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Markets are efficient if and only if P = NP

  • Philip Maymin
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    I prove that if markets are weak-form efficient, meaning current prices fully reflect all information available in past prices, then P = NP, meaning every computational problem whose solution can be verified in polynomial time can also be solved in polynomial time. I also prove the converse by showing how we can "program" the market to solve NP-complete problems. Since P probably does not equal NP, markets are probably not efficient. Specifically, markets become increasingly inefficient as the time series lengthens or becomes more frequent. An illustration by way of partitioning the excess returns to momentum strategies based on data availability confirms this prediction.

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    Paper provided by in its series Papers with number 1002.2284.

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    Date of creation: Feb 2010
    Date of revision: May 2010
    Handle: RePEc:arx:papers:1002.2284
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    1. Lo, Andrew W. (Andrew Wen-Chuan) & MacKinlay, Archie Craig, 1955-., 1989. "When are contrarian profits due to stock market overreaction?," Working papers 3008-89., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    2. Sanford J Grossman & Joseph E Stiglitz, 1997. "On the Impossibility of Informationally Efficient Markets," Levine's Working Paper Archive 1908, David K. Levine.
    3. Nicholas Barberis & Richard Thaler, 2002. "A Survey of Behavioral Finance," NBER Working Papers 9222, National Bureau of Economic Research, Inc.
    4. Jensen, Michael C., 1978. "Some anomalous evidence regarding market efficiency," Journal of Financial Economics, Elsevier, vol. 6(2-3), pages 95-101.
    5. G. William Schwert, 2002. "Anomalies and Market Efficiency," NBER Working Papers 9277, National Bureau of Economic Research, Inc.
    6. Narasimhan Jegadeesh, 2001. "Profitability of Momentum Strategies: An Evaluation of Alternative Explanations," Journal of Finance, American Finance Association, vol. 56(2), pages 699-720, 04.
    7. Doran, James S. & Peterson, David R. & Wright, Colby, 2010. "Confidence, opinions of market efficiency, and investment behavior of finance professors," Journal of Financial Markets, Elsevier, vol. 13(1), pages 174-195, February.
    8. Jegadeesh, Narasimhan & Titman, Sheridan, 1993. " Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency," Journal of Finance, American Finance Association, vol. 48(1), pages 65-91, March.
    9. Fama, Eugene F, 1991. " Efficient Capital Markets: II," Journal of Finance, American Finance Association, vol. 46(5), pages 1575-617, December.
    10. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
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