For this paradox to function, information would have to be static, unless I'm missing something.

This seems to be a case of a feedback loop creating emergent behavior.

Let's say almost everyone believed in the Efficient Market Hypothesis (EMH). Then, trading would decrease significantly, since most people would think that stocks are already fairly priced. That means the few people who trade would move the market significantly, based on whatever idiosyncratic value-theories they had.

But then the EMH believers would see wild moves in the market and stop believing in EMH. They would start trading more to gain profits.

And as more traders participated, the market would behave more and more like the EMH were true. Eventually, the market would stabilize. Prices wouldn't swing so much. This would increase the number of EMH believers.

It would be interesting to survey belief in EMH among traders. If my model is correct, the percentage of EMH believers should be roughly constant, or at least oscillate around some optimum value.

The EMH is a description of how the market behaves when a sufficiently large number of independent actors are looking for alpha. It is not a prescription of how the market should behave.

The conclusion is that with a sufficiently large number of actors in the market all seeking profits by trying to find misevaluation of stock prices, the excess profits of any individual actor will (assuming they all have access to the same information) converge to zero.

Its less a paradox and more a matter of game theory. Every investment firm which gives up trying to look for alpha (believing it is fruitless) means the remaining firms have more opportunities to find stocks with available information not reflected in the price. There's no paradox here: each individual actor is incentivized to participate in order to not miss out on that potential for excess profits, and the net effect is the EMH.

See also:

> The Grossman-Stiglitz Paradox is a paradox introduced by Sanford J. Grossman and Joseph Stiglitz in a joint publication in American Economic Review in 1980[1] that argues perfectly informationally efficient markets are an impossibility since, if prices perfectly reflected available information, there is no profit to gathering information, in which case there would be little reason to trade and markets would eventually collapse.[2]

* https://en.wikipedia.org/wiki/Grossman-Stiglitz_paradox

So the more efficient markets are, the hard it will be to find "alpha" (returns), and so more people will stop trying. But as more people stop trying, markets will become more inefficient, in which case people can find alpha again, which encourages more participants.

Anyone who has lived through a market correction (the tariff announcements in early April this year being a recent example, though there have been far worse) should be able to see that market prices do not always accurately reflect even the consensus view of value (which itself can be wrong). As people are forced to de-lever, everything goes down at once, often by very similar amounts, even though it cannot be possible that everything suddenly lost the same amount of value simultaneously.

To quote Richard Bookstaber, "The principal reason for intraday price movement is the demand for liquidity... the role of the market is to provide immediacy for liquidity demanders. ...market crises... are the times when liquidity and immediacy matter most. ...the defining characteristic is that time is more important than price. ...diversification strategies fail. Assets that are uncorrelated suddenly become highly correlated, and all positions go down together. The reason for the lack of diversification is that in a high-energy market, all assets in fact are the same.... What matters is who holds the assets." (from A Framework for Understanding Market Crises, 1999)

Was the market drop an accurate reflection of the value that would have been destroyed by those tariffs, discounted by the probability that they would have been enacted as drafted? Nobody knew then, and I maintain that nobody even knows now. That was not the calculation that was being made.

    the hypothesis maintains that
    stock prices reflect all relevant
    information about the stock

This is a common description of the EMH. But every time I read it, I think: Does information really directly impact the price of a stock? How?

What if it takes 12 months of hard thinking to draw the right conclusion from the information? Are there many investors who go to such lengths? Are they all thinking at the same speed? And if not, what does that tell us about the EMH?

Google released DeepDream in 2015. My feeling is that with enough thinking, one could have predicted where image generation is going in the next decade and that language generation would go a similar route. And that this will lead to a high demand in Nvidia's GPUs. But that thinking would not be instantly. It would take months or years.

I think what is unquestionable is that statistically, given available information, it is hard to make money against other market participants.

It is a form of informational efficiency, but it does not necessarily follow that prices are even statistically correct. The market can be irrational for longer than you can remain solvent.

I forget where I first heard it, but there's a joke about two economists walking down the street. One of them notices a $20 bill on the ground and points it out out, saying "Look, it's $20 just lying there on the sidewalk!" The other shakes his head and says "No, that can't be true; if it were, someone else would have picked it up already"

My practical interpretation of the EMH is more that easily accessible, public information is already priced in. But non-obvious insights may not be simply because the volume of people trading on that information will be smaller.

EMH is nonsense that is repeated routinely to scare people from trading the market.

Information characterizing a company’s value isn’t the same thing as information indicating a company’s value. There can be a lot of analysis and model building in between. And different models can behave very differently, even if their prediction strength is similar.

Information publicly available doesn’t mean anyone can process it all. Every actor is operating off a different subset of information.

Lots of intentionally low information investors (inhabitants of indexed funds) demand stock or supply stock, pushing prices in directions unrelated to value changes, due to index list changes and rebalancing events.

Investors, of all magnitudes of wealth, have unending personal or private idiosyncratic reasons for the timing of many investments or sales.

The value of a stock rises and falls as its absolute expected return rises and falls relative to the changing returns of the rest of the entire market of investment vehicles. Everything impacts everything.

All these shifts happen over varying time frames.

Many relevant market facts are time varying themselves, often with turbulence and ambiguity.

The fast moving investors most influential in setting prices, must model the whole market’s 2nd order and even 3rd order reactions (by similar actors) due to feedback effects and dynamics.

Sudden market wide changes trigger waves of low analysis buying and selling. Compounded by the higher order risk this creates to leverage, annuity responsibikities, hedging, and many other amplifiers of behavior.

Meanwhile the market, business and information keep moving, so only highly predictable or illiquid assets are ever going come close to matching any ideal value with price.

The efficient market hypothesis is an interesting and enlightening thought experiment. A reduced dimension toy/sim market.

But not a credible model.

Even if every single participant was frantically and relentlessly re-valuing and re-balancing to a firehose of comprehensive market information.

Does the EMH state that prices will reflect on the price of a stock instantly? If not, I don’t think there’s a paradox. EMH would just mean it will eventually converge? I guess that makes it pretty toothless in practice then.

I feel like the stock market is pretty divorced from fundamentals at this point i.e. speculation makes it more like a Keynesian beauty contest (picking stocks you think other people will think are valuable).

https://en.m.wikipedia.org/wiki/Keynesian_beauty_contest