
Markets are Efficient if and Only if P = NP - ionfish
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1773169
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3pt14159
Title should read: "If markets are perfectly efficient P=NP" rather than
"Markets are efficient if and only if P = NP". For example, say P = NP, but
the only person that knows the proof is me. If I start using my knowledge that
P = NP to trade I will not have enough capital to swing the market to truly
reflect the efficient price. Therefore it does not follow that if P = NP the
market will be perfectly efficient, which is required in an "if and only if"
proof.

~~~
gwern
> If I start using my knowledge that P = NP to trade I will not have enough
> capital to swing the market to truly reflect the efficient price.

How long would it take you to gain enough capital to start moving prices? If
you have a systematic edge on all trades...

In any event, I didn't find OP interesting the first time and I don't know.
Most people aren't using OP's extremely strong definition of efficient market,
but merely saying that humans and current algorithms cannot over long periods
extract money; it's a statement about the market vs other actors, not markets
versus omniscient gods.

~~~
kragen
Results like general equilibrium are conditional on the OP's extremely strong
definition of _efficient market_. Whether or not you personally can get rich
by beating the market is not the only possible interesting question about
economics!

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tokenadult
Hacker News submission and discussion from 540 days ago of previous version of
same author's paper:

<http://news.ycombinator.com/item?id=1144548>

~~~
nopassrecover
I also posted the author's video explanation here the other day:
<http://news.ycombinator.com/item?id=2867429>

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ColinWright
It feels to me that all he's done is show that the "instantly" in the usual
definition of markets being "efficient" is a nonsense. Prices must take time
to compute, you can't know the correct price instantly even with access to all
the past information.

He proves that, but it doesn't seem that surprising to me.

~~~
peteretep
I was coming here to write almost exactly this.

Markets are provably not 'instantly' efficient because arbitrage exists.
Arbitrage is simply not possible in an efficient market, because it's an
exploit of inefficiency.

However, exploitation of abitrage (and of knowledge generally) is what makes
markets largely efficient.

~~~
Rickasaurus
The point though is that whoever has the most computational power has the most
power to exploit arbitrage.

~~~
peteretep
That's /a/ point. Whenever people start harping on about Market Efficiency,
you need to find out "why do you care?". The answer to "Are markets efficient?
I have this hot stock tip I read on Tech Crunch" then the answer is yes,
because other people have more time, money, expertise and - as you point out -
computational power - as well things like preferential data access and
physical proximity to the exchange.

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aphyr
If we allow that large, computationally capable entities are likely to form in
free markets, it is probable that individuals will be faced with a market in
which the prices of major goods vary wildly from minute to minute, from person
to person, and are predicated on both fantastically complicated loyalty
programs and data collected about the individual and current market
circumstances, processed in statistical models that no human has ever
understood or evaluated. A market in which machines algorithmically game
humans and each other by adjusting prices and the nature of the goods
themselves to exploit cognitive or algorithmic flaws in other actors.[1]

The classical model of efficient, free markets ignores computational
complexity and time bounds, as the article notes. These were reasonable
approximations for a hundred or even twenty years ago, but I can forsee
environments in which these factors lead to significant asymmetry. I question
whether humans can really compete successfully in this environment, and
whether the process of doing so is really _best_ for us.

[1] Cases in point: Amazon, insurance companies, grocery stores, every major
retailer, Google, high-frequency trading firms, airline ticket sales.

~~~
artsrc
Even fairly simple tools must be able to game humans. We must be so bad at
making rational decisions that prices typically are set just below a
psychologically significant level for example $2.99. This of course assumes
the market is correct in its assessment of us.

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zeteo
Even if the problem that markets are trying to solve is NP hard, this doesn't
mean anything. Market forces are always subject to random factors. For
practical purposes, randomized approximation algorithms are actually a great
choice for tackling NP hard problems.

~~~
tmeasday
Sometimes. I think the simple answer to that is 'it depends on the problem'.

~~~
knowtheory
That's not an answer, that's an IOU for an answer, unless you can begin to
describe broad classes of problems and how they differ.

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aklein
"The majority of financial academics believe in market efficiency and the
majority of computer scientists believe that P ≠ NP. The result of this paper
is that they cannot both be right: either P = NP and the markets are
efficient, or P ≠ NP and the markets are not efficient."

I'll hazard a guess the computer scientists are right, but most financial
academics will probably get by just fine if markets are approximately
efficient - if prices can be estimated in probabilistic polynomial time.

~~~
mseebach
I'm pretty sure financial academics don't claim that markets are efficient,
but that they _tend towards_ efficiency.

~~~
wpietri
For those wanting to know more about the efficient-markets hypothesis,
Wikipedia has a good article: <http://en.wikipedia.org/wiki/Efficient_markets>

My amateur understanding is that most academics get that it's a simplifying
assumption, but that a lot of other people treat it as a guarantee. It's sort
of like people who learn a little about evolution and then conclude that a) we
are the most highly evolved organism on the planet, and b) we are therefore
perfect.

~~~
artsrc
> a) we are the most highly evolved organism on the planet

I know little about evolution and assume that bacteria are the most evolved
because they have a faster cycle of reproduction, and stronger selective
pressure.

> My amateur understanding is that most academics get that it's a simplifying
> assumption, but that a lot of other people treat it as a guarantee.

Most practitioners do understand that it is a simplifying assumption, and then
ignore that fact, just as most engineers ignore quantum and relativity effects
when calculating the required size of beams. The difference between the better
and the simpler models is big enough to cause problems in economics.

~~~
JonnieCache
_> I know little about evolution and assume that bacteria are the most evolved
because they have a faster cycle of reproduction, and stronger selective
pressure._

That you know what selective pressure means probably puts you in the top
couple of percentiles for evolution knowledge. The whole world is emphatically
not like Hacker News.

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bradshaw1965
People get tied up in knots about the Efficient Market Hypothesis. The factor
that often gets ignored when approaching the problem is the costs factor.
Trading fees, Analysis, Commissions, etc. make it very hard in practicality to
beat passive investment with the markets only being passably efficient.

~~~
artsrc
I think that analysis ignores tax effects. To have a stable excess return you
need some collection of people accept a stable lower return. This is possible
if you have different tax regimes. Tax advantaged entities can accept
coupons/dividends, and highly taxed entities want capital gains.

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hahaonlysirius
Since politicians have no business trying to solve NP problems, perhaps we'd
better deregulate the market.

~~~
rvkennedy
Been there, done that, bought the recession. Regulation, of course, isn't
"solving the NP problem", it's modifying the boundary conditions to prevent
the system from getting too far out of whack.

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bugsy
Just the concept of the proposition of this paper is pretty amazing. The
author Philip Maymin is a serious bad ass for doing this proof. What a dude.

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adas
YOU'RE GAY

------
adas
FUCK YOU

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imogynn
Free markets are a great heuristic.

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adas
shut up!!!

------
adas
PENIS

------
adas
ASSS

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NY_Entrepreneur
He's mostly smoking funny stuff: He's talking applications of optimization.
Okay. Optimization contributes problems, e.g., integer linear programming, in
set NP-complete only if one insists on exact optimality down to the last tiny
fraction of a penny of cost in the worst problems that can occur, even in
principle, in execution time that grows no faster than a polynomial in the
size of the problem. That's a LOT of very special and quite unrealistic
context.

E.g., it's not the least bit clear that finance needs to attack the worst case
problems. Even if so, finance, anywhere close to reality, doesn't need to get
solutions that save all of the last tiny fraction of a penny.

If relax worst case problems and saving the last tiny fraction of a penny,
then the situation is MUCH different. E.g., once I got a feasible solution to
an ILP with 40,000 constraints and 600,000 variables within 0.025% of
optimality on a 90 MHz Intel processor in 905 seconds. More generally, here's
an easy approach to the ILP problems: Just drop the integer constraints, solve
with LP, and then round to integer values. For the LP solution, if insist,
then use a polynomial LP solver. Crude? Sometimes. Always crude? No.

He's making a common mistake: He's assuming that because in general ILP is in
NP-complete that good work on all practical ILP problems has to be too
challenging, and that's nonsense.

