Markets are efficient if and only if P = NP
Abstract
I prove that if markets are weakform 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 NPcomplete 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.
 Publication:

arXiv eprints
 Pub Date:
 February 2010
 arXiv:
 arXiv:1002.2284
 Bibcode:
 2010arXiv1002.2284M
 Keywords:

 Quantitative Finance  General Finance;
 Computer Science  Computational Complexity
 EPrint:
 33 pages