But your proof also works against any system that involves people (i.e. all of them), so is the real question whether markets are as efficient as possible given the constraints of having to use fallible people?

The word market loses all meaning without people. Markets are inherently a trade relationship between people.

I agree with your examples and I agree that markets aren't efficient, but the "proof" you present is invalid because individual investors could be inefficient yet that doesn't mean that in aggregate markets are inefficient. (Informally, this reminds me of the central limit theorem.)

I agree with your logic. To self-interpret: I think my rationale demonstrates that the claim "markets are inefficient" is coherent, and my examples demonstrate that its true.

The central limit theorem doesn't get you close enough to perfect efficiency to distinguish between P and NP.

As a fan of the EMH..

It is a model. All models are wrong. Some are useful.

The EMH is very useful. For example, a good understanding of its failure modes can lead to opportunities for profit. You list a few potential failure modes.

or an understanding that "efficiency" depends on diffusion of information, thus when information has uneven diffusion times-- an efficient market still allows for information-diffusion arbitrage.

I'm going to throw this out there as an idea (it's probably not new) - I would argue the markets are efficient on a long enough time scale. Yes, stock prices don't always instantaneously reflect true value, but on a long enough time scale, months to years, they do.

The time scale is usually dependent on the transparency of the company's financials to investors. For public companies, the time scale is measured in quarters. For private companies, it could be measured in years or decades.

And this actually lines up with the EMH - stock prices reflects all available information. Nothing about the hypothesis says it reflects the true value when key information is unavailable (e.g. fraud or a private company that doesn't open their books).

> Markets are obviously not efficient. The proof is trivial. Have you ever made a mistake? Congrats, that’s your proof.

The problem with your comment (and this paper) is that it misrepresents what economists mean when they talk about the EMH. A more widely accepted interpretation of the EMH is just that it's impossible to reliably predict asset prices, or colloquially "beat the market", and it has a lot of evidence going for it (e.g. the poor track record of professional traders and fund managers over long periods of time).

That version is also obviously wrong. It is possible for individual people to more correctly analyze the value of an asset than the stock market. People who looked carefully into the mortgages underlying mortgage-backed securities during the housing bubble (e.g., Michael Burry) are a good example of this. They clearly were not right "by accident" - they were right because they carefully analyzed the underlying assets, at a time when most people were not doing so.

In order to make the EMH plausible, you have to restrict it so much that it's essentially meaningless: something on the order of, "If you take the ensemble of market players, they do not beat the market on average." But it's clear that individual market players do often better understand the value of particular assets than the market, and not just because they're lucky, but because they just do better analysis than the crowd does.

This doesn't prove the EMH wrong. In order to prove EMH is wrong you need to show someone like Michael Burry can consistently outperform the market using only publically available information. Making one good trade (no matter how large) isn't that.

In fact, following your reasoning every trade would invalidate the EMH. If the price goes up afterward then the buyer was "right" and if the price goes down afterward then the seller was "right".

One trade is enough, if the reason for that trade is something other than dumb luck. The idea behind demanding consistency is that you can get lucky with one trade, but that over the long run, your luck will average out, and your true ability will show. The EMH says that your true ability to judge value won't be greater than the market's ability to judge value. But there are cases where it's clear that the trade wasn't merely luck. That's why I gave the example of the housing bubble: people using only public information were able to better judge the value of MBSs, and it wasn't just luck. They were objectively smarter than the market, because they did something that most people weren't doing: they analyzed the underlying assets. Put another way, the market can behave irrationally, and can seriously mis-price assets. In fact, it often does so, and the reason is not simply that there's missing information. The reason is that people are irrational, lazy, hubristic, etc.

> In fact, following your reasoning every trade would invalidate the EMH.

No, only trades in which the person making the right call was right by something other than luck.

The strongest version of the EMH that actually holds is probably something on the order of, "If you pick a random investor, their expected returns are the same as those of the broader market." That is, you have to weaken it until it's trivially correct.

I almost totally agree, and want to add a related observation - it isn't so much that the market is efficient (it isn't) but that anyone who makes the market more significantly more efficient will become very wealthy. So the market has big incentives to move towards efficiency.

This is interesting to me. It makes me wonder "are there cases where someone made the market more efficient and was not made very wealthy?" I think you're right that there is a massive incentive for the market to be more efficient, but I suspect there are cases where people were able to develop alpha without being able to capitalize on it, because the market denied or neglected the insight.

Were there free markets in the 17th century, would they have been able to incorporate Galileo's insight? Or would they have joined the church in denunciation? Part of me thinks that if they did eventually come around to the solar system, it wouldn't be all that quick.

Did Jonas Salk make the market more efficient?

"Markets can remain irrational longer than you can remain solvent."[1]

In other words, you can also lose money, even if you're right.

1. Pseudo-Keynes: https://quoteinvestigator.com/2011/08/09/remain-solvent/

Perhaps, but the Google anti-trust suit would seem a timely contradiction too. Monopolies are incentivised to keep the market inefficient (or roughly as efficient as it is) because change jeopardises their dominant position.

A monopoly is not a market. One person is not a group.

A monopoloy dominates a market but you are welcome to ignore that.

interesting. Let me see if I can parrot that back in a different way. If one investor 'messes up' (an inefficiency). Another one may step in and make it 'closer to efficient' as there is some value to be made. That would assume an unlimited number of investors maybe? inefficiency is therefore removed from the system. On a static scale which most people forget the market is most certainly not one, it would be in an inefficient state. But as time iterates on it would tend towards it as inefficient actors remove themselves.

It’s kind of amazing in retrospect that “the markets are efficient” was a position leading up to 2008 that didn’t get you laughed out of the room.

Nowadays we know that markets aren’t perfectly efficient, 2008 was quite the instruction, and we can now have a serious discussion about degrees of efficiency and inefficiency that the markets achieve.

That's not the definition of an efficient market though. An efficient market isn't a guarantee of a correct price. It just means the known information is reflected in the price:

"The efficient-market hypothesis (EMH) is a hypothesis in financial economics that states that asset prices reflect all available information."

2008 is not a contradiction and the other examples by the parent aren't contradictions either.

This is a misinterpretation of what is meant by the efficient market hypothesis. "a hypothesis that states that share prices reflect all information and consistent alpha generation is impossible". What they're saying is that the market correctly sets share prices based on available information. To say that the market is considering available information is tautological and not interesting. The EMH as its popularly understood is not just "the market considers information" (again, not an interesting claim) but "the market considers all information and synthesizes it correctly" which is deflating to hopeful investors and trivially false. My examples are contradictions to this hypothesis.

> "the market considers all information and synthesizes it correctly"

This is a further misrepresentation of the efficient market hypothesis. The efficient market hypothesis states that the price agreed upon by the market is accurate to a risk-adjusted level, to the extent that it is not possible to consistently beat the returns of the market.

This is generally proven true by the fact that most funds fail to beat their benchmarks in any given year, and the more long term you start to look, the closer the number of funds that outperform their benchmarks gets to 0.

Page 9 of this document shows this quite conclusively: https://www.spglobal.com/spdji/en/documents/spiva/spiva-us-y...

Anybody who "beats the market" on any given day could only achieve that by discovering an inefficiency in the markets decision making. The efficient market hypothesis doesn't say that this is impossible. It says that it's impossible to do this consistently, which is reflected quite accurately in the historical performance of mutual funds. I guess the theory is flawed in the sense that it doesn't define how long you have to beat the market for before you can be considered 'consistent' at it, but I'd consider the small number of funds that achieve this over any significant period as being within the error bars of luck.

The point is that you can not beat the market with your interpretation of the available information. This is not a question of the correctness of any given interpretation. Correctness can never be determined, there is no "correct" or "incorrect" interpretation of the available information.

EDIT: So one thing to consider is that markets are predictive. A "correct" interpretation is only correct if it can predict what will happen in the future. And because the future is not predictable (proof needed but whatever) there is no way to know which interpretation is "correct".

But this is also obviously false. Markets are subject to human phenomena, like mob mentality, which is the theme of the examples I listed.

The same way fantastic tennis players can consistently outperform the rest of the competition, fantastic traders can certainly outperform others. Of course, in an ultra competitive environment, with a massive number of constant competitors, its very hard to retain a number one spot. Its also hard to predict markets because of the very fact that they're inefficient and irrational. There are so many active participants its hard to predict how they will react to available information.

Take 2008 for instance. There was public information demonstrating fatal weakness in the housing market, but it was neglected en masse. This makes it very hard to beat the market. Even if you're correct, the market could decide to ignore the facts, and you wouldn't be able to reap any alpha from your observation.

You don't seem to understand the problem. If there is a way to consistently "beat" the market then everyone will adopt the strategy and you're no longer ahead. The only way you can beat the market is by having exclusive access to information or opportunities (dumb luck) and by definition the vast majority of people do not have these, otherwise they wouldn't be exclusive.

But that’s obviously not true, at least not all of the time. In 2008 there was plenty of information indicating that the market was not healthy, and a number of market actors spotted this early on and won big betting against what the market was doing. They neither had insider information nor was it luck; the market in 2008 was catastrophically wrong about what the price of mortgage backed CDOs should be.

> If there is a way to consistently "beat" the market then everyone will adopt the strategy and you're no longer ahead.

Sure, assuming every market participant has knowledge of the winning strategy, and the skills to employ it..which is a pretty big caveat.

By this logic why do some chess players beat others? Wouldn't they all simply adopt the same strategy?

I'm stuck between these definitions, which seem to represent polar opposites. On the one hand, I can follow the argument and agree that by that definition, it is "trivially false". However, how do you square this with the generally correct observation that investors in the long term cannot / don't seem to be able to outperform the markets? Or do you feel this is wrong?

I think it is true that it is very hard to beat the market. That can be true without the market being perfectly efficient. The way I see it is that the market is ultra competitive and full of very competent & very rational (not perfectly rational) individuals with a very high incentive to interpret facts correctly. So its not easy to beat the market. You have to be very knowledgeable, and invest very deeply in order to generate insights your competitors dont have. As another commenter mentioned, its not clear to me how economically sensible it is to make this kind of investment.

If you play chess against someone, and you discover a winning strategy, and you play it repeatedly, they'll eventually discover your strategy and be able to counter you. Your opponents in the market are adaptive in this same way, so trying to always stay ahead is very hard. Some funds find some way (which I am not privy to) to succeed at this, and people still make boat loads of money as professional traders or quants, so there is reason to believe it is possible.

The fact that it is possible to have a very successful career in finance as a quant or trader also seems to me like evidence the efficient market hypothesis (taken in its strongest form, that markets are perfectly efficient) is false.

>The fact that it is possible to have a very successful career in finance as a quant or trader also seems to me like evidence the efficient market hypothesis (taken in its strongest form, that markets are perfectly efficient) is false.

It's the opposite. Traders increase market efficiency up to a certain point. If traders didn't exist then markets couldn't be efficient in the first place. Liquidity problems would persist and cause large spreads between buy and sell prices.

This just isn't true that investors don't beat the markets in the long term though. Sure many don't, but there are plenty of examples who do. And really all it takes is one who does to disprove itt.

To be more clear, the statement should have been that on average, they don't. As far as I am aware, this _is_ true, although quite surprising, and not a popular idea among investors. The second part of the argument is interesting. On the one hand, a la Warren Buffet's analogy of thousands of professional coin flippers, it is obvious that a small number will do great, while the average will do average (or slightly worse, because of fees). This does not imply that there are _zero_ people who can consistently and on average outsmart the markets, only that it seems to take more than the median full time, relatively highly trained professional to do so.

I mean the market literally is the average of everybody's position so I would say it's a tautology that the average performance of everyone who participates in a market will equal an index of that market.

But sure you could always define efficiency in an unattainable way by saying no matter how much you beat the market your streak could end down the line and the limited sample size means it doesn't prove anything.

And to me that's what efficient markets are. This unfalsifiable word game you can play where as long as the definition is flexible enough, you get to say the sentence "markets are efficient".

Is warren buffet himself not an example of someone who has been able to consistently generate alpha?

I think this question is hard to comprehend when you blow it up to this massive scale. Heres a simpler (and I claim) equivalent problem.

Imagine you're in a room with a friend. You're both tasked with estimating the price of a company. You both read through the companies 10Ks and whatever other information you can dig up. You read a bit more carefully than your friend, and detect an issue in the company's finances. Now you have alpha, and can develop a better estimate.

The market is this same scenario, but there are millions of folks playing the same game. That means its harder to find that undiscovered blip of insight, but that doesn't mean it doesn't lie in wait for the diligent. Just as there are still original thoughts, there are still original insights, and possessing them means, for a moment, you can beat the market.

>Is warren buffet himself not an example of someone who has been able to consistently generate alpha?

Sure but the exception proves the rule. We don't have a whole generation of Warren Buffets, we only have one.

They might just be statistical outliers. Given infinite time, would any investor beat the market? That's the real question (sticking to the mathematical theory here).

Be careful before holding up a single example as an exception to the rule. Some basic statistical analysis show there was a 30% chance the Red Baron, the most famous WW1 fighter pilot, was just lucky. And obviously his luck eventually ran out.

https://www.scientificamerican.com/article/news-bytes-red-ba...

Or thee might not be. If your burden of proof is that no data is valid because new data might come in that disagrees, then sure it's easy to see why you can't acknowledge that someone has disproved the theory. It also makes the theory unfalsifiable ie meaningless. So we are right back at it not being meaningfully true.

2008 was an example in which known information was not reflected in the price. There was a huge amount of mortgage-backed securities that were backed by non-performing loans. Anyone who did due diligence could have figured this out, and some did. But most people didn't do due diligence, so extremely important, publicly available information was not factored into the price of MBSs.

I have a competing hypothesis. "Efficiently inefficient markets hypythesis". It says that alpha is possible, but that it takes a lot of work and smarts and that you may be better off working your dayjob than trying to beat the market unless you have comparative advantages.

The thing is that there is a limited of value that the market generates. Like producing half a million tons of steel or something. If you extract more value than the market generates then you have to take that value from someone else who made a mistake. Therefore maximum upside by "beating the market" is limited by the amount of mistakes other people are making and that upside is much smaller than you get from simply taking market returns.

I think we're arguing semantics. Markets are obviously more efficient than a single investor or you would be able to beat the market with public information. And when you're able to beat the market you're making it more efficient.

It's easy for politicians to blame 2008 on the markets, but I think it was caused by Keynesian government policies.

I assume we'll have similar problems soon with all the stimuli being granted.

Wasn’t 2008 crisis due to excessive risk-taking by government-backed banks?

I doubt it is an “instruction” on markets efficiency — yes, if a government puts a lot of tax and newly-printed money in ponzi-schemes, bad things will happen.

Actually markets are efficient, they just aren't maximally efficient.

That is like saying that Bubblesort is efficent because it is more efficient than https://en.wikipedia.org/wiki/Bogosort :-) Unless you come up with an upper bound of efficiency loss your statement is IMHO pretty meaningless.

You're talking about real world markets which are obviously not efficient by theoretical standards. They are not efficient the same way a physical ball is not spherical compared to a mathematical sphere.

Of course there are some errors in real life. The more interesting question is how far from optimality the markets are. To carry on your analogy, a tennis ball is not perfectly spherical but it is round enough for practical use.

Similarly, the market can be 99.99% efficient, in which case it's obviously not entirely perfect but close enough that the average citizen is extremely unlikely to find any real arbitrages (which is what the EMH is essentially about).

I didn't read the full paper carefully, but does this mean P != NP? :)

The paper blatantly lies about proving that if P=NP, then markets are efficient.

It actually argues that if P=NP, and Moore's law continues indefinitely, then eventually someone could build an efficient market.

If Moore's law continues indefinitely, then we will climb the 2^n NP problem cost with a 2^t computer speed, which means that any specific NP-hard problem will become solvable in an amount of time linear in n.

However the number of stock data points goes up over time, making it more like 2^(n*t) cost.

lol

we did it reddit

Right. The idea that anybody takes efficient markets seriously is outlandish.

Another simple proof is that not everybody bets on the market for every opinion they have but the market only prices info if you act in the market.