Markets are efficient if and only if P = NP

Philip Z. Maymin

Research output: Contribution to journalArticlepeer-review


I prove that if markets are 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.

Original languageEnglish (US)
Pages (from-to)1-11
Number of pages11
JournalAlgorithmic Finance
Issue number1
StatePublished - 2011

ASJC Scopus subject areas

  • Finance
  • Computer Vision and Pattern Recognition
  • Computer Science Applications
  • Computational Mathematics


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