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Unformatted text preview: it will discourage risk-averse liquidity traders
from trading together. In fact, the reverse occurs; that is, risk-averse liquidity traders have an even greater incentive to trade together than do
The following heuristic discussion uses the basic model of Sections 1
to 3. Given our assumptions, the conditional distribution of
and the public information available at time t. Thus,
liquidity trader j is concerned only with the first two moments of this
conditional distribution. Consider first the unconditional variance of
is the expectation of
given the order flow at time t (and
public information), the variance of
is the variance of the prediction
error. Suppose that all liquidity traders trade in period t*. Recall from
Section 1 that because of the more intense trading by informed traders at
t*, the prediction variance (which is related to Qt) is independent of Ψ t,
the variance of liquidity trading. Thus, as long as the number of informed
traders is constant over time, the concentration of liquidity trading in
period t* does not increase the variance of
relative to other periods. We have also seen that the prediction variance is decreasing in nt,
the number of informed traders. This implies that with endogenous information acquisition, since more informed traders trade in period t*, the
prediction variance is even lower.
Now, liquidity trader j also knows his own demand
so we must consider the conditional variance of
If ft(nt) is the unconditional variance d&cussed above, then the conditional variance is equal
if trader j trades in period t and is equal to ft(nt) if
he trades in a different period. It is clear now that the fact that trader j
does not change the direction of the results outlined in the
preceding paragraph; if all discretionary liquidity traders trade in period 30 t* and for all j. Thus, the equilibrium in which discretionary liquidity
traders concentrate their trading in one period is still viable even if these
traders are risk-averse.
5.3 Correlated demands of liquidity traders
We have assumed that the demands of discretionary liquidity traders are
independent of each other. This assumption seems to be reasonable if
liquidity demands are driven by completely idiosyncratic life-cycle motives
that are specific to individual traders. If liquidity demands are correlated
across traders because of some common factors affecting these demands,
and if these factors are observed by the market maker before he forms
prices, then our analysis is still valid, with the interpretation that liquidity
trading corresponds to the unpredictable part of these demands.
It is possible to extend our analysis to the case where common factors
in liquidity demands are not observable (or, in general, to the case of
correlated liquidity demands). Two considerations arise in this case. First,
if liquidity traders trade in different periods, then past order flows may
provide information to the market maker concerning the liquidity component in the current order flow. Second, if more than one liquidity trader
trades in a given period, then the cost of trading in this period, which is
proportional to the correlation of his demands with the total order flow,
involves an additional term that reflects the correlation of the trader’s
demand with the other liquidity demands.
If liquidity demands are negatively correlated, then it can be shown that
concentrated-trading equilibria always exist, so our results are still valid.
The same is true if the variance of nondiscretionary liquidity demands is
small enough, that is, if there is very little nondiscretionary liquidity trading. The results may be different if liquidity demands are positively correlated. In this case it is possible that an equilibrium in which trading is
completely concentrated does not exist, or that equilibria in which different
traders trade in different periods also exist, in addition to the concentratedtrading equilibria (and they are robust to slight perturbations in the parameters). Examples are not difficult to construct.
6. Empirical Implications
The result that trading is concentrated in particular periods during the day
and that the variability of price changes is higher in periods of concentrated
trading is clearly consistent with empirical observations of financial markets, as discussed in the Introduction and in the following section. Our
models also provide a number of more specific predictions, examples of
which we will spell out below. For simplicity, we will mostly use the model
of Sections 1 to 3, where discretionary liquidity traders trade only once
within the period in which they have to satisfy their liquidity demands.
In the context of our model, it seems reasonable to treat prices
as observables. Specifically, if we define the periods to be,
31 say, 30 minutes long, then the relevant price would be the last transaction
price of the interval, and the order flow would be th...
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- Spring '12