Markets are efficient if and only if P = NP

Philip Z. Maymin

Research output: Contribution to journalArticle

Abstract

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
Volume1
Issue number1
DOIs
StatePublished - 2011

Fingerprint

Polynomials
If and only if
Time series
Computational complexity
Momentum
Polynomial time
Availability
Converse
Excess
Partitioning
NP-complete problem
Market
Prediction
Meaning
Strategy
NP-complete
Excess returns
Momentum strategies

ASJC Scopus subject areas

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

Cite this

Markets are efficient if and only if P = NP. / Maymin, Philip Z.

In: Algorithmic Finance, Vol. 1, No. 1, 2011, p. 1-11.

Research output: Contribution to journalArticle

Maymin, Philip Z. / Markets are efficient if and only if P = NP. In: Algorithmic Finance. 2011 ; Vol. 1, No. 1. pp. 1-11.
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