On the marginal impact of information and arbitrage
Introduction It is self-evident that information is valuable, even indispensable, for optimal decision making when investing in ﬁnancial markets. A question which naturally arises is: at what point, if any, does the cost of additional information gathering exceed the beneﬁts? The question is complicated by the fact that information is not a homogeneous commodity. This distinguishes our question from that posed by Stigler (1961) on the diminishing marginal returns to (homogeneous) searching for the lowest price of a commodity. Under certain conditions, Radner and Stiglitz (1984) showed that for an expected utility maximisation problem under constraint, themarginal value of information at the point of no information is non-positive. For a similar result in a principal-agent setting see Singh (1985). These results suggest that information has a risingmarginal value when information is ﬁrst accumulated. Indeed, it is easy to ﬁnd examples of particular scenarios where the marginal value of information1 is negative, see below, or not diminishing. The problem arises from the heterogeneity of information in ﬁnancial markets and is complicated by the existence of both public and private information. On the other hand, it may be that, if the investors gather information about a large number of stocks, the proposition of positive but diminishing returns to information at the successive going market equilibrium points, which develop and change over time, holds true on average. The purpose of this chapter is to present a formal representation of the information accumulation process and to use this representation to formulate the testable hypotheses that, in a ﬁnancial market, the marginal value of information is, on average, positive and diminishing. Using data from a horse-betting market, it will be shown that this hypothesis cannot be rejected, in spite of the fact that it does not hold for particular horses or races. We show that the ﬂow of inside information to the market, when its gainful exploitation is permitted, positively impacts upon the market by eradicating remainingbiases in prices and that this impact is diminishing.