Unformatted text preview: e net change in the
position of the market maker during the interval. (It should be noted,
however, that in practice the order-flow data may not be easily available
from market makers.)
Suppose for simplicity that trading periods are divided into two types,
those with high trading volume and those with low trading volume. We
will use H and L to denote the set of periods with high and low trading
volumes, respectively. (We also use superscript parameters accordingly.)
The basic pricing equation in our model is
for periods with high volume (t ∈ H) and for periods with low volume (t ∈ L).
Three hypotheses follow directly from our results in Sections 1 to 3.
Hypothesis 1. λ H < λ L.
That is, our model predicts that the market-depth coefficient (defined by
l/A,) is higher when the volume is lower. This hypothesis can easily be
tested by using standard statistical procedures, as long as we can estimate
λ H and λ L from price and order-flow observations. To see how this can be
An estimate of λ can be obtained by regressing the observations of
t ∈ H on the order-flow observations
This follows because all the terms
in the above expression, except
, are independent of ii, and because,
by construction, λ t, is set by the market maker as the regression coefficient
Similarly, a regression of the observations
in the prediction of
, g iven
for t ∈ L on
would give an estimate of λ L.16
H Hypothesis 2.
This simply says that prices are more informative in periods in which the
trading volume is heavier. Although it is less transparent to see, Hypothesis
16 Note that in the model of Section 4, where liquidity traders can allocate their trades, previous order flows
must be included in the regression as well, since they (indirectly) provide relevant information in predicting 32 2 can also be tested empirically using price and order-flow observations.
This is shown in the Appendix.
Hypothesis 3. The variance of the price change from t ∈ L to t + 1 ∈ H is
larger than the variance of the price change from t ∈ L to t + 1 ∈ L, and
this exceeds the variance of the price change from t ∈ H to t + 1 ∈ L.
It is straightforward to test this hypothesis, given price and volume
Cross-sectional implications can also be derived from our analysis. For
example, it is reasonable to assume that a typical discretionary liquidity
trader is a large institutional trader. Our models predict that trading patterns will be more pronounced for stocks that are widely held by these
7. Concluding Remarks
This article has presented a theory of trading patterns in financial markets.
Some of the conclusions of our theory are these:
• In equilibrium, discretionary liquidity trading is typically concentrated.
• If discretionary liquidity traders can allocate their trades across different periods, then in equilibrium their trading is relatively more concentrated in periods closer to the realization of their demands.
• Informed traders trade more actively in periods when liquidity trading
• If information acquisition is endogenous, then in equilibrium more
traders become privately informed in periods of concentrated liquidity
trading, and prices are more informative in those periods.
We have obtained our results in models in which the information process
and the amount of nondiscretionary liquidity trading are completely stationary over time. All the patterns we have identified in volume and price
variability emerge as consequences of the interacting strategic decisions
of informed and liquidity traders. The main innovation in our theory is the
explicit inclusion of discretionary liquidity traders, who can time their
trading. As discussed in the Introduction, observations similar to the last
two points above have been made as comparative statics results in Kyle
(1984), where the variance of liquidity trading is parametrically varied in
a single period model. We have shown that these results continue to hold
in equilibrium when the timing of liquidity trading is endogenized. As we
have seen, it is a delicate matter whether the strategic interaction between
liquidity traders and informed traders actually leads to pronounced patterns
of trading over time. Among other things, what is important in this regard
is the degree of competition among informed traders. When informed
traders observe highly correlated signals, competition between them is
33 intense, and this improves the terms of trade for liquidity traders, promoting
concentration of trading. If private signals are weakly correlated, however,
then competition among informed traders is less intense, and an increase
in the number of informed traders can actually worsen the terms of trade.
This may lead to the nonexistence of an equilibrium. However, despite
the complexity of the strategic interaction among traders, our analysis
shows that whenever an equilibrium exists, it is characterized by the concentration of liquidity and informed trading and by the resulting patterns
in volume and pri...
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