W CHICAGO JOURNALS Market Efficiency in a Market with Heterogeneous Information Author(s): Stephen Figlewski Source: Journal of Political Economy, Vol 86, No 4(Aug, 1978), pp. 581-597 Published by: The University of Chicago Press StableUrl:http://www.jstor.org/stable/1840380 Accessed:11/09/20130302 Your use of the JSTOR archive indicates your acceptance of the Terms Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@ jstor. org he University of Chicago Press is collaborating with JSTOR to digitize, preserve and extend access to Journal of Political Economy 的d http://www.jstororg This content downloaded from 202. 115.118.13 on Wed, I I Sep 2013 03: 02: 16 AM All use subject to STOR Terms and Conditions
Market "Efficiency" in a Market with Heterogeneous Information Author(s): Stephen Figlewski Source: Journal of Political Economy, Vol. 86, No. 4 (Aug., 1978), pp. 581-597 Published by: The University of Chicago Press Stable URL: http://www.jstor.org/stable/1840380 . Accessed: 11/09/2013 03:02 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. . The University of Chicago Press is collaborating with JSTOR to digitize, preserve and extend access to Journal of Political Economy. http://www.jstor.org This content downloaded from 202.115.118.13 on Wed, 11 Sep 2013 03:02:16 AM All use subject to JSTOR Terms and Conditions
Market""in a Market with Heterogeneous Information Stephen Figlewski New York Unicersity It is commonly felt that a financial market achieves informational efficiency as traders with the best information and the most skill make profits at the expense of those with inferior information or ability and come to dominate the market. This paper develops a model of a specula- tive market in which this redistribution of wealth among traders with different information and ability can be studied. In the short run the mar ket tends toward increased efficiency, but in neither the short nor the ong run is full efficiency likely. The average deviation from efficiency is shown to depend on traders' characteristics such as the quality and diversity of their information and their risk aversion From the time of Adam Smith, economists have extolled the virtues of the competitive price system as a mechanism for allocating scarce resources among competing use en the proper assumptions, the free operation of the competitive market can be shown to result in a Pareto-optimal allo- cation of goods. But for certain goods whose characteristics are not com- pletely known, the market has the additional role of aggregating the avai able information about these characteristics. a share of ibm stock represents a claim on future earnings whose total value cannot be known n the present. The market price for IBM represents an aggregate opinion about the company's future prospects based on whatever information may be currently available to the participants in the market. And in general if we define a speculative market broadly as a market for a good demande ot(entirely) for its own sake but for resale(or potential resale) in th future, the current price in a speculative market will always have at least a component which is the market's estimate of the future price. In most to Glenn Loury, Steven Sheffrin, Jerry low for an extraordinarily in- Hausman and iversity of Ch:ica:. 6022- 3808/78/8604-004501 4 Sep201303:16AM I use subject to
Market "Efficiency" in a Market with Heterogeneous Information Stephen Figlewski New York University It is commonly felt that a financial market achieves informational efficiency as traders with the best information and the most skill make profits at the expense of those with inferior information or ability and come to dominate the market. This paper develops a model of a speculative market in which this redistribution of wealth among traders with different information and ability can be studied. In the short run the market tends toward increased efficiency, but in neither the short nor the long run is full efficiency likely. The average deviation from efficiency is shown to depend on traders' characteristics such as the quality and diversity of their information and their risk aversion. From the time of Adam Smith, economists have extolled the virtues of the competitive price system as a mechanism for allocating scarce resources among competing uses. Given the proper assumptions, the free operation of the competitive market can be shown to result in a Pareto-optimal allocation of goods. But for certain goods whose characteristics are not completely known, the market has the additional role of aggregating the available information about these characteristics. A share of IBM stock represents a claim on future earnings whose total value cannot be known in the present. The market price for IBM represents an aggregate opinion about the company's future prospects based on whatever information may be currently available to the participants in the market. And in general, if we define a speculative market broadly as a market for a good demanded not (entirely) for its own sake but for resale (or potential resale) in the future, the current price in a speculative market will always have at least a component which is the market's estimate of the future price. In most I am indebted to Glenn Loury, Steven Sheffrin, Jerry Hausman, and an anonymous referee for many valuable suggestions and to Robert Solow for an extraordinarily insightful conjecture which proved to be the basis of this essay. [Journal of Political Economy, 1978, vol. 86, no. 4] (? 1978 by The University of Chicago. 0022-3808/78/8604-0004$01.44 58i This content downloaded from 202.115.118.13 on Wed, 11 Sep 2013 03:02:16 AM All use subject to JSTOR Terms and Conditions
OURNAL OF POLITICAL ECONOMY cases,of course, speculative prices serve as signals which affect produc decisions in the rest of the economy. Equity prices affect firms tment decisions, commodity futures prices determine storage and production, ar so on. We would like to know how information is actually incorporated into a market price and especially whether the information-processing function of a competitive speculative market has optimality properties like those which apply to the allocative function. Is there formational invisible hand" which leads a competitive speculative market to make the optimal use of the information that society has available? One answer to this question comes in the form of the"efficient-markets hypothesis. Under this hypothesis, a competitive speculative market is typically asserted to be"efficient"in the sense that the current marke price always fully reflects"all available information or the current price, plus normal profits, is the "best estimate 'of the future price. Although there is clearly some kind of optimality property involved, such terms as fully reflects"or"best estimate "are sufficiently imprecise that there is a wide latitude among economists on what"efficiency"should mean exactly Fama(1970) distinguishes three degrees of market efficiency,"weak semistrong, 'and"strong, " according to what type of information is fully reflected in the market price. A market is weakly efficient if the current price always completely discounts the information contained in the history of past market prices. The semistrong form of efficiency widens the scope to include all publicly available information. In addition to the history of past prices, the market accurately evaluates such things as dividend decla- rations, crop reports, and, we might expect, Wall Street Journal articles Finally, the strong form of efficiency occurs when the market accurately discounts all information, including that held only by small numbers of market participants Obviously there is a large difference between weak and strong efficiency in terms of the optimality properties they imply for information processing in a decentralized market. The social value of a mechanism for aggregat- g information depends on its ability to generate price signals that accu rately reflect all of society s information. Thus only a market that is effi- cient in the strong sense can really be said to have the optimality properties we would like. Throughout this paper, "efficiency"will be taken to mean strong efficiency. ine the mechanism by which a speculative market would achieve and maintain informational efficiency, we are led, like Cootner, to the following kind of story: Given the uncertainty of the real world, the many actual and virtual investors will have many, perhaps equally many, price If any group of consistently]better than average in forecasting stock price, they would accumulate Sep201303:16AM I use subject to
582 JOURNAL OF POLITICAL ECONOMY cases, of course, speculative prices serve as signals which affect productive decisions in the rest of the economy. Equity prices affect firms' investment decisions, commodity futures prices determine storage and production, and so on. We would like to know how information is actually incorporated into a market price and especially whether the information-processing function of a competitive speculative market has optimality properties like those which apply to the allocative function. Is there an informational "invisible hand" which leads a competitive speculative market to make the optimal use of the information that society has available? One answer to this question comes in the form of the "efficient-markets hypothesis." Under this hypothesis, a competitive speculative market is typically asserted to be "efficient" in the sense that the current market price always "fully reflects" all available information or the current price, plus normal profits, is the "best estimate" of the future price. Although there is clearly some kind of optimality property involved, such terms as "fully reflects" or "best estimate" are sufficiently imprecise that there is a wide latitude among economists on what "efficiency" should mean exactly. Fama (1970) distinguishes three degrees of market efficiency, "weak," "semistrong," and "strong," according to what type of information is fully reflected in the market price. A market is weakly efficient if the current price always completely discounts the information contained in the history of past market prices. The semistrong form of efficiency widens the scope to include all publicly available information. In addition to the history of past prices, the market accurately evaluates such things as dividend declarations, crop reports, and, we might expect, Wall Street Journal articles. Finally, the strong form of efficiency occurs when the market accurately discounts all information, including that held only by small numbers of market participants. Obviously there is a large difference between weak and strong efficiency in terms of the optimality properties they imply for information processing in a decentralized market. The social value of a mechanism for aggregating information depends on its ability to generate price signals that accurately reflect all of society's information. Thus only a market that is efficient in the strong sense can really be said to have the optimality properties we would like. Throughout this paper, "efficiency" will be taken to mean strong efficiency. If we try to imagine the mechanism by which a speculative market would achieve and maintain informational efficiency, we are led, like Cootner, to the following kind of story: Given the uncertainty of the real world, the many actual and virtual investors will have many, perhaps equally many, price forecasts. . . . If any group of investors was consistently better than average in forecasting stock price, they would accumulate This content downloaded from 202.115.118.13 on Wed, 11 Sep 2013 03:02:16 AM All use subject to JSTOR Terms and Conditions
MARKET“ EFFICIENCY wealth and give their forecasts greater and greater weight In the process, they would bring the present price closer to the true value. Conversely, investors who were worse than average in forecasting ability would carry less and less weight. If this process orked well enough, the present price would reflect the best information about the future in the sense that the present price, plus normal profits, would be the best estimate of the future price [967,P.80] In this view market efficiency is a condition that is achieved in the long run as wealth is redistributed from investors with inferior information to hose with better information. Of course in the short run. before this has a chance to happen, the distribution of wealth and the distribution of ormation quality may be very different. Since the market weights traders'information by"dollar votes, " not quality, a trader with superior information but little wealth may have his information undervalued in the market price, and the market will be inefficient. However, there will exist some distribution of wealth--we might call it the efficient-market distribu tion-for which the dollar- vote weights are identical with information quality weights and each trader's information is accurately reflected in the market price. If the distribution of wealth ultimately converges to thi efficient-market distribution, in the long run the market does become informationally efficient. The purpose of this paper is to develop a model of a speculative market in which the convergence can be analyzed. We find that in the short run the distribution of wealth tends to move toward the efficient-market distribution. a trader whose information was under- valued has an expected profit, and one whose information was overvalued has an expected loss. But in the longer run, random fluctuations in wealth sulting from the inability st prices perfectly lead to deviatio from the efficient-market wealth distribution and consequently from market efficiency. In general the market price is not the best estimate of the future price, given the currently available information. From the long run orsteady-state distribution of wealth we can calculate the average fficiency of the market, as measured by the average variance of the market's forecast error, and compare it with the efficient-market vari ance. The difference can be thought of as the efficiency cost of processing information through a decentralized market rather than a centralized hority. A series of examples will give some idea of how this cost depends on the underlying parameters of the market such as the traders' risk aversion, the disparity in their forecasting abilities, and so on The existence of the efficient-market wealth distribution undoubtedly requires some on traders'demands In the model presented below, these are satis- fied. and market distribution exists and is unique. Sep201303:16AM I use subject to
MARKET EFFICIENCY 1 583 wealth and give their forecasts greater and greater weight. In the process, they would bring the present price closer to the true value. Conversely, investors who were worse than average in forecasting ability would carry less and less weight. If this process worked well enough, the present price would reflect the best information about the future in the sense that the present price, plus normal profits, would be the best estimate of the future price. [1967, p. 80] In this view market efficiency is a condition that is achieved in the long run as wealth is redistributed from investors with inferior information to those with better information. Of course in the short run, before this has a chance to happen, the distribution of wealth and the distribution of information quality may be very different. Since the market weights traders' information by "dollar votes," not quality, a trader with superior information but little wealth may have his information undervalued in the market price, and the market will be inefficient. However, there will exist some distribution of wealth we might call it the efficient-market distribution-for which the dollar-vote weights are identical with informationquality weights and each trader's information is accurately reflected in the market price.1 If the distribution of wealth ultimately converges to this efficient-market distribution, in the long run the market does become informationally efficient. The purpose of this paper is to develop a model of a speculative market in which the convergence can be analyzed. We find that in the short run the distribution of wealth tends to move toward the efficient-market distribution. A trader whose information was undervalued has an expected profit, and one whose information was overvalued has an expected loss. But in the longer run, random fluctuations in wealth resulting from the inability to forecast prices perfectly lead to deviations from the efficient-market wealth distribution and consequently from market efficiency. In general the market price is not the best estimate of the future price, given the currently available information. From the long run or "steady-state" distribution of wealth we can calculate the average efficiency of the market, as measured by the average variance of the market's forecast error, and compare it with the efficient-market variance. The difference can be thought of as the efficiency cost of processing information through a decentralized market rather than a centralized authority. A series of examples will give some idea of how this cost depends on the underlying parameters of the market such as the traders' risk aversion, the disparity in their forecasting abilities, and so on. I The existence of the efficient-market wealth distribution undoubtedly requires some regularity conditions on traders' demands. In the model presented below, these are satisfied, and the efficient market distribution exists and is unique. This content downloaded from 202.115.118.13 on Wed, 11 Sep 2013 03:02:16 AM All use subject to JSTOR Terms and Conditions
JOURNAL OF POLITICAL ECONOMY The question of the informational efficiency of a decentralized financial market has already been raised in a different manner in a series of recent papers by Grossman(1975, 1976)and Grossman and Stiglitz(1975, 1976 They show that when information is costly to obtain it cannot be true that the market price will accurately reflect all available information. If the market price revealed all information for free, it would not pay anyone invest in information gathering individually, But if no one gathered information there would be none for the market to reveal. Thus an infor nationally efficient market is incompatible with costly information. Gross- man and Stiglitz 's solution to this difficulty is to expand the traditional concept of market equilibrium to one of"informational equilibrium In addition to the standard equilibrium condition that supply equals demand in every period, there is the further condition that the market price must reveal just enough of the costly information that participants are indifferent between becoming"informed" or remaining"uninformed In full equilibrium, the market price does not reveal all the information, nd traders who buy information do earn a higher return in the market But the extra return is just sufficient to offset the cost of the information and the expected return, including the cost of information, is equal for informed and uninformed traders An important feature of the Grossman and Stiglitz models is that the redistribution of wealth among bad and good forecasters which Cootner (1967)talks about is not a factor. In all of their models, investors are assumed to have constant absolute risk-aversion utility functions which have the property that the demand for a given risky asset is independent of wealth. Even if the good forecasters do accumulate wealth over time, this does not lead to a heavier weighting of their forecasts in the marke price. Adjustment to informational equilibrium occurs not because of re- distribution of wealth among traders but because of entry into and exit from the information-collection business. Thus deviation from market ciency arising from wealth redistribution, which will be a principal feature of the model I analyze below, is over and above the informational inefficiency that Grossman and Stiglitz discuss. The foregoing discussion has revolved around the question of how a ompetitive financial market processes information without considering specifically what"information"consists of. In the Grossman and Stiglitz framework, information is a datum which allows a trader to reduce h forecast variance of the next period price. If every trader possessed the formation, they would have identical expectations about the future price learly, this view of information is rather restrictive. We can easily think of things which not all market participants would consider even to be information at all. For example, the news that IBM had just completed a perfect"head and shoulders"top would be information to some, not others. More generally, even if all traders accept a certain piece of informa Sep201303:16AM I use subject to
584 JOURNAL OF POLITICAL ECONOMY The question of the informational efficiency of a decentralized financial market has already been raised in a different manner in a series of recent papers by Grossman (1975, 1976) and Grossman and Stiglitz (1975, 1976). They show that when information is costly to obtain it cannot be true that the market price will accurately reflect all available information. If the market price revealed all information for free, it would not pay anyone to invest in information gathering individually. But if no one gathered information, there would be none for the market to reveal. Thus an informationally efficient market is incompatible with costly information. Grossman and Stiglitz's solution to this difficulty is to expand the traditional concept of market equilibrium to one of "informational equilibrium." In addition to the standard equilibrium condition that supply equals demand in every period, there is the further condition that the market price must reveal just enough of the costly information that participants are indifferent between becoming "informed" or remaining "uninformed." In full equilibrium, the market price does not reveal all the information, and traders who buy information do earn a higher return in the market. But the extra return is just sufficient to offset the cost of the information, and the expected return, including the cost of information, is equal for informed and uninformed traders. An important feature of the Grossman and Stiglitz models is that the redistribution of wealth among bad and good forecasters which Clootner (1967) talks about is not a factor. In all of their models, investors are assumed to have constant absolute risk-aversion utility functions which have the property that the demand for a given risky asset is independent of wealth. Even if the good forecasters do accumulate wealth over time, this does not lead to a heavier weighting of their forecasts in the market price. Adjustment to informational equilibrium occurs not because of redistribution of wealth among traders but because of entry into and exit from the information-collection business. Thus deviation from market efficiency arising from wealth redistribution, which will be a principal feature of the model I analyze below, is over and above the informational inefficiency that Grossman and Stiglitz discuss. The foregoing discussion has revolved around the question of how a competitive financial market processes information without considering specifically what "information" consists of. In the Grossman and Stiglitz framework, information is a datum which allows a trader to reduce his forecast variance of the next period price. If every trader possessed the information, they would have identical expectations about the future price. Clearly, this view of information is rather restrictive. We can easily think of things which not all market participants would consider even to be information at all. For example, the news that IBM had just completed a perfect "head and shoulders" top would be information to some, not to others. More generally, even if all traders accept a certain piece of informaThis content downloaded from 202.115.118.13 on Wed, 11 Sep 2013 03:02:16 AM All use subject to JSTOR Terms and Conditions