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

Three informed traders are present in each of the

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Unformatted text preview: te their trades across periods 2, 3, and 4. If information acquisition is endogenous and if the cost of perfect information is c = 0.13, then we obtain the equilibrium parameters given in Table 6. In this example, each discretionary liquidity trader j trades about in period 2, in period 3, and in period 4. Note that the measure of liquidity-trading volume is highest in period 2 and then falls off in periods 3 and 4. Three informed traders are present in each of the periods except period 2, when it is profitable for a fourth to enter. The behavior of prices is therefore similar to that when traders could only time their trades. In the second example, illustrated in Table 7, we assume that there is less nondiscretionary liquidity trading. Specifically, we set the variance of nondiscretionary liquidity trading to be 0.1. With the cost of information at c = 0.04 and with endogenous information acquisition, we obtain pronounced patterns. For example, there are 11 informed traders in period 2 and three informed traders in each of the other periods. Liquidity trading is much heavier in period 2 as well, and the patterns of the volume and price behavior are very pronounced. In this example, each discretionary liquidity trader j trades in period 2, in period 3, and in period 4. 5. Extensions In this section we discuss a number of additional extensions of our basic model. We show that the main conclusions of the model do not change 28 Table 7 An example of pronounced patterns of volume and price behavior when discretionary liquidity traders allocate trading across several periods The same example as in Table 6, except that the variance of nondiscretionary liquidity trading is lower (0.1). The cost of information is assumed to be c = 0.04. in more general settings. This indicates that our results are robust to a variety of models. 5.1 Different timing constraints for liquidity traders For simplicity, we have assumed so far that the demands of all the discretionary liquidity traders are determined at the same time and must be satisfied within the same time span. In reality, of course, different traders may realize their liquidity demands at different times, and the time that can elapse before these demands must be satisfied may also be different for different traders. Our results can be extended to this more general case, and their basic nature remains unchanged. For example, suppose that there are three discretionary liquidity traders, A, B, and C, whose demands have the variances 5, 1, and 7, respectively. Suppose that trader A realizes his liquidity demand at 9:00 A.M. and must satisfy it by 2:00 P.M. that day. Trader B realizes his demand at 11:00 A.M. and must satisfy it by 4:00 P.M., and trader C realizes his demand at 2:30 P.M. and must satisfy it by 10:00 A.M. on the following day. If each of these traders trades only once to satisfy his liquidity demands, then it is an equilibrium that traders A and C trade at the same time between 9:00 A.M. and 10:00 A.M. (e.g., 9:30 A.M.) and that trader B trades sometime between 11:00 A.M. and 4:00 P.M. Now suppose that the variance of Bs demand is 9 instead of 1. Then the equilibrium described above is possible only if trader B trades before 2:30 P.M.; otherwise, trader C would prefer to trade at the same time that B trades rather than at the same time that A trades, and the equilibrium would break down. Two other equilibrium patterns exist in this situation. In one, traders B and C trade at the same time between 2:30 P.M. and 4:00 P.M. (e.g., 3:00 P.M.), and trader A trades sometime between 9:00 A.M. and 2:00 P.M. In another equilibrium, traders A and B trade at the same time between 11:00 A.M. and 2:00 P.M. (e.g., 11:30 A.M.), and trader C trades sometime between 4:00 P.M. and 10:00 A.M. of the next morning. All these equilibria involve trading patterns in which two of the traders trade at the same time. If informed traders can enter the market, then their trading would also be concentrated in the periods with heavier liquidity trading. 29 Thus, we obtain trading patterns similar to those discussed in the simple model. 5.2 Risk-averse liquidity traders We now ask whether our results change if, instead of assuming that all traders are risk-neutral, it is assumed that some traders are risk-averse. We focus on the discretionary liquidity traders, since their actions are the prime determinants of the equilibrium trading patterns we have identified. In the discussion below we continue to assume that informed traders and the market maker are risk-neutral. (A model in which these traders are also risk-averse is much more complicated and is therefore beyond the scope of this article.) A risk-averse liquidity trader, say trader j, is concerned with more than the conditional expectation of given his own demand Since he submits market orders, the price at which he trades is uncertain. In those periods in which a large amount of liquidity trading takes place, the variance of the order flow is higher. One may think that since this will make the price more variable,...
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