1 research outputs found
Markets are efficient if and only if P = NP
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: 33 pages; extended literature review and some addition