

Markets are Efficient if and Only if P = NP - VanL
http://www.moneyscience.com/pg/bookmarks/Admin/read/2400/markets-are-efficient-if-and-only-if-p-np

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VanL
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.

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This is basically an attack on the efficient market hypothesis - i.e., that
markets price in all available information and market moves over the long term
accurately reflect the best consensus guess as to the future of a particular
company. For background, see
Wikipedia:<http://en.wikipedia.org/wiki/Efficient-market_hypothesis>

What I see as the interesting part of this paper is way in which the author
uses market mechanisms - a trading strategy - to test problems as being in the
P or NP space, basically equating the market to a type of computational
machine. He argues that if the EMF is true, then a properly set up experiment
should be able to come up with a solution to an NP problem in polynomial time
(implying P=NP).

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akeck
Read the paper here:
<http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1773169>

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dfc
Has anyone with the required background read the paper and would like to give
a quick summary of the argument?

~~~
equark
The basic idea is that given a financial time series of N periods with three
states (up, neutral, or down) there are 3^N possible "strategies" to test,
which is an NP problem.

This doesn't seem right. It's completely atheoretical and ignores the market
or asset structure. The question is not how many strategies there are, but how
hard is it to compute the optimal price. Basic economic theory often can be
used to derive the optimal price as a simple function of information (data).

There may an argument that markets are inefficient that follows an NP=P style
argument, but I suspect it would require a specific market structure, such as
a set of agents that can only communicate via a sparse network.

