MARKET“ EFFICIENC tion such as an earnings report as being important, they will not necessarily agree completely on its implications, It is not possible to separate the impact of elementary information such as news releases, crop reports, etc from the subjective evaluation of this information by the participants in the market. Thus, rather than dealing with differences in"information, it will be more convenient to work with differences in forecasting ability- aring in mind that access to elementary information is a major determi nant of forecasting ability. The operational definition of an efficient market, then, is one in which the market price at any time(plus normal profits)is the best, that is, minimum variance, estimate of the future price, given the individual forecasts of all the market participant In the next section I develop a model of a speculative market with two types of traders who have differing information. I derive the stochastic difference equation which describes the redistribution of wealth among the two groups and analyze the market's short-run behavior. In the following section, I approximate the difference equation by a discrete Marke model and analyze its long-run properties, Although it is not possible to derive the steady-state wealth distribution analytically, several illustrative examples show how the market behaves with different values of the under- lying parameters. This allows me to draw some tentative conclusions about how the informational efficiency of a decentralized market should be affected by heterogeneous information, differences in the quality of traders formation, risk aversion, and so on. The final section gives a summary and conclusion I. The model A competitive market weights a trader's information by the size of his investment, so a market's informational efficiency depends on the distrib tion of wealth among its participants. In this section I develop a model of a speculative market in which the interaction of information and wealth and the resulting effects on market efficiency can be analyzed The market is made up of equal numbers of two types of traders, a and b All a traders are alike, as are all b traders, but members of the two groups may differ in price expectations, risk aversion, predictive ability, and wealth. The assumption of just two types of traders is made purely fo expositional convenience, The model developed below can readily be extended to n traders with no change in the basic results. Although there are only two groups, we will assume that each trader himself rading in a perfectly competitive market. Otherwise we would have the problem that the a traders could solve back from the observed market price to obtain the b group's information and vice versa. In a market with more han two groups, it would not be possible to determine the information held by every other participant from the market price alone Sep201303:16AM I use subject to
MARKET "EFFICIENCY 585 tion such as an earnings report as being important, they will not necessarily agree completely on its implications. It is not possible to separate the impact of elementary information such as news releases, crop reports, etc., from the subjective evaluation of this information by the participants in the market. Thus, rather than dealing with differences in "information," it will be more convenient to work with differences in forecasting abilitybearing in mind that access to elementary information is a major determinant of forecasting ability. The operational definition of an efficient market, then, is one in which the market price at any time (plus normal profits) is the best, that is, minimum variance, estimate of the future price, given the individual forecasts of all the market participants. In the next section I develop a model of a speculative market with two types of traders who have differing information. I derive the stochastic difference equation which describes the redistribution of wealth among the two groups and analyze the market's short-run behavior. In the following section, I approximate the difference equation by a discrete Markov model and analyze its long-run properties. Although it is not possible to derive the steady-state wealth distribution analytically, several illustrative examples show how the market behaves with different values of the underlying parameters. This allows me to draw some tentative conclusions about how the informational efficiency of a decentralized market should be affected by heterogeneous information, differences in the quality of traders' information, risk aversion, and so on. The final section gives a summary and conclusion. I. The Model A competitive market weights a trader's information by the size of his investment, so a market's informational efficiency depends on the distribution of wealth among its participants. In this section I develop a model of a speculative market in which the interaction of information and wealth and the resulting effects on market efficiency can be analyzed. The market is made up of equal numbers of two types of traders, a and b. All a traders are alike, as are all b traders, but members of the two groups may differ in price expectations, risk aversion, predictive ability, and wealth. The assumption of just two types of traders is made purely for expositional convenience. The model developed below can readily be extended to n traders with no change in the basic results. Although there are only two groups, we will assume that each trader views himself as trading in a perfectly competitive market. Otherwise we would have the problem that the a traders could solve back from the observed market price to obtain the b group's information and vice versa. In a market with more than two groups, it would not be possible to determine the information held by every other participant from the market price alone. 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 market is for claims on an asset which pays a random return P at the end of each period. The net supply of claims is zero, so that the only way for one trader to buy a claim is for another to sell one short. All trad ing takes place between the two groups, since all members of a given group are identical. Two features of this setup lead to considerable simplification First, Pi is independent of the operation of the market, so we have avoided the"beauty contest" problem which Keynes talked about with respect to e stock market. Second, this is a zero-sum game, so that the"normal profits"to a trader are zero, and also the analysis is not complicated by hanges in the scale of the market over time. Both characteristics are fairly closely approximated by a typical futures market in which P, represents the spot price in the contract month At the outset of each period, the two groups receive information abe Pf. Next, the market opens and an equilibrium market price is achiev by a tatonnement process.(Expectations may be revised at any point up to equilibrium, so that the market clearing price P, is part of the information set upon which expectations are ultimately based. At the equilibrium the demands of the a traders, n ", are exac tly offset by the(algebraic)demands of the b traders, n Finally the market closes, Pi is revealed, and there is a net transfer of na(p* -Pi) from b to a traders. [Of course n (Pr-Pu) may be negative, so that b traders receive money from a traders. I There will only be a wealth transfer when Pt differs from Pr, tha hen the market price is an inaccurate forecast of the future price. But the market's forecast error is just a combination of the traders'forecast errors, so the wealth redistribution in period t is a function of the traders individual errors in forecasting PI. We will derive expressions for n, and P:-,)in terms of the traders characteristics such as forecasting ability and risk aversion and their random forecast errors. The latter drive the model, and their known distribution allows us to derive an equation for the stochastic process governing the redistribution of wealth within the We now consider the expectations formation of the two groups.(In what follows the subscript t will be dropped for simplicity when it is not essential There should be no confusion about what period the variables refer to No information about P* is available before the beginning of the period traders come into the d with nonin (flat)prior di ribu 2 arises when a price change is so large that one trader cannot cover hi losses. Treating the possibility of bankruptcy explicitly would greatly complicate th takes place through a well-capitalized clearing corporation which insures all trady A odel. Instead, we will assume that in th Thus traders can transact withe that their con ts will not be fulfilled. In a case, a trader's acceptable level of risk exposure de pends on his risk aversion. In this f traders are sufficiently risk averse the probabil
586 JOURNAL OF POLITICAL ECONOMY The market is for claims on an asset which pays a random return P* at the end of each period. The net supply of claims is zero, so that the only way for one trader to buy a claim is for another to sell one short. All trading takes place between the two groups, since all members of a given group are identical. Two features of this setup lead to considerable simplification. First, P,* is independent of the operation of the market, so we have avoided the "beauty contest" problem which Keynes talked about with respect to the stock market. Second, this is a zero-sum game, so that the "normal profits" to a trader are zero, and also the analysis is not complicated by changes in the scale of the market over time. Both characteristics are fairly closely approximated by a typical futures market in which P,* represents the spot price in the contract month. At the outset of each period, the two groups receive information about PJ*. Next, the market opens and an equilibrium market price is achieved by a t67tonnement process. (Expectations may be revised at any point up to equilibrium, so that the market clearing price Pt is part of the information set upon which expectations are ultimately based.) At the equilibrium the demands of the a traders, na, are exactly offset by the (algebraic) demands of the b traders, n'. Finally the market closes, P* is revealed, and there is a net transfer of n (Pt* - Pt) from b to a traders.2 [Of course na (p -Pt) may be negative, so that b traders receive money from a traders.] There will only be a wealth transfer when P,* differs from Pt, that is, when the market price is an inaccurate forecast of the future price. But the market's forecast error is just a combination of the traders' forecast errors, so the wealth redistribution in period I is a function of the traders' individual errors in forecasting P1*. We will derive expressions for n a and (Pt* - Pt) in terms of the traders' characteristics such as forecasting ability and risk aversion and their random forecast errors. The latter drive the model, and their known distribution allows us to derive an equation for the stochastic process governing the redistribution of wealth within the market. We now consider the expectations formation of the two groups. (In what follows the subscript t will be dropped for simplicity when it is not essential. There should be no confusion about what period the variables refer to.) No information about P* is available before the beginning of the period, so traders come into the period with noninformative (flat) prior distribu- 2 A question arises when a price change is so large that one trader cannot cover his losses. Treating the possibility of bankruptcy explicitly would greatly complicate the model. Instead, we will assume that in this market (as in many actual markets) trading takes place through a well-capitalized clearing corporation which insures all trades. Thus traders can transact without fear that their contracts will not be fulfilled. In any ease, a trader's acceptable level of risk exposure depends on his risk aversion. In this model, if traders are sufficiently risk averse the probability of a bankruptcy becomes arbitrarily small. 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