### 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 language | English (US) |
---|---|

Pages (from-to) | 1-11 |

Number of pages | 11 |

Journal | Algorithmic Finance |

Volume | 1 |

Issue number | 1 |

DOIs | |

State | Published - 2011 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*Algorithmic Finance*,

*1*(1), 1-11. https://doi.org/10.3233/AF-2011-007

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

Research output: Contribution to journal › Article

*Algorithmic Finance*, vol. 1, no. 1, pp. 1-11. https://doi.org/10.3233/AF-2011-007

}

TY - JOUR

T1 - Markets are efficient if and only if P = NP

AU - Maymin, Philip Z.

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84893503068&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84893503068&partnerID=8YFLogxK

U2 - 10.3233/AF-2011-007

DO - 10.3233/AF-2011-007

M3 - Article

VL - 1

SP - 1

EP - 11

JO - Algorithmic Finance

JF - Algorithmic Finance

SN - 2158-5571

IS - 1

ER -