Live data from Hacker News

Markets are Efficient if and Only if P = NP

papers.ssrn.com

11–20 of 86 posts

Re: Markets are Efficient if and Only if P = NP

#11

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.

[deleted]

Re: Markets are Efficient if and Only if P = NP

#12
post #4

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, whi…

> 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.

Re: Markets are Efficient if and Only if P = NP

#13
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.

Re: Markets are Efficient if and Only if P = NP

#14
post #10

"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 approximatel…

I'm pretty sure financial academics don't claim that markets are efficient, but that they tend towards efficiency.

Re: Markets are Efficient if and Only if P = NP

#15
post #8

Earlier quoted context omitted.

While I'm pretty much a free-market zealot, I'm also a Hayek groupie. It seems to me that Hayek's work should show us that markets approach perfect efficiency. Because the market is a hideously complex system that only produces its information as an evolved, emergent system, then it is likely that its output is not precise but only extremely close to optimal.

Was the fall of 2008 "extremely close" to optimal? I'd submit that worldviews based on 1-dimensional criteria like "market!" or "hayek!" fall pretty far short of the mark. Although I can see the attraction. It's nice to simplify things to a level where a human being can actually have the answers with a high degree of confidence. Both the tea-party-hayekians and the linked paper fall into this trap.. what about inform…

I'm not sure you understand what the free market is, or how it works.

The fall of 2008 wasn't a free market. In particular, the government was forcing lenders to accept more risk (viz sub-prime borrowers) than they would otherwise have done. Also, the lenders themselves incorrectly modeled their risk exposures.

None of your objections:

what about information asymmetry? What about borked incentives? What about just plain stupid? "I played golf with the guy so I'll buy it"? "I know these instruments are crap but I'll sell them to my clients to get them off my balance sheet"?

hold any water:

Information asymmetry (also, incorrect information as with lenders in '08): This has nothing to do with the efficiency of markets. The efficient market hypothesis depends on actors behaving rationally to achieve their goals. That does not mean that those actors will always be correct. For example, in The Myth of the Rational Voter[1], Caplan describes how it's actually rational behavior for voters to vote irrationally: the benefit of the degree they can sway the election is far smaller than the cost of acquiring sufficient knowledge to determine what candidate would most benefit them.

Bad incentives: it's the incentives (see "Invisible Hand") that make things work properly! To the extent that the incentives are wrong, these are the regulations, the aberrations that make things deviate from the free market. In your '08 complaint, that was the Congress forcing lenders to take on borrowers that would not normally have qualified. It also comes from externalities, places where our laws prevent the free market from completely accounting for the costs of an action. For example, because air and waterways are held in common by the government, without a real owner, there is nothing capturing the cost of pollution. Thus, incomplete property rights leads to market failures. If the government got out of the way, the market could resolve it (see "Coase Theorem")

Stupidity: as separate from your other points, well, there's no such thing -- at least not that we can perceive. Mises shows that (a) each person acts to maximize his own utility, and (b) it's impossible for outside observers (and frequently even the individual himself) to know what ends he is attempting to achieve. Thus, if your hypothetical golfer places some personal value on the relationship with his golf buddy, it may be perfectly rational for him to spend extra few bucks buying from the guy. And you and I certainly aren't privy to enough information to decide that it's not so.

Fraud: your Yankees example seems to be an example of fraud, and thus can't be considered a free market transaction. Fooling someone into a transaction is no different from forcing them into a transaction.

That said, research in psychology and econometrics has shown that people do systematically misconstrue very large or very small values, leading us to sometimes choose differently from what we really intend. The only solution to this, of course, is to formally model the problem to enable us to act rationally. In this day and age, such models are de rigeur, but -- as I note above -- the investment in the models itself has some risk: we're balancing correctness against cost to develop and feed the model. As with the rational voter, this can lead us to "rationally irrational" behavior, but this is just a meta-behavior of the free market, not an indictment of it.

Moreover, there is no way around any of the issues that you cite. All of these things can be applied equally -- if not more -- to government regulators (see "public choice economics", "regulatory capture", etc.). Why would you want to give power to entities who won't be able to use it any more wisely than the people themselves?

[1] http://en.wikipedia.org/wiki/The_Myth_of_the_Rational_Voter

[2] http://en.wikipedia.org/wiki/Human_Action

Re: Markets are Efficient if and Only if P = NP

#16
post #8

Earlier quoted context omitted.

Was the fall of 2008 "extremely close" to optimal? I'd submit that worldviews based on 1-dimensional criteria like "market!" or "hayek!" fall pretty far short of the mark. Although I can see the attraction. It's nice to simplify things to a level where a human being can actually have the answers with a high degree of confidence. Both the tea-party-hayekians and the linked paper fall into this trap.. what about inform…

I'm not sure you understand what the free market is, or how it works. The fall of 2008 wasn't a free market. In particular, the government was forcing lenders to accept more risk (viz sub-prime borrowers) than they would otherwise have done. Also, the lenders themselves incorrectly modeled their risk exposures. None of your objections: what about information asymmetry? What about borked incentives? What about just pl…

So, no true scotsman?

We're in the real world here. If the real world held up to a given person's theory, communism would've worked. You just have a different theory.

I'm not claiming markets are terrible, they're usually the best way to do things. But when you pigeonhole yourself into an absolutist position, you've guaranteed that you're going to be flagrantly wrong sometimes.

Re: Markets are Efficient if and Only if P = NP

#17
post #8

Earlier quoted context omitted.

Was the fall of 2008 "extremely close" to optimal? I'd submit that worldviews based on 1-dimensional criteria like "market!" or "hayek!" fall pretty far short of the mark. Although I can see the attraction. It's nice to simplify things to a level where a human being can actually have the answers with a high degree of confidence. Both the tea-party-hayekians and the linked paper fall into this trap.. what about inform…

I'm not sure you understand what the free market is, or how it works. The fall of 2008 wasn't a free market. In particular, the government was forcing lenders to accept more risk (viz sub-prime borrowers) than they would otherwise have done. Also, the lenders themselves incorrectly modeled their risk exposures. None of your objections: what about information asymmetry? What about borked incentives? What about just pl…

> The fall of 2008 wasn't a free market. In particular, the government was forcing...

To the extent that government regulations are less strong than physical laws, isn't the market still free? For instance, methamphetamines are illegal, but they're still produced, distributed, and retailed; just with a higher cost for all involved than if they didn't have to take precautions against, and accept the probability of, detection and punishment. Given the incentives in place, the supply and demand curves for methamphetamines still meet, and the market clears.

I've always found the belief that markets can withstand any form of interference except government regulation fairly bemusing.

One side-effect that falls out of this more cosmopolitan view of free markets is that the fall of 2008 was the efficient outcome. If market participants had information about what would happen strong enough that they were willing to bet on it in 2005-2007, the catastrophic drop in 2008 would not have happened as it did.

Re: Markets are Efficient if and Only if P = NP

#18
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.

Re: Markets are Efficient if and Only if P = NP

#19
post #8

Earlier quoted context omitted.

While I'm pretty much a free-market zealot, I'm also a Hayek groupie. It seems to me that Hayek's work should show us that markets approach perfect efficiency. Because the market is a hideously complex system that only produces its information as an evolved, emergent system, then it is likely that its output is not precise but only extremely close to optimal.

Was the fall of 2008 "extremely close" to optimal? I'd submit that worldviews based on 1-dimensional criteria like "market!" or "hayek!" fall pretty far short of the mark. Although I can see the attraction. It's nice to simplify things to a level where a human being can actually have the answers with a high degree of confidence. Both the tea-party-hayekians and the linked paper fall into this trap.. what about inform…

Was the fall of 2008 "extremely close" to optimal?

Home prices crashed and then more or less stabilized. So yeah, I'd say the crash was close to an optimal price correction.

http://research.stlouisfed.org/fred2/series/SPCS20RSA?rid=19...

I'm a little confused how why you would believe people who follow Hayek are unfamiliar with questions of information asymmetry and borked incentives. After all, don't they form the basis of "The Road to Serfdom"?

Re: Markets are Efficient if and Only if P = NP

#20
post #17

Earlier quoted context omitted.

I'm not sure you understand what the free market is, or how it works. The fall of 2008 wasn't a free market. In particular, the government was forcing lenders to accept more risk (viz sub-prime borrowers) than they would otherwise have done. Also, the lenders themselves incorrectly modeled their risk exposures. None of your objections: what about information asymmetry? What about borked incentives? What about just pl…

> The fall of 2008 wasn't a free market. In particular, the government was forcing... To the extent that government regulations are less strong than physical laws, isn't the market still free? For instance, methamphetamines are illegal, but they're still produced, distributed, and retailed; just with a higher cost for all involved than if they didn't have to take precautions against, and accept the probability of, de…

Given the incentives in place, the supply and demand curves for methamphetamines still meet, and the market clears.

Sure it does. But the individual actions that occur in so doing are different than they would otherwise be. So you've got hordes of young black men (yes, stereotyping, but to make a point) killing themselves supplying drugs. This wouldn't be happening in the free market; you'd be buying it legally from your pharmacist, or even the local convenience store. Those young men would still be alive.

the fall of 2008 was the efficient outcome.

I've no doubt that this is true. Unfortunately, even in that, the perversions of the market have not been allowed to resolve themselves. We've got the "too-big-to-fail" thing that is continuing to incent risky behavior, and we've got the government shoring up housing prices, preventing that bubble from deflating.

Post reply on HN