Admati And Pfleiderer-A Theory Of Intraday Patterns - Volume And Price Variability

If the number and precision of the information of

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Unformatted text preview: ncentrated. If the number and precision of the information of informed traders is constant over time, however, then the information content and variability of equilibrium prices will be constant over time as well. We then discuss the effects of endogenous information acquisition and of diverse private information. It is assumed that traders can become informed at a cost, and we examine the equilibrium in which no more traders wish to become informed. We show that the patterns of trading volume that exist in the model with a fixed number of informed traders become more pronounced if the number of informed traders is endogenous. The increased level of liquidity trading induces more informed trading. Moreover, with endogenous information acquisition we obtain patterns in the informativeness of prices and in price variability. Another layer is added to the model by allowing discretionary liquidity traders to satisfy their liquidity needs by trading more than once if they choose. The trading patterns that emerge in this case are more subtle. This is because the market maker can partially predict the liquidity-trading 6 component of the order flow in later periods by observing previous order BOWS. This article is organized as follows. In Section 1 we discuss the model with a fixed number of (identically) informed traders. Section 2 considers endogenous information acquisition, and Section 3 extends the results to the case of diversely informed traders. In Section 4 we relax the assumption that discretionary liquidity traders trade only once. Section 5 explores some additional extensions to the model and shows that our results hold in a number of different settings. In Section 6 we discuss some empirically testable predictions of our model, and Section 7 provides concluding remarks. 1. A Simple Model of Trading Patterns 1.1 Model description We consider a single asset traded over a span of time that we divide into T periods. It is assumed that the value of the asset in period T is exogenously given by where , t = 1,2, . . . , T, are independently distributed random variables, each having a mean of zero. The payoff can be thought of as the liquidation value of the asset: any trader holding a share of the asset in period T receives a liquidating dividend of dollars. Alternatively, period T can be viewed as a period in which all traders have the same information about the value of the asset and is the common value that each assigns to it. For example, an earnings report may be released in period T. If this report reveals all those quantities about which traders might be privately informed, then all traders will be symmetrically informed in this period. In periods prior to T, information about is revealed through both public and private sources. In each period t the innovation becomes public knowledge. In addition, some traders also have access to private information, as described below. In subsequent sections of this article we will make the decision to become informed endogenous; in this section we assume that in period t, nt traders are endowed with private information. A privately informed trader observes a signal that is informative about Specifically, we assume that an informed trader observes where Thus, privately informed traders observe something about the piece of public information that will be revealed one period later to all traders. Another interpretation of this structure of private information is that privately informed traders are able to process public information faster or more efficiently than others are. (Note that it is assumed here that all informed traders observe the same signal. An alternative formulation is considered in Section 3.) Since the private information becomes useless 7 one period after it is observed, informed traders only need to determine their trade in the period in which they are informed. Issues related to the timing of informed trading, which are important in Kyle (1985), do not arise here. We assume throughout this article that in each period there is at least one privately informed trader. All traders in the model are risk-neutral. (However, as discussed in Section 5.2, our basic results do not change if some traders are risk-averse.) We also assume for simplicity-and ease of exposition that there is no discounting by traders.3 Thus, if ,summarizes all the information observed by a particular trader in period t, then the value of a share of the asset to that trader in period t is where E ( • • ) is the conditional expectation operator. In this section we are mainly concerned with the behavior of the liquidity traders and its effect on prices and trading volume. We postulate that there are two types of liquidity traders. In each period there exists a group of nondiscretionary liquidity traders who must trade a given number of shares in that period. The other class of liquidity traders is composed of traders who have liquidity demands that need not be satisfied immediately. We call these discretionary liquidity traders and assume that their demand for shares is determined in some period T’ and needs to be satisfied before period T",...
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