Markets are efficient if and only if P = NP
AbstractI 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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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1002.2284.
Date of creation: Feb 2010
Date of revision: May 2010
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- 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.
- Lo, Andrew W. (Andrew Wen-Chuan) & MacKinlay, Archie Craig, 1955-., 1989.
"When are contrarian profits due to stock market overreaction?,"
3008-89., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- Lo, Andrew W & MacKinlay, A Craig, 1990. "When Are Contrarian Profits Due to Stock Market Overreaction?," Review of Financial Studies, Society for Financial Studies, vol. 3(2), pages 175-205.
- Andrew W. Lo & A. Craig MacKinlay, 1991. "When are Contrarian Profits Due to Stock Market Overreaction?," NBER Working Papers 2977, National Bureau of Economic Research, Inc.
- Fama, Eugene F, 1991. " Efficient Capital Markets: II," Journal of Finance, American Finance Association, vol. 46(5), pages 1575-617, December.
- 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.
- 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
- Jensen, Michael C., 1978. "Some anomalous evidence regarding market efficiency," Journal of Financial Economics, Elsevier, vol. 6(2-3), pages 95-101.
- 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.
- 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.
- 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.
- Sanford J Grossman & Joseph E Stiglitz, 1997. "On the Impossibility of Informationally Efficient Markets," Levine's Working Paper Archive 1908, David K. Levine.
- Barberis, Nicholas & Thaler, Richard, 2003.
"A survey of behavioral finance,"
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 18, pages 1053-1128
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