# Markets are efficient if and only if P = NP

• Published in 2011
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.

## Other information

journal
Algorithmic Finance
volume
2010

### BibTeX entry

@article{Maymin2011,
title = {Markets are efficient if and only if P = NP},
author = {Maymin, PZ},
url = {https://arxiv.org/abs/1002.2284 https://arxiv.org/pdf/1002.2284},
urldate = {2013-02-11},
year = 2011,
abstract = { 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. },
comment = {},
journal = {Algorithmic Finance},
volume = 2010,
collections = {computational-complexity-of-games}
}