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

With more liquidity trading in a given period more

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Unformatted text preview: f trading for the liquidity traders was shown to be λ (nt, Ψ t) Ψ t. That this cost is decreasing in n follows from the fact that Ψ (nt, Ψ t) is decreasing in nt. Thus, endogenous information acquisition intensifies the effects that bring about the concentration of trading. With more liquidity trading in a given period, more informed traders trade, and this makes it even more attractive for liquidity traders to trade in that period. As already noted, the intuition behind this result is that competition among the privately informed traders reduces their total profit, which benefits the liquidity traders. The following proposition describes the effect of endogenous information acquisition on the trading volume and price process.14 Proposition 4. Suppose that the number of informed traders in period t is the unique nt satisfying π (nt + 1, Ψ t) < c ≤π (nt, Ψ t) (i.e., determined by the second model of entry). Consider an equilibrium in which all discretionary liquidity traders trade in period t*. Then Proof The first three statements follow simply from the fact that V, and VtI are increasing in nt, and that Qt, is decreasing in nt. The last follows from Equation (16). n Example (continued). We consider again our example, but now with endogenous information acquisition. Suppose that the cost of acquiring perfect information is 0.13. In periods 1, 2, and 4, when no discretionary liquidity traders trade, there will continue to be three informed traders trading, as seen in Table 4. In period 3, when both of the discretionary liquidity traders trade, the number of informed traders will now be 6, as seen in Table 3. Table 5 shows what occurs with the increased number of informed traders in period 3. With the higher number of informed traders, the value of λ 3 is reduced even further, to the benefit of the liquidity traders. It is therefore still an equilibrium for the two discretionary liquidity traders to trade in period 3. Because three more informed traders are present in the market in this period, the total trading cost of the liquidity traders (discretionary and nondiscretionary) is reduced by 0.204, or 19 percent. 14 A comparative statics result analogous to part 3 is discussed in Kyle (1984). 20 Table 5 Effects of discretionary liquidity trading on volume and price behavior when the number of informed traders is endogenous A four-period example in which the number of informed traders, n,, is determined endogenously, assuming that the cost of information is 0.13. IFor t = 1, 2, 3, 4, the table gives λ t, the market-depth parameter; V,, a measure of total trading volume; Vt , a measure of the informed-trading volume; VtL, a measure of liquiditytrading volume; VtM, a measure of the trading volume of the market maker; Qt, a measure of the amount of private information revealed in the price; and Rt, the variance of the price change from period t - 1 to period t. The addition of the three informed traders affects the equilibrium in significant ways. First note that the volume in period 3 is even higher now relative to the other periods. With the increase in the number of informed traders, the amount of informed trading has increased, Increased liquidity trading generates trade because (1) it leads to more informed trading by a given group of informed traders and (2) it tends to increase the number of informed traders. More importantly, the change in the number of informed traders in response to the increased liquidity trading in period 3 has altered the behavior of prices. The price in period 3 is more informative about the future public-information release than are the prices in the other periods. Because of the increased competition among the informed traders in period 3, more private information is revealed and Q3 < Qt for t ≠ 3. With endogenous information acquisition, prices will generally be more informative in periods with high levels of liquidity trading than they are in other periods. The variance of price changes is also altered around the period of higher liquidity trading. From Equation (16) we see that if nt = nt-1, then Rt = 1. When the number of informed traders is greater in the later period, Rt > 1. This is because more information is revealed in the later period than in the earlier one. When the number of informed traders decreases from one period to the next, Rt < 1, since more information is revealed in the earlier period. It is interesting to contrast our results in this section with those of Clark (1973), who also considers the relation between volume and the rate of information arrival. Clark takes the flow of information to the market as exogenous and shows that patterns in this process can lead to patterns in volume. In our model, however, the increased volume of trading due to discretionary trading leads to changes in the process of private-information arrival. 21 3. A Model with Diverse Information So far we have assumed that all the informed traders observe the same piece of information. In th...
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