Lesson 3 of 7
The paradox at the centre
If prices already reflected everything, nobody would be paid to gather information, so nobody would and prices would not. The 1980 paper that says so.
By Javier Sanz
Founder of ValueScreener. Built Ninety Nine, a securities services provider, and sold it to a tier-one global bank; ran operations and internationalization at Alpaca, the brokerage API.
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In one minute
- Gathering information costs money, so somebody must be paid for doing it.
- If prices reflected all information perfectly, the payment would be zero and nobody would gather it, so prices could not reflect it.
- Grossman and Stiglitz resolve this with an equilibrium degree of disequilibrium: prices reflect informed traders' information only partially.
The strongest argument that some opportunity must exist is not a story about human weakness. It is an argument about incentives, made in 1980, and it starts by taking market efficiency completely seriously.
The circle the paper describes
- 1Prices reflect everythingInformation is free to read off the price
- 2Nobody is paid to researchCostly gathering earns no return
- 3Nobody gathers informationThe activity stops
- 4Prices stop reflecting itThere is nothing putting it there
Then back to step 1, Prices reflect everything.
The argument in the authors' words
They open with the question directly. If competitive equilibrium is defined as a situation in which prices are such that all arbitrage profits are eliminated, is it possible that a competitive economy is always in equilibrium. Their answer is that it clearly is not, because then those who arbitrage make no private return from their privately costly activity.
So the assumptions that all markets, including the market for information, are always in equilibrium and always perfectly arbitraged are inconsistent when arbitrage is costly.
What they put in its place
The paper proposes a model with what they call an equilibrium degree of disequilibrium: prices reflect the information of informed individuals, but only partially, so that those who spend resources to obtain information do receive compensation.
What this does and does not license
It does not say that opportunity is abundant, or that any particular reader can find it. The compensation in the model is the return to gathering information at its cost, which is a wage for work rather than a windfall.
What it does say is that the return to research cannot be zero in equilibrium, because at zero nobody would do the research the price depends on. That is a floor, and it is the only theoretical argument in this course for why the activity this site supports can be worth anything at all.
The question it hands back to the reader
If the compensation is a payment for costly work, then the honest question is what work you are doing that others are not, and whether the compensation exceeds your cost of doing it.
For a professional that cost is a salary and a research budget. For an individual it is hours that could have been spent elsewhere, and the comparison is not against zero but against the return on a low-cost index fund bought in ten minutes. That comparison is the subject of the last lesson in this course, and it is a harder test than the paradox.
Check yourself
What contradiction do Grossman and Stiglitz identify?
- That prices cannot fall and rise at once
- That perfectly informative prices leave no return to the costly activity that makes prices informative
- That investors disagree about value
Show the answer
Answer: B.
If arbitrage profits are all eliminated, those who arbitrage earn no private return from a privately costly activity, so the activity would not happen.What do they propose instead of perfect efficiency?
- That prices are random
- An equilibrium degree of disequilibrium, where prices reflect informed traders' information only partially
- That regulation should set prices
Show the answer
Answer: B.
Partial reflection is what leaves a return to information gathering, which is what keeps the gathering going.What kind of return does the model leave to research?
- A windfall available to anyone
- Compensation for a costly activity, which has to be judged against the cost of doing it
- None at all
Show the answer
Answer: B.
The compensation exists precisely because the work is costly, so the question for any individual is whether their return exceeds their own cost.Sources
- Grossman and Stiglitz, "On the Impossibility of Informationally Efficient Markets", American Economic Review, 1980: the inconsistency of costless arbitrage with costly information, the equilibrium degree of disequilibrium, and the number of informed individuals as an endogenous variable.
What this leaves out
- The paper is a theoretical model with strong assumptions. It shows that a return to information must exist in that model, not how large it is in any market.
- It says nothing about who earns that return, and nothing about whether any individual can.
- Nothing here is advice about any security.