Markets are efficient if and only if P = NP
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.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Sanford J Grossman & Joseph E Stiglitz, 1997.
"On the Impossibility of Informationally Efficient Markets,"
Levine's Working Paper Archive
1908, David K. Levine.
- 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.
- Jensen, Michael C., 1978. "Some anomalous evidence regarding market efficiency," Journal of Financial Economics, Elsevier, vol. 6(2-3), pages 95-101.
- 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, 1989. "When are Contrarian Profits Due to Stock Market Overreaction?," NBER Working Papers 2977, National Bureau of Economic Research, Inc.
- 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.
- 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.
- 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.
- G. William Schwert, 2002.
"Anomalies and Market Efficiency,"
NBER Working Papers
9277, 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.
- 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
- 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.
When requesting a correction, please mention this item's handle: RePEc:arx:papers:1002.2284. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators)
If references are entirely missing, you can add them using this form.