On the Impossibility of Informationally Efficient Markets: Comment - Cothren, Richard (American Economic Review, 1982)
In a recent paper in this Review, Sanford Grossman and Joseph Stiglitz challenge the Efficient Markets notion that in an asset market any time prices fully reflect all available (p. 404). The purpose of this comment is to argue that certain theorems and comments of Grossman and Stiglitz do not necessarily follow when an error in the specification of the informed trader's demand function for the risky asset is corrected. In Theorem 5(b) (p. 401), Grossman and Stiglitz show that when informed traders have perfect information concerning a risky asset's yield, no overall equilibrium will exist; that is, there will be no equilibrium value for the proportion of informed traders, X. Inspection of equations (8), (8'), and (9) (p. 396) helps to give intuitive reasons why this is so. If no individual purchases an observation of the information point 0, that is, if X = 0, then for a sufficiently small value of C, the cost of obtaining an observation of the information point 0, an individual could increase his expected utility by purchasing the information. If some fraction of traders purchase the information point 0, that is, if X >0, from equation (8) it is seen that as 0,2 0 (as informed traders obtain better information) small movements in 0 have a nearly infinite effect upon the informed trader's demand for the risky asset and hence upon the asset's price. Thus, according to Grossman and Stiglitz, for a fixed X > 0, as q2 0, the price system becomes perfectly informative as to the informed trader's observation of 0. Thus for X > 0 and a,2 = 0, no individual will wish to purchase 0 at cost C. But for XA-c2 0 and small C it pays an individual to purchase 0. Clearly then for q,2= 0 no equilibrium exists. Equation (8) plays a crucial role in Theorem 5(b). However, equation (8) ignores the fact that X1i, the ith informed trader's demand for the risky asset, is constrained by his wealth, Woi. In fact, if the informed trader has perfect information (so that 0 is the return on the risky asset), then the informed trader simply invests in the asset with the higher yield. Thus for UE2 = 0, equation (8) ought to read