On the Impossibility of Efficient Markets

On the Impossibility of Informationally Efficient Markets — Sanford Grossman and Joseph Stiglitz

Information, efficiency, and impossibility

Sanford Grossman and Joseph Stiglitz ask a seemingly innocuous question in their famous paper On the Impossibility of Informationally Efficient Markets: can a competitive economy achieve equilibrium such that all profits are arbitraged away (and prices adjust accordingly)? Their response is short and incisive:

“Clearly not, for then those who arbitrage make no return from their costly activity. Hence, the assumptions that all markets, including that for information, are always in equilibrium and always perfectly arbitraged are inconsistent when arbitrage is costly.”
Sandford Grossman & Joseph Stiglitz. (1980). On the Impossibility of Informationally Efficient Markets.

Grossman-Stiglitz model

Their conclusion stems from a simple market model consisting of profit-seeking traders. In their model, traders can buy information to identify mispricings. But they can also rely on the market price system, which is a partial signal of information. After all, we’d expect informed traders to bid up prices when the security is undervalued, and to bid down prices when it’s not.

It follows that in equilibrium, we’d expect traders to inform themselves as long as their expected utility from doing so (less the cost of information) exceeds their expected utility from staying uninformed. Mathematics and modelling aside, the Grossman-Stiglitz paper contains several intuitions that I feel are worth highlighting, many decades after its original publication.

Informed and uninformed

Firstly, from the model’s standpoint, as more traders procure information, being informed becomes relatively less attractive. For one, informed traders makes the price system more informative, which reduces the marginal benefit of acquiring costly information. What’s more, arbitrage gets tougher as more people inform themselves. It raises the ratio between informed and uninformed traders, shrinking the scope for mispricing in the marketplace.

But do we really expect being uninformed to become relatively more attractive as others inform themselves? True, the marketplace for passive instruments continues to grow. And there remains a burgeoning legion of uninformed speculators (although probably not because of rational choice). I suspect, however, that most professionals dislike the idea of being at an informational disadvantage. Psychology plus competition in turn might create a bias towards information and efficiency by extension.

Cost, quality, and noise

That aside, Grossman and Stiglitz highlight three parameters in their model that influence the informativeness of the price system: the (1) cost of information; (2) quality of information; and (3) noise. The first two factors are intuitive. Cheaper and better information makes it more attractive for traders to inform themselves. So as more traders acquire and act on their information, the informativeness of the price system rises.

By contrast, an increase in noise in the marketplace makes prices a less useful signal. This, in turn, makes it more attractive for traders to gather information. So, in a Grossman-Stiglitz world, we’d expect to find more informed traders in the equilibrium of a noisy world. Curiously, this implies a more informative price system, offsetting the detrimental effect that noise originally has on the system.

The impossibility

As good modelers do, Grossman and Stiglitz push their model to the extreme. They show that in a noiseless world, “prices convey all information” such that “there is no incentive to purchase information”. “But if everyone is uninformed”, as Grossman and Stiglitz write, then “it clearly pays some individuals to become informed”. As such, “there does not exist a competitive equilibrium” — bringing us back to the paradox we began this post with.

The authors go on to say:

“Thus, in general, the price system does not reveal all the information about “the true value” of the risky asset. … We have argued that because information is costly, prices cannot perfectly reflect the information which is available, since if it did, those who spent resources to obtain it would receive no compensation.”
Sandford Grossman & Joseph Stiglitz. (1980). On the Impossibility of Informationally Efficient Markets.

Investing without people

The Efficient Market Hypothesis tells us that there is no free lunch — that beating the market is a futile endeavor given how effectively the system aggregates information. Indeed, this is in part why many people advocate for passive index funds. Yet the reasoning behind the Grossman-Stiglitz impossibility is just as emblematic here.

Passive instruments, after all, are brainless vehicles. Its performance, as Howard Marks points out in Investing Without People, depends, somewhat ironically, on active investors for price discovery. The dichotomy between active and passive investing is akin to a Hawk-Dove problem in game theory. A world full of mindless investors is a boon for active investors. But in an environment where everybody is hyper informed, being passive might be a reasonable bet.

As Marks writes:

Nothing in a market always continues, independent and unchanged. A market is nothing more than the people in it and the decisions they make, and the behavior of those people shapes the market. … And when everyone decides to refrain from performing the functions of analysis, price discovery and capital allocation, the appropriateness of market prices can go out the window.
Howard Marks. (2018). Investing Without People. Memo to Oaktree Clients.

A fundamental conflict

The impossible results of simple models and thought experiments are telling of market realities. While we might not need the Grossman-Stiglitz paper to point out the many flaws of the Efficient Market Hypothesis, their work is a reminder that:

“There is a fundamental conflict between the efficiency with which markets spread information and the incentives to acquire information.”
Sandford Grossman & Joseph Stiglitz. (1980). On the Impossibility of Informationally Efficient Markets.

References

Grossman, Sanford., & Stiglitz, J. (1980). On the Impossibility of Informationally Efficient Markets. The American Economic Review, Vol. 70, No. 3 (Jun., 1980), pp. 393-408
Marks, Howard. (2018). Investing Without People. Memo to Oaktree Clients. Oaktree Capital. Archived memos available at <https://www.oaktreecapital.com/insights/memos>