but are they accurate in a predictive sense, or only in their reaction to events? If the latter, which I think is more likely, it seems kind of a useless way to try and answer questions...
The idea is that they create an incentive to discover all possible information that may effect the price of the stock in the future, and so the eventual market price ends up reflecting all that information. That in turn lets people use that price as a signal for how to allocate capital and make decisions in the future.
It's not that they're totally accurate, it's that they're as accurate as it is possible to be. Why? Because if you knew of a better way to determine the truth, you would do so, trade on that information, bump up (or down, if shorting) the price to reflect that information, and take your profits so you could do so again. Conversely, if you're just trading randomly, somebody with better information will take all your money and you won't be able to continue trading.
The price that's reflected in a market could be considered residual uncertainty that nobody knows, i.e. if the prediction market for "Will Donald Trump win the 2020 election ?" sells at $0.60 on the $1.00, it means that after all the market participants have crunched their models, aggregated their polls, gone out and canvassed neighborhoods, ran their economic analyses, spoken to campaign insiders, and whatever else they can do, the equilibrium price assumes he has a 60% chance of winning. You don't have to actually perform all those information-gathering tasks to figure this out, you can assume that other people have been incentivized to do so and their results are now reflected in the price.
Plenty of market participants are not actually doing this. Day traders, high speed traders, even index funds come to mind. And even "real" investors are influenced by psychology that has little to do with an impartial analysis of all possible information. (It's not what you know, but what
"everybody knows that everybody knows" [1])
Sure, but markets ensure that traders who don't effectively do this lose money and get flushed out. That's the case with most day-traders, who are losing money they would otherwise put into consumption and using it to get an emotional high off price movements. Gambling, basically.
Quant high-speed traders (and arbitragers) are using information in a different way. Typically, the way these strategies work is that they discover correlations between prices. For example, when China enacts tariffs on soybeans in response to Trump's tariffs on steel & aluminum, that's going to depress demand (and hence prices) on soybeans. However, it will also have a lot of knock-on effects on other industries: shipping companies transporting soybeans will lose money, railroads connecting soybean farms to the Great Lakes will lose money, railroads connecting soybean farms to domestic demand will gain money, ranchers and chicken farms and other domestic food producers who use soybeans as feed will gain money, commodity traders could go either way, house prices in wealthy Chicago neighborhoods might increase if commodity traders are making a killing, etc. Say that the inside information entering the market is "China is enacting tariffs on soybeans". A bunch of people with that information will short soybean futures, and then it's the job of an HFT to spread that information through all the other markets that it may affect, updating the relevant prices on their securities before the profits actually trickle down through the economy.
Index funds are the freeriders of the markets. The philosophy there is that all of the work that people do is going to produce some value, and the shareholders will capture some of that value as returns to equity. And if the rest of the financial system is functioning effectively, all of this will be reflected in prices. So rather than worry about what the price will be, just buy & hold securities in proportion to their value, let the price mechanism do its job, and profit in proportion to the initial amount of capital you put in.
What does being "predictively inaccurate" mean in the context of the stock market? I assume that any time a stock jumps or falls is a symptom of inaccuracy--investors were surprised by some previously unknown--and unpriced--event.
So the low volatility of the stock market would indicate that it is actually predictively accurate, and that it is getting more so.
Then again, volatility is kind of a silly measure, because we also care about the frequency domain. The market could be very good at predicting the very short term or the very long term or both.
I wonder what a Fourier transform of the market would show?
