlinear and time-varying risk premia

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  • Ma, Chaoqun
  • Mi, Xianhua
  • Cai, Zongwu

Abstract

Facing the puzzling risk-return trade-off, this paper proposes a new model for risk premia to capture nonlinear and time-varying features under the influence of trading volume. Using high-frequency data for the US stock market in Wharton Research Data Services' Trade and Quote database, our empirical findings suggest a significant nonlinear and time-varying contemporary relationship between return and realized volatility, ranging from positive to negative with an up-down-up pattern, summarized as follows. First, the contemporary relationship is positive on inactive trading days when the trading volume is smaller than usual, in which case traders may face no new information or event uncertainty. Second, the relationship is significantly negative when the trading volume is large on active trading days, in which case traders may be overconfident and behave in a risk-seeking fashion. Third, the risk premium tends toward zero during extremely abnormal trading days. Finally, low and high levels of trading volume have asymmetrical influences on risk premia, with a larger absolute value of risk premia for high levels of trading volume. Furthermore, the nonlinear changing autocorrelation of returns is insignificant from zero on normal trading days and most likely different from zero on abnormal trading days. These results provide explanations for the conflicts between financial theoretic and empirical studies.

Suggested Citation

  • Ma, Chaoqun & Mi, Xianhua & Cai, Zongwu, 2020. "Nonlinear and time-varying risk premia," China Economic Review, Elsevier, vol. 62(C).
    • Handle: RePEc:eee:chieco:v:62:y:2020:i:c:s1043951x2030064x
    DOI: 10.1016/j.chieco.2020.101467
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    as
    1. Chan, Choon Chat & Fong, Wai Mun, 2006. "Realized volatility and transactions," Journal of Banking & Finance, Elsevier, vol. 30(7), pages 2063-2085, July.
    2. Nyberg, Henri, 2012. "Risk-Return Tradeoff in U.S. Stock Returns over the Business Cycle," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 47(1), pages 137-158, February.
    3. Harvey, Campbell R., 2001. "The specification of conditional expectations," Journal of Empirical Finance, Elsevier, vol. 8(5), pages 573-637, December.
    4. Caner, Mehmet & Hansen, Bruce E., 2004. "Instrumental Variable Estimation Of A Threshold Model," Econometric Theory, Cambridge University Press, vol. 20(5), pages 813-843, October.
    5. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    6. Terrance Odean., 1996. "Volume, Volatility, Price and Profit When All Trader Are Above Average," Research Program in Finance Working Papers RPF-266, University of California at Berkeley.
    7. Joon Chae, 2005. "Trading Volume, Information Asymmetry, and Timing Information," Journal of Finance, American Finance Association, vol. 60(1), pages 413-442, February.
    8. Lakonishok, Josef & Vermaelen, Theo, 1986. "Tax-induced trading around ex-dividend days," Journal of Financial Economics, Elsevier, vol. 16(3), pages 287-319, July.
    9. Andrew J. Patton & Kevin Sheppard, 2015. "Good Volatility, Bad Volatility: Signed Jumps and The Persistence of Volatility," The Review of Economics and Statistics, MIT Press, vol. 97(3), pages 683-697, July.
    10. Torben G. Andersen & Tim Bollerslev & Nour Meddahi, 2005. "Correcting the Errors: Volatility Forecast Evaluation Using High-Frequency Data and Realized Volatilities," Econometrica, Econometric Society, vol. 73(1), pages 279-296, January.
    11. Jacod, Jean & Li, Yingying & Mykland, Per A. & Podolskij, Mark & Vetter, Mathias, 2009. "Microstructure noise in the continuous case: The pre-averaging approach," Stochastic Processes and their Applications, Elsevier, vol. 119(7), pages 2249-2276, July.
    12. Guillermo Llorente & Roni Michaely & Gideon Saar & Jiang Wang, 2002. "Dynamic Volume-Return Relation of Individual Stocks," The Review of Financial Studies, Society for Financial Studies, vol. 15(4), pages 1005-1047.
    13. Ghysels, Eric & Santa-Clara, Pedro & Valkanov, Rossen, 2005. "There is a risk-return trade-off after all," Journal of Financial Economics, Elsevier, vol. 76(3), pages 509-548, June.
    14. Whitelaw, Robert F, 1994. "Time Variations and Covariations in the Expectation and Volatility of Stock Market Returns," Journal of Finance, American Finance Association, vol. 49(2), pages 515-541, June.
    15. Jones, Charles M & Kaul, Gautam & Lipson, Marc L, 1994. "Transactions, Volume, and Volatility," Review of Financial Studies, Society for Financial Studies, vol. 7(4), pages 631-651.
    16. Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005. "A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1394-1411, December.
    17. Craig W. Holden & Stacey Jacobsen, 2014. "Liquidity Measurement Problems in Fast, Competitive Markets: Expensive and Cheap Solutions," Journal of Finance, American Finance Association, vol. 69(4), pages 1747-1785, August.
    18. John T. Scruggs, 1998. "Resolving the Puzzling Intertemporal Relation between the Market Risk Premium and Conditional Market Variance: A Two-Factor Approach," Journal of Finance, American Finance Association, vol. 53(2), pages 575-603, April.
    19. Tim Bollerslev & Julia Litvinova & George Tauchen, 2006. "Leverage and Volatility Feedback Effects in High-Frequency Data," Journal of Financial Econometrics, Oxford University Press, vol. 4(3), pages 353-384.
    20. French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, vol. 19(1), pages 3-29, September.
    21. Fulvio Corsi, 2009. "A Simple Approximate Long-Memory Model of Realized Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 7(2), pages 174-196, Spring.
    22. De Santis, Giorgio & imrohoroglu, Selahattin, 1997. "Stock returns and volatility in emerging financial markets," Journal of International Money and Finance, Elsevier, vol. 16(4), pages 561-579, August.
    23. Bekaert, Geert & Wu, Guojun, 2000. "Asymmetric Volatility and Risk in Equity Markets," Review of Financial Studies, Society for Financial Studies, vol. 13(1), pages 1-42.
    24. Kent Daniel & David Hirshleifer & Avanidhar Subrahmanyam, 1998. "Investor Psychology and Security Market Under- and Overreactions," Journal of Finance, American Finance Association, vol. 53(6), pages 1839-1885, December.
    25. Chordia, Tarun & Subrahmanyam, Avanidhar, 2004. "Order imbalance and individual stock returns: Theory and evidence," Journal of Financial Economics, Elsevier, vol. 72(3), pages 485-518, June.
    26. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
    27. Ole E. Barndorff‐Nielsen & Neil Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280, May.
    28. Cai, Zongwu & Das, Mitali & Xiong, Huaiyu & Wu, Xizhi, 2006. "Functional coefficient instrumental variables models," Journal of Econometrics, Elsevier, vol. 133(1), pages 207-241, July.
    29. R. Glen Donaldson & Mark J. Kamstra, 2005. "Volatility Forecasts, Trading Volume, And The Arch Versus Option‐Implied Volatility Trade‐Off," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 28(4), pages 519-538, December.
    30. Michael J. Cooper & Roberto C. Gutierrez & Allaudeen Hameed, 2004. "Market States and Momentum," Journal of Finance, American Finance Association, vol. 59(3), pages 1345-1365, June.
    31. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    32. Easley, David & Kiefer, Nicholas M & O'Hara, Maureen, 1997. "One Day in the Life of a Very Common Stock," Review of Financial Studies, Society for Financial Studies, vol. 10(3), pages 805-835.
    33. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    34. Lo, Andrew W & Wang, Jiang, 2000. "Trading Volume: Definitions, Data Analysis, and Implications of Portfolio Theory," The Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 257-300.
    35. Ole E. Barndorff-Nielsen, 2004. "Power and Bipower Variation with Stochastic Volatility and Jumps," Journal of Financial Econometrics, Oxford University Press, vol. 2(1), pages 1-37.
    36. Giot, Pierre & Laurent, Sébastien & Petitjean, Mikael, 2010. "Trading activity, realized volatility and jumps," Journal of Empirical Finance, Elsevier, vol. 17(1), pages 168-175, January.
    37. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-131, February.
    38. Zongwu Cai & Ying Fang & Ming Lin & Jia Su, 2019. "Inferences for a Partially Varying Coefficient Model With Endogenous Regressors," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(1), pages 158-170, January.
    39. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    40. Liu, Xiaochun, 2017. "Unfolded risk-return trade-offs and links to Macroeconomic Dynamics," Journal of Banking & Finance, Elsevier, vol. 82(C), pages 1-19.
    41. Harrison Hong & Jeremy C. Stein, 1999. "A Unified Theory of Underreaction, Momentum Trading, and Overreaction in Asset Markets," Journal of Finance, American Finance Association, vol. 54(6), pages 2143-2184, December.
    42. Fleming, Jeff & Kirby, Chris, 2011. "Long memory in volatility and trading volume," Journal of Banking & Finance, Elsevier, vol. 35(7), pages 1714-1726, July.
    43. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    44. Federico M. Bandi & Benoit Perron, 2006. "Long Memory and the Relation Between Implied and Realized Volatility," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(4), pages 636-670.
    45. Bollerslev, Tim & Jubinski, Dan, 1999. "Equity Trading Volume and Volatility: Latent Information Arrivals and Common Long-Run Dependencies," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(1), pages 9-21, January.
    46. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
    47. Cai, Zongwu & Fan, Jianqing & Yao, Qiwei, 2000. "Functional-coefficient regression models for nonlinear time series," LSE Research Online Documents on Economics 6314, London School of Economics and Political Science, LSE Library.
    48. Frazier, David T. & Liu, Xiaochun, 2016. "A new approach to risk-return trade-off dynamics via decomposition," Journal of Economic Dynamics and Control, Elsevier, vol. 62(C), pages 43-55.
    49. Badshah, Ihsan & Frijns, Bart & Knif, Johan & Tourani-Rad, Alireza, 2016. "Asymmetries of the intraday return-volatility relation," International Review of Financial Analysis, Elsevier, vol. 48(C), pages 182-192.
    50. Das, M., 2005. "Instrumental variables estimators of nonparametric models with discrete endogenous regressors," Journal of Econometrics, Elsevier, vol. 124(2), pages 335-361, February.
    51. Kinnunen, Jyri, 2014. "Risk-return trade-off and serial correlation: Do volume and volatility matter?," Journal of Financial Markets, Elsevier, vol. 20(C), pages 1-19.
    52. Richardson, Gordon & Sefcik, Stephan E. & Thompson, Rex, 1986. "A test of dividend irrelevance using volume reactions to a change in dividend policy," Journal of Financial Economics, Elsevier, vol. 17(2), pages 313-333, December.
    53. Terrance Odean, 1998. "Volume, Volatility, Price, and Profit When All Traders Are Above Average," Journal of Finance, American Finance Association, vol. 53(6), pages 1887-1934, December.
    54. Alberto G. Rossi & Allan Timmermann, 2015. "Modeling Covariance Risk in Merton's ICAPM," Review of Financial Studies, Society for Financial Studies, vol. 28(5), pages 1428-1461.
    55. Brandt, Michael W. & Kang, Qiang, 2004. "On the relationship between the conditional mean and volatility of stock returns: A latent VAR approach," Journal of Financial Economics, Elsevier, vol. 72(2), pages 217-257, May.
    56. Easley, David & O'Hara, Maureen, 1992. "Time and the Process of Security Price Adjustment," Journal of Finance, American Finance Association, vol. 47(2), pages 576-605, June.
    57. Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1992. "Stock Prices and Volume," Review of Financial Studies, Society for Financial Studies, vol. 5(2), pages 199-242.
    58. Andersen, Torben G, 1996. "Return Volatility and Trading Volume: An Information Flow Interpretation of Stochastic Volatility," Journal of Finance, American Finance Association, vol. 51(1), pages 169-204, March.
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    More about this item

    Keywords

    Endogeneity; High-frequency data; Partially varying coefficient; Nonparametric; Nonlinearity; Realized volatility; Risk premium;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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