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The Gambler's and Hot-Hand Fallacies: Theory and Applications

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  • Rabin, Matthew
  • Vayanos, Dimitri

Abstract

We develop a model of the gambler's fallacy -- the mistaken belief that random sequences should exhibit systematic reversals. We show that an individual who holds this belief and observes a sequence of signals can exaggerate the magnitude of changes in an underlying state but underestimate their duration. When the state is constant, and so signals are \textit{i.i.d.}, the individual can predict that long streaks of similar signals will continue -- a hot-hand fallacy. When signals are serially correlated, the individual typically under-reacts to short streaks, over-reacts to longer ones, and under-reacts to very long ones. We explore several applications, showing, for example, that investors may move assets too much in and out of mutual funds, and exaggerate the value of financial information and expertise.

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Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 6081.

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Date of creation: Feb 2007
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Handle: RePEc:cpr:ceprdp:6081

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Keywords: behavioural finance; gambler's fallacy; hot-hand fallacy;

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References

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  1. Erik R. Sirri & Peter Tufano, 1998. "Costly Search and Mutual Fund Flows," Journal of Finance, American Finance Association, vol. 53(5), pages 1589-1622, October.
  2. Charles T. Clotfelter & Philip J. Cook, 1991. "The "Gambler's Fallacy" in Lottery Play," NBER Working Papers 3769, National Bureau of Economic Research, Inc.
  3. Matthew Rabin., 2000. "Inference by Believers in the Law of Small Numbers," Economics Working Papers E00-282, University of California at Berkeley.
  4. Nicholas Barberis & Andrei Shleifer & Robert W. Vishny, 1997. "A Model of Investor Sentiment," NBER Working Papers 5926, National Bureau of Economic Research, Inc.
  5. Jonathan B. Berk & Richard C. Green, 2002. "Mutual Fund Flows and Performance in Rational Markets," FAME Research Paper Series rp100, International Center for Financial Asset Management and Engineering.
  6. Baquero, G. & Verbeek, M.J.C.M., 2006. "Do Sophisticated Investors Believe in the Law of Small Numbers?," ERIM Report Series Research in Management ERS-2006-033-F&A, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
  7. Ravi Jagannathan & Alexey Malakhov & Dmitry Novikov, 2006. "Do Hot Hands Exist Among Hedge Fund Managers? An Empirical Evaluation," NBER Working Papers 12015, National Bureau of Economic Research, Inc.
  8. R. C. Merton, 1970. "Optimum Consumption and Portfolio Rules in a Continuous-time Model," Working papers 58, Massachusetts Institute of Technology (MIT), Department of Economics.
  9. Camerer, Colin F, 1989. "Does the Basketball Market Believe in the 'Hot Hand'?," American Economic Review, American Economic Association, vol. 79(5), pages 1257-61, December.
  10. Chevalier, Judith & Ellison, Glenn, 1997. "Risk Taking by Mutual Funds as a Response to Incentives," Journal of Political Economy, University of Chicago Press, vol. 105(6), pages 1167-1200, December.
  11. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
  12. Terrell, Dek, 1994. "A Test of the Gambler's Fallacy: Evidence from Pari-mutuel Games," Journal of Risk and Uncertainty, Springer, vol. 8(3), pages 309-17, May.
  13. Matthew Rabin & Dimitri Vayanos, 2005. "The Gambler's and Hot-Hand Fallacies In a Dynamic-Inference Model," Levine's Bibliography 122247000000000972, UCLA Department of Economics.
  14. Carhart, Mark M, 1997. " On Persistence in Mutual Fund Performance," Journal of Finance, American Finance Association, vol. 52(1), pages 57-82, March.
  15. Fama, Eugene F, 1991. " Efficient Capital Markets: II," Journal of Finance, American Finance Association, vol. 46(5), pages 1575-617, December.
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Cited by:
  1. Shleifer, Andrei, 2012. "Psychologists at the Gate: Review of Daniel Kahneman’s Thinking, Fast and Slow," Scholarly Articles 10735580, Harvard University Department of Economics.
  2. Andrei Shleifer, 2012. "Psychologists at the Gate: A Review of Daniel Kahneman's Thinking, Fast and Slow," Journal of Economic Literature, American Economic Association, vol. 50(4), pages 1080-91, December.
  3. Daniel L. Tortorice, 2014. "Equity Return Predictability, Time Varying Volatility and Learning About the Permanence of Shocks," Working Papers 70, Brandeis University, Department of Economics and International Businesss School.
  4. Andrey Kudryavtsev & Gil Cohen & Shlomit Hon-Snir, 2013. "“Rational” or “Intuitive”: Are Behavioral Biases Correlated Across Stock Market Investors?," Contemporary Economics, University of Finance and Management in Warsaw, vol. 7(2), June.
  5. Matthew Rabin, 2013. "Incorporating Limited Rationality into Economics," Journal of Economic Literature, American Economic Association, vol. 51(2), pages 528-43, June.
  6. Livingston, Jeffrey A., 2012. "The hot hand and the cold hand in professional golf," Journal of Economic Behavior & Organization, Elsevier, vol. 81(1), pages 172-184.
  7. Ran Spiegler, 2014. "Bayesian Networks and Boundedly Rational Expectations," Discussion Papers 1417, Centre for Macroeconomics (CFM).

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