Joseph Stiglitz. I think a paradox would be the best thing to have named after me. Photographer: Jerome Favre/Bloomberg
Joseph Stiglitz. I think a paradox would be the best thing to have named after me. Photographer: Jerome Favre/Bloomberg

A while back, I wrote a post about high-frequency trading and the Grossman-Stiglitz paradox. Today, Joseph Stiglitz gave a speech about high-frequency trading and the Grossman-Stiglitz paradox, and if you usually come here for your Grossman-Stiglitz paradox news, I guess you should go there. It's his paradox. Half his paradox. It's not my paradox, anyway.

A brief refresher:

  • The Grossman-Stiglitz paradox says that if asset prices perfectly reflected all information, then there would be no reason for anyone to collect information and trade assets, so asset prices couldn't perfectly reflect all information.
  • High-frequency trading is really fast trading that tends to make asset prices really quickly reflect certain kinds of information -- particularly, the information that informed traders are buying a stock.

Stiglitz is not pro-HFT:

If sophisticated market players can devise algorithms that extract information from the patterns of trades, it can be profitable. But their profits come at the expense of someone else. And among those at whose expense it may come can be those who have spent resources to obtain information about the real economy. These market players can be thought of as stealing the information rents that otherwise would have gone to those who had invested in information. But if the returns to investing in information are reduced, the market will become less informative. Better "nanosecond" price discovery comes at the expense of a market in which prices reflect less well the underlying fundamentals. As a result, resources will not be allocated as efficiently as they otherwise would be.

Because one reason that market efficiency matters is that prices are a signal to companies about where they should invest. Facebook's recent purchases, for instance, tell entrepreneurs that developing new messaging apps is an order of magnitude more valuable for society than is developing virtual reality. And high-frequency trading does not do much for those signals, because, you know, the usual: High-frequency trading happens faster than you can blink, and the people deciding what real investments to make are too busy blinking to pay attention to it.

Those making real decisions, e.g. about how much to invest in a steel mill, are clearly unlikely to be affected by these variations in prices within a nanosecond. In that sense, they are fundamentally irrelevant for real resource allocations.

This is perhaps not the whole story, but it is a story.

Coincidentally, today Noah Smith wrote a review of Michael Lewis's "Flash Boys." The core oddity of "Flash Boys" is that the victims of high-frequency trading identified in the book tend to be billionaire hedge-fund managers. So why should we feel bad for them?

Lewis' answer is that the investors are investing money on behalf of you and me - pension fund managers, for example, or mutual fund managers. But why should that require a lot of trading? Your pension manager is not Warren Buffett - he is not going to beat the market year after year. What he should do is to put your retirement money into a nice diversified basket of assets - ETFs, index funds, and the like - and just let it sit there for decades, maybe rebalancing it once a year or so. If he does that, the tiny amount that he gets front-run by HFTs at the beginning and end of those decades is going to make precisely zilch of a difference to your retirement account. ...

In other words, HFT acts as a tax on trading, but much of that trading is hurting your mom and dad's retirement accounts in the first place. In fact, if HFTs prompt pension funds to shift to passive management (or to "patient capital" investing that improves corporate governance), that could A) improve the efficiency of the financial sector, and B) boost returns for you and your mom and dad. In fact, there are signs that this is already happening! Led by California's massive CALPERS, big pension funds are shifting more and more money into ETFs, index funds, and the like.

Indexing is basically the contrapositive of the Grossman-Stiglitz paradox. If everyone tries to beat the market, then it will be hard to beat the market: You'll be competing with everyone else to get information that you can use to outperform the market. If it's hard to beat the market, it makes good sense to index. If everyone starts indexing, then it's easy to beat the market: Nobody else is gathering information, so any information that you gather will make you money.

If Calpers, which has massive resources and can pay massive fees to professional outside investment advisers, decides to stop doing that -- or at least scale back on it -- and just throw its money into index funds, then it will contribute less to capital allocation decisions. But that doesn't necessarily mean that capital allocation decisions will get worse. Other active investors will have less competition, and so will be able to make more money from doing their own research. They'll allocate capital, and Calpers will happily piggyback on their efforts. If it's unsatisfied, it can always just increase its own active investment efforts.

You could build a model where there are two counteracting forces in modern equity markets:

  1. The rise of passive indexing increases the potential rewards to fundamental informed investors.
  2. The rise of high-frequency trading decreases the potential rewards to fundamental informed investors.

It is not obvious which of these effects predominates. All in all, though, there's probably no reason to get too worked up about it. The fact that there are still massive amounts of active investment, and that many of high-frequency trading's victims are billionaires, suggests that the rewards to information gathering are still large.

(Matt Levine writes about Wall Street and the financial world for Bloomberg View.)

  1. Here is a good description of the Grossman-Stiglitz paradox from, er, Stiglitz, in that speech:

    They pointed out that if the market instantaneously and fully conveyed information from the informed to the uninformed, it would not pay anyone to obtain information. If it were true that markets were informationally efficient, it would thus mean that they would only convey costless information. The market would, in some sense, be very uninformative, even though it conveyed all the information that had been acquired. That in turn would mean that if there were a social value to price discovery, the market could only perform that function well if it were not informationally efficient. Grossman and Stiglitz show that there can in fact exist an equilibrium amount of disequilibrium, where prices do not fully convey all the information from the informed to the uninformed.

    Here is the relevant paper. Grossman is Sanford J. Grossman, btw.

  2. What? Ugh. Also, I mean, this is kind of wrong; efficiency is more about liquid traded markets than it is about Mark Zuckerberg's whims. But of course markets are aggregators of whims.

  3. Also it can send false signals. Stiglitz:

    There is an additional level of distortions: the informed, knowing that there are those who are trying to extract information from observing (directly or indirectly) their actions, will go to great lengths to make it difficult for others to extract such information. But these actions to reduce information disclosure are costly. And, of course, these actions induce the flash traders to invest still more to figure out how to de-encrypt what has been encrypted.
    If, as we have suggested, the process of encryption and de-encryption is socially wasteful -- worse than a zero sum game -- then competition among firms to be the best de-encryptor is also socially wasteful. Indeed, flash traders may have incentives to add noise to the market to disadvantage rivals, to make their de-encryption task more difficult. Recognizing that it is a zero sum game, one looks for strategies that disadvantage rivals and raise their costs. But of course, they are doing the same.
  4. When we last discussed it I cited Cliff Asness and Austin Gerig as advocates of HFT's efficiency. In particular, the rapid dissemination of information makes markets in some sense "fairer," so if you are an uninformed investor you are more likely to get the right price. This is not necessarily good (or bad) for capital allocation, but I guess it's nice for someone. Also the quicker synchronization may, as Gerig argues, make it less important to have so much fundamental research: You can get the same allocation efficiency with less work.

    That sounds implausible if you talk about "flash trading," but if you instead think about "algorithms that identify correlations between one asset and another" then it makes more sense. If generations of informed investors making fundamental decisions have made Company X and Company Y move in tandem with each other, then maybe you don't need as many analysts to cover Company Y. The algorithms can do it.

  5. I've linked to it before, but Smith's previous high-frequency trading/"Flash Boys" post was also very good.

  6. Here by "everyone" I'm sort of ignoring uninformed individual investors and focusing on people and institutions who research and make investment decisions for a living and try to be informed investors, whether or not they actually succeed.

  7. Certainly as a class, active managers tend to underperform passive strategies, though this is a matter of arithmetic and expenses. The potential rewards to active management -- and, in particular, the private rewards to the managers themselves -- remain large.

  8. By the way, on the topic of my thesis that Grossman-Stiglitz should be the basis of any system of market regulation, here is a paper that I found a little unsatisfying. The title -- "Beyond Efficiency in Securities Regulation" -- sounds like the law review article I've always wanted to write, and the author identifies important issues like the the lower returns to informed traders caused by HFT, and the weirdness of "materiality" standards in a world of algorithmic trading (a pet cause of mine). But she's not big on offering concrete proposals, and sometimes treats high-frequency trading as essentially random noise trading rather than as Grossman-Stiglitzian rapid information propagation, which leads her into error in discussing materiality.

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Matthew S Levine at

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