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Markets are efficient if and only if P = NP

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  • Philip Maymin

Abstract

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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  • Philip Maymin, 2010. "Markets are efficient if and only if P = NP," Papers 1002.2284, arXiv.org, revised May 2010.
  • Handle: RePEc:arx:papers:1002.2284
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    References listed on IDEAS

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    1. 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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    5. Grossman, Sanford J & Stiglitz, Joseph E, 1980. "On the Impossibility of Informationally Efficient Markets," American Economic Review, American Economic Association, vol. 70(3), pages 393-408, June.
    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, April.
    7. Schwert, G. William, 2003. "Anomalies and market efficiency," Handbook of the Economics of Finance,in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 15, pages 939-974 Elsevier.
    8. 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.
    9. Jensen, Michael C., 1978. "Some anomalous evidence regarding market efficiency," Journal of Financial Economics, Elsevier, vol. 6(2-3), pages 95-101.
    10. 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.
    11. Fama, Eugene F, 1991. " Efficient Capital Markets: II," Journal of Finance, American Finance Association, vol. 46(5), pages 1575-1617, December.
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