1. For example, Robert Lucas, who was recently awarded a Nobel Prize in economics, used a rational-choice analysis when he argued that high unemployment could not be eliminated through a Keynesian strategy of short-term interest rate cuts because rauonal employers and investors would anticipate that such measures would be short-lived. Great Expectations, and Rational Too, Economist 96 (1995)Google Scholar; see generally Redman, Deborah A., A Reader's Guide to Rational Expectations (1992).Google Scholar

2. Hart, Oliver D. & Kreps, David M., Price Destabilizing Speculation, 94 J. Pol. Econ. 927, 928 (1986)CrossRefGoogle Scholar. See Fridson, Martin S., Exactly What Do You Mean by Speculation? J. Portfolio Mgmt. 29 (Fall 1993).CrossRefGoogle Scholar

3. Stein, Jeremy C., Informational Externalities and Welfare-Reducing Speculation, 95 J. Pol Econ. 1123 (1987)CrossRefGoogle Scholar. See Hart, & Kreps, , supra note 2, at 927Google Scholar (citing large literature on the question); infra text accompanying notes 7 and 8 (discussing differing theories of normative consequences of speculation).

4. See Keynes, John Maynard, A Treatise on Money (1930)Google Scholar; Hicks, John R., Value and Capital (1946).Google Scholar

5. See Grossman, Sanford & Stiglitz, Joseph, On The Impossibility of Informationally Efficient Markets, 70 Am. Econ. Rev. 393 (1980)Google Scholar; see also Kyle, Albert S., Informed Speculation with Imperfect Competition, 56 Rev. Econ. Stud. 317 (1989).CrossRefGoogle Scholar

6. Yet a third approach occasionally found in literature equates speculation with storage of inventory. According to this model, speculators are traders who make a living by holding themselves out as willing to buy from — or sell to — other traders willing to suffer the bid-ask spread that compensates the speculator for the costs and risks of maintaining inventory. In effect, this liquidity-dealing approach likens speculators to used-car dealers who can “buy low and sell high” because other traders value the convenience they offer. See, e.g., Hart, & Kreps, , supra note 2, at 928Google Scholar (developing model of consumers and speculators where “‘speculation’ is synonymous with storage”).

Like the risk-hedging model, the liquidity model implies that speculation provides mutual gains from trade, because consumption traders willingly suffer liquidity dealers' bid-ask spreads in return for being able to buy and sell quickly and conveniently, while dealers enjoy reliable profits from providing liquidity.

7. Though often cited, this argument fails to recognize that improved price accuracy is not enough, alone, to conclude that trading produces a net social benefit. Acquiring and analyzing information is costly. Information arbitrageurs incur research costs not out of altruism, but because they extract wealth from the uninformed traders with whom they deal. Thus, uninformed traders bear the cost of arbitrageurs' becoming informed, and there is no guarantee that the social value of more accurate prices exceeds the costs of information arbitrage to uninformed traders. Hirshleifer, Jack, The Private and Social Value of Information and the Reward to Inventive Activity, 61 Am. Econ. Rev. 561 (1971).Google Scholar

As an example of this point, consider the extreme case of information that allows an arbitrageur to forecast with certainty that a particular company's assets will be destroyed within minutes by a meteorite strike. Assume no steps can be taken to prevent, or even alleviate, the loss. The ability to predict the meteorite strike has no social value, because acquiring the information does not permit society to allocate resources more efficiently. The prediction nevertheless has substantial private value to the arbitrageur who can extract wealth from uninformed traders by shorting the company's stock. Thus, the arbitrageur might spend substantial resources on meteorite prediction, even though such expenditures are wasteful from a social perspective.

8. See, e.g., Posner, Richard A., Economic Analysis of Law 47–48 (4th ed. 1992)Google Scholar (arguing that speculation “performs a valuable economic function” by improving price accuracy and allowing mutually beneficial trades between speculators and hedgers).

9. Although these profits might be statistically risky, they should also be certain. See infra text and note 14 (risk and uncertainty).

10. Similarly, the possibility that speculators are paid for storing goods over time and providing liquidity to buyers and sellers seems better captured by the label “dealing” than “speculating.” See supra note 6 (liquidity-dealing model).

11. See Stout, Lynn A., Are Stock Markets Costly Casinos? Disagreement, Market Failure, and Securities Regulation, 81 Va. L. Rev. 611, 661–07 (1995)CrossRefGoogle Scholar (discussing evidence that trading in the secondary stock market is dominated by actively managed pension and mutual funds that try to outperform the market by buying and selling securities they perceive to be “mispriced”).

12. See id. at 664 (actively managed pension funds and mutual funds that try to achieve higher returns through short-term trading on average underperform the market); Telser, Lester G., Why There Are Organized Futures Markets, 24 J. Law & Econ. 1, 7, 9 (1981)CrossRefGoogle Scholar (reviewing studies finding that traders in futures markets who identify themselves as profit-seeking speculators on average incur losses).

13. This unflattering view is reflected in the fact that hostility toward speculation appears a fundamental characteristic of American law. A variety of common-law and statutory legal doctrines work to raise the costs of speculative transactions, confine them to limited venues, or ban them entirely. Examples include the Commodities Exchange Act; insurance law's rules of indemnity and insurable interest; the common-law doctrine of champerty; the Securities Exchange Act's margin requirements and short sales restrictions; and the Internal Revenue Code's minimum holding period requirement for favorable capital gains treatment of income from the sale of assets. See generally Stout, Lynn A., Derivatives, Difference Contracts, and the Social Value of Antispeculative Rules (1997) (manuscript on file with the author).Google Scholar

14. Although “risk” and “uncertainty” are often used interchangeably, the two words are not synonyms. Finance theorists apply the word “risk” to circumstances where a future outcome is unknown, but the probability distribution of possible future outcomes is known. Thus a coin toss is merely risky. Although we do not know whether a tossed coin will come up heads or tails, we know–and can agree— there is a 50 percent chance of either occurring. “Uncertainty” applies to situations where the probability distribution itself is unknown, permitting different individuals to make differing estimates of probabilities. The stock market, for example, is uncertain as well as risky.

15. Thus the standard Capital Asset Pricing Model (CAPM), a staple of modern Finance, explicitly assumes that all investors make identical subjective estimates of the likely future risks and returns associated with individual securities. The CAPM accordingly takes account of risk while ignoring uncertainty. Stout, Lynn A., How Efficient Markets Undervalue Stocks: CAPM and ECMH under Conditions of Disagreement and Uncertainty, 19:2Cardozo L. Rev. (1997).Google Scholar

16. The requisite of statistical uncertainty provides a fundamental distinction between the HE approach and the risk-hedging model. This is because trading inspired by differential risk aversion requires risk, but not uncertainty: As long as agents' tastes for risk differ, hedging deals would be negotiated even between agents who shared identical expectations for the probable distribution of risky future prices.

The relationship between uncertainty and the information-arbitrage model is more complex. In a sense, arbitrageurs armed with superior information hold differing subjective estimates of asset values than their less-informed counterparties who are trading for consumption or similar nonspeculative reasons. At the same time, the counterparties do not really disagree with arbitrageurs' estimates, so much as they deliberately choose to remain relatively less-informed and avoid the costs of research.

17. Speculator losses are inconsistent with the risk-hedging and information-arbitrage models, which each predict that speculators on average ought to profit from their trades. Of course, price volatility (risk) implies that speculators occasionally lose money on a transaction. Over time, however, a speculator willing to accept risk or to invest in truly superior information should reap certain profits. In contrast, the HE model also incorporates the common intuition that speculation involves a high probability of loss for speculators. After all, when two people trade on disagreeing predictions, at least one must be disappointed.

18. The ex post error characteristic of HE trading can be described as a consequence of imperfect information that permits uncertainty (subjective disagreement). Given perfect information regarding the future, bull and bear both would know whether gold were going to rise or fall. No trade would occur because if one were willing to buy the other would be unwilling to sell, and vice versa. Imperfect information permits uncertainty, however, and uncertainty permits bull and bear to hold differing expectations that lead them to perceive opportunities to extract trading profits from each other despite the zero-sum nature of such transactions.

19. The phrase “common-value asset” refers to any asset that agents who share homogeneous expectations would value equally. Thus, a payment of money, or a highly liquid financial instrument reflecting the right to a stream of payments, usually is regarded as a common value asset on the theory that people attach identical values to money. Noncommon value assets are assets for which agents have unique tastes, such as mango ice cream or opera tickets. Agents who share identical expectations for the future may nevertheless display varying willingness to pay for noncommon value assets.

20. This result is in contrast to hedging trades that redistribute risk, which can be mutually beneficial to both speculator and nonspeculator ex post as well as seeming mutually beneficial ex ante. Information arbitrage perhaps should not be described as mutually beneficial, because rational consumption traders would prefer a market witliout information arbitrageurs to a market with them. Information arbitrage does not, however, involve ex post error: The consumption traders who trade at a systematic disadvantage relative to information arbitrageurs decline to invest in information because the costs, to them, outweigh the benefits.

21. See Stout, Lynn A., Betting the Dank: How Derivatives Trading Can Increase Risks and Erode Returns in Financial Markets, 21 J. Corp. L. 53, 62 (1995).Google Scholar

22. Because the prices of nongold assets are likely to vary in different patterns from gold prices (e.g., stock prices rise when gold prices fall), diversifying can reduce the overall risk or variation in an asset portfolio. See generally Brealey, Richard A. & Myers, Stewart C., Principles of Corporate Finance 129–74 (4th ed. 1991)Google Scholar (discussing risk-reducing benefits of diversification).

23. In effect, speculators' ex post mistaken belief they will earn trading profits creates the illusion of a “risk premium” that compensates them for increasing their risk exposure.

24. Readers who are interested in more formal expositions of this intuition can consult a large and growing finance literature on heterogeneous expectations asset pricing models. See, e.g., Sharpe, William F., Portfolio Theory and Capital Markets 104–13 (1970)Google Scholar (chapter entitled “Disagreement”); Lintner, John, The Aggregation of Investor's Diverse Judgments and Preferences in Purely Competitive Securities Markets, 4 J. Fin. & Quant. Analysis 347 (1969)CrossRefGoogle Scholar; Miller, Edward R., Risk, Uncertainty, and Divergence of Opinion, 32 J. Fin. 1151 (1977)CrossRefGoogle Scholar; Williams, Joseph T., Capital Asset Prices with Heterogeneous Beliefs, 5 J. Fin. Econ. 219 (1977)CrossRefGoogle Scholar; Jarrow, Robert, Heterogeneous Expectations, Restrictions on Short Sales, and Equilibrium Asset Prices, 35 J. Fin. 1105 (1980)CrossRefGoogle Scholar; Mayshar, Joram, On Divergence of Opinion and Imperfections in Capital Markets, 73 Am. Econ. Rev. 114 (1983)Google Scholar; Varian, Hal R., Divergence of Opinion in Complete Markets: A Note, 40 J. Fin. 309 (1985)CrossRefGoogle Scholar; Stout, Lynn A., Are Takeover Premiums Really Premiums? Market Price, Fair Value, and Corporate Law, 99 Yale L. J. 1235 (1990)CrossRefGoogle Scholar; Booth, Richard A., Discounts and Other Mysteries of Corporate Finance, 79 Cal. L. Rev. 1053CrossRefGoogle Scholar; Kurz, Mordecai, Asset Prices with Rational Beliefs (Monograph, Center for Economic Policy Research, Stanford University) (02 1994)Google Scholar; Stout, , supra note 15Google Scholar. One of the more interesting implications of this literature is that, when markets are in some form incomplete or imperfect, the introduction of speculators can in some cases destabilize prices, leading to a speculative “bubble.” See, e.g, Stout, , supra note 13 (discussing bubbles)Google Scholar; Treynor, Jack, “Bulls, Bears and Market Bubbles” (unpublished manuscript on file with author).Google Scholar

25. See Stein, , supra note 3, at 1125Google Scholar (noting that papers on speculation tend “to ignore the issue of heterogeneous information among market participants”); see, e.g., Hart, & Kreps, , supra note 2 at 928–29Google Scholar (focusing on storage function and assuming speculators have access to the same information and draw identical inferences); Leach, John, Rational Speculation, 99 J. Pol. Econ. 131, 132 (1991)CrossRefGoogle Scholar (modeling speculation where all agents place an identical value on an asset). Of course, the information-arbitrage model implies heterogeneity in the sense that informed arbitrageurs' expectations differ from uninformed consumption traders' expectations. This heterogeneity, however, is due to differential information costs rather than statistical uncertainty. See supra text and notes 14–16,18 (discussing requisite of uncertainty in heterogeneous expectations analysis).

26. Hirshleifer, Jack, Speculation and Equilibrium, 89 Q. J. Econ. 519 (1975)CrossRefGoogle Scholar; Hirshleifer, Jack, The Theory of Speculation Under Alternative Regimes of Markets, 32 J. Fin. 975 (1977)CrossRefGoogle Scholar. Hirshleifer attributes a similar approach to Holbrook Working.

27. I have argued at length elsewhere that a heterogeneous expectations approach may solve a number of mysteries that have long plagued scholars studying financial markets and speculative behavior. See, e.g, Stout, , supra note 11Google Scholar; Stout, , supra note 13Google Scholar; Stout, , supra note 15Google Scholar; and Stout, , supra note 11.Google Scholar

28. A recent search of the LEXIS “lawrev” database did not uncover a single citation to either of Hirshleifer's articles on speculation.

29. See, e.g., Aumann, Robert J., Agreeing to Disagree, 4 Annals Stat. 1236 (1976)CrossRefGoogle Scholar; Geanakoplos, John D. & Polmarchkis, Heraklis M., We Can't Disagree Forever, 28 J. Econ. Theory 192 (1982)CrossRefGoogle Scholar; Milgrom, Paul & Stokey, Nancy, Information, Trade, and Common Knowledge, 26 J. Econ. Theory 17 (1982)CrossRefGoogle Scholar; Tirole, Jean, On the Possibility of Speculation under Rational Expectations, 50 Econometrica 1163 (1982).CrossRefGoogle Scholar

30. Interestingly, the idea that mistaken disagreement with market price may inspire some trading has recently reappeared in form of “noise theory,” which postulates that some subset of traders in the market suffer from cognitive defects that make them value securities irrationally. Curiously, noise theorists generally cite neither Hirshleifer nor his critics. See, e.g., De Long, J. Bradford et al. , The Size and Incidence of the tosses from Noise Trading, 44 J. Fin. 681 (1989)CrossRefGoogle Scholar; De Long, J. Bradford et al. , Noise Trader Risk in Financial Markets, 98 J. Pol. Econ. 703 (1990)CrossRefGoogle Scholar; Shleifer, Andrei & Summers, Lawrence H., The Noise Trader Approach to Finance, J. Econ. Persp. (Spring 1990), 19CrossRefGoogle Scholar; Campbell, John Y. &: Kyle, Albert S., Smart Money, Noise Trading, and Stock Price Behaviour, 60 Rev. Econ. Stud. 1 (1993).CrossRefGoogle Scholar

31. The underlying idea has sometimes been termed the “Groucho Marx Theorem” in honor of Groucho's observation that he would never want to belong to any club that would have him as a member.

32. Unless, of course, they have a taste for risk.

33. It can be argued, however, that different individuals' priors may tend to converge over time as they gain experience by repeatedly drawing from the same urn (the world) and revise their estimates. This approach suggests die value of a “learning” model of trading behavior. See infra Part VI.A. (learning model).

34. Milgrom, & Stokey, , supra note 29, at 18.Google Scholar

35. See, e.g., Tirole, , supra note 29 at 1164Google Scholar (trading on subjective disagreement irrational); Mahoney, Paul G., Is There a Cure for “Excessive” Trading?, 81 Va. L. Rev. 713, 722–24 (same)CrossRefGoogle Scholar; see also supra note 30 (“noise” theorists who presume some speculators are irrational).

36. See Hirshleifer, Jack, Two Models of Speculation and Information, in Time, Uncertainty, and Information 292–99Google Scholar (Hirshleifer, Jack ed., 1989)Google Scholar; Stout, Lynn A., Agreeing to Disagree over Excessive Trading, 81 Va. L. Rev. 751 (1995).CrossRefGoogle Scholar

37. See supra note 19 (common-value assets).

38. See generally Thaler, Richard H., The Winner's Curse: Paradoxes and Anomalies of Economic Life 50–62 (1992).Google Scholar

39. Id. at 51, 61, & n. 10 (winner's curse inconsistent with rational expectations).

40. Id. at 52.

41. Thaler, , supra note 40, at 54–55.Google Scholar

42. See sources cited supra note 30.

43. See sources cited supra note 24.