Complexity and the Character of Stock Returns: Empirical Evidence and a Model of Asset Prices Based on Complex Investor Learning
Empirical evidence on the distributional characteristics of common stock returns indicates: (1) A power-law tail index close to three describes the behavior of the positive tail of the survivor function of returns (pr(r > x) ~ x -\alpha ), a reflection of fat tails; (2) general linear and nonlinear dependencies exist in the time series of returns; (3) the time-series return process is characterized by short-run dependence (short memory) in both returns as well as their volatility, the latter usually characterized in the form of autoregressive conditional heteroskedasticity; and (4) the time-series return process probably does not exhibit long memory, but the squared returns process does exhibit long memory. We propose a model of complex, self-referential learning and reasoning amongst economic agents that jointly produces security returns consistent with these general observed facts and which are supported here by empirical results presented for a benchmark sample of 50 stocks traded on the New York Stock Exchange. The market we postulate is populated by traders who reason inductively while compressing information into a few fuzzy notions that they can in turn process and analyze with fuzzy logic. We analyze the implications of such behavior for the returns on risky securities within the context of an artificial stock market model. Dynamic simulation experiments of the market are conducted, from which market-clearing prices emerge, allowing us to then compute realized returns. We test the effects of varying values of the parameters of the model on the character of the simulated returns. The results indicate that the model proposed in this paper can jointly account for the presence of a power-law characterization of the positive tail of the survivor function of returns with exponent on the order of three, for autoregressive conditional heteroskedasticity, for long memory in volatility, and for general nonlinear dependencies in returns.
Volume (Year): 53 (2007)
Issue (Month): 7 (July)
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- Lo, Andrew W, 1991.
"Long-Term Memory in Stock Market Prices,"
Econometric Society, vol. 59(5), pages 1279-313, September.
- Tom Doan, . "RSSTATISTIC: RATS procedure to compute R/S Statistic (classical or Lo's modified)," Statistical Software Components RTS00191, Boston College Department of Economics.
- Andrew W. Lo, 1989. "Long-term Memory in Stock Market Prices," NBER Working Papers 2984, National Bureau of Economic Research, Inc.
- Lo, Andrew W. (Andrew Wen-Chuan), 1989. "Long-term memory in stock market prices," Working papers 3014-89., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- V. Plerou & P. Gopikrishnan & L. A. N. Amaral & M. Meyer & H. E. Stanley, 1999. "Scaling of the distribution of price fluctuations of individual companies," Papers cond-mat/9907161, arXiv.org.
- Parameswaran Gopikrishnan & Vasiliki Plerou & Luis A. Nunes Amaral & Martin Meyer & H. Eugene Stanley, 1999. "Scaling of the distribution of fluctuations of financial market indices," Papers cond-mat/9905305, arXiv.org.
- LeBaron, Blake, 2000. "Agent-based computational finance: Suggested readings and early research," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 679-702, June.
- Bollerslev, Tim & Wright, Jonathan H., 2000. "Semiparametric estimation of long-memory volatility dependencies: The role of high-frequency data," Journal of Econometrics, Elsevier, vol. 98(1), pages 81-106, September.
- Scheinkman, Jose A & LeBaron, Blake, 1989. "Nonlinear Dynamics and Stock Returns," The Journal of Business, University of Chicago Press, vol. 62(3), pages 311-37, July.
- Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
- Barnett, William A. & Gallant, A. Ronald & Hinich, Melvin J. & Jungeilges, Jochen A. & Kaplan, Daniel T. & Jensen, Mark J., 1997.
"A single-blind controlled competition among tests for nonlinearity and chaos,"
Journal of Econometrics,
Elsevier, vol. 82(1), pages 157-192.
- William Barnett & A. Ronald Gallant & Melvin J. Hinich & Jochen A. Jungeilges & Daniel T. Kaplan & Mark J. Jensen, 2012. "A Single-Blind Controlled Competition Among Tests For Nonlinearity And Chaos," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201219, University of Kansas, Department of Economics, revised Sep 2012.
- William A. Barnett & A. Ronald Gallant & Melvin J. Hinich & Jochen A. Jungeilges & Daniel T. Kaplan & Mark J. Jensen, 1996. "A Single-Blind Controlled Competition among Tests for Nonlinearity and Chaos," Econometrics 9602005, EconWPA, revised 20 Sep 1996.
- Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
- Brock, W.A. & Hommes, C.H., 1996.
"Hetergeneous Beliefs and Routes to Chaos in a Simple Asset Pricing Model,"
9621, Wisconsin Madison - Social Systems.
- Brock, William A. & Hommes, Cars H., 1998. "Heterogeneous beliefs and routes to chaos in a simple asset pricing model," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1235-1274, August.
- W. Brian Arthur, 1992. "On Learning and Adaptation in the Economy," Working Papers 854, Queen's University, Department of Economics.
- Tesfatsion, Leigh S., 2002. "Agent-Based Computational Economics: Growing Economies from the Bottom Up," Staff General Research Papers Archive 5075, Iowa State University, Department of Economics.
- LeBaron, Blake & Arthur, W. Brian & Palmer, Richard, 1999.
"Time series properties of an artificial stock market,"
Journal of Economic Dynamics and Control,
Elsevier, vol. 23(9-10), pages 1487-1516, September.
- Arthur, W.B. & LeBaron, B. & Palmer, R., 1997. "Time Series Properties of an Artificial Stock Market," Working papers 9725, Wisconsin Madison - Social Systems.
- Leigh Tesfatsion & Kenneth L. Judd (ed.), 2006. "Handbook of Computational Economics," Handbook of Computational Economics, Elsevier, edition 1, volume 2, number 2.
- 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.
- Lawrence R. Glosten & Ravi Jagannathan & David E. Runkle, 1993. "On the relation between the expected value and the volatility of the nominal excess return on stocks," Staff Report 157, Federal Reserve Bank of Minneapolis.
- Arthur, W Brian, 1994. "Inductive Reasoning and Bounded Rationality," American Economic Review, American Economic Association, vol. 84(2), pages 406-11, May.
- Engle III, Robert F., 2003.
"Risk and Volatility: Econometric Models and Financial Practice,"
Nobel Prize in Economics documents
2003-4, Nobel Prize Committee.
- Robert Engle, 2004. "Risk and Volatility: Econometric Models and Financial Practice," American Economic Review, American Economic Association, vol. 94(3), pages 405-420, June.
- W. Brian Arthur, 1994. "Inductive Reasoning, Bounded Rationality and the Bar Problem," Working Papers 94-03-014, Santa Fe Institute.
- Carmela Quintos & Zhenhong Fan & Peter C. B. Phillips, 2001. "Structural Change Tests in Tail Behaviour and the Asian Crisis," Review of Economic Studies, Oxford University Press, vol. 68(3), pages 633-663.
- Tay, Nicholas S. P. & Linn, Scott C., 2001. "Fuzzy inductive reasoning, expectation formation and the behavior of security prices," Journal of Economic Dynamics and Control, Elsevier, vol. 25(3-4), pages 321-361, March.
- Arthur, W Brian, 1991. "Designing Economic Agents that Act Like Human Agents: A Behavioral Approach to Bounded Rationality," American Economic Review, American Economic Association, vol. 81(2), pages 353-59, May.
- Hsieh, David A, 1991. " Chaos and Nonlinear Dynamics: Application to Financial Markets," Journal of Finance, American Finance Association, vol. 46(5), pages 1839-77, December.
- Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2006.
"Institutional Investors and Stock Market Volatility,"
The Quarterly Journal of Economics,
Oxford University Press, vol. 121(2), pages 461-504.
- Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2005. "Institutional Investors and Stock Market Volatility," NBER Working Papers 11722, National Bureau of Economic Research, Inc.
- Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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