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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 liquiditytrading 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 riskneutral. (However, as discussed in
Section 5.2, our basic results do not change if some traders are riskaverse.)
We also assume for simplicityand 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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 Spring '12
 Svendsson

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