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Unformatted text preview: ce behavior.
The actual timing and shape of trading patterns in financial markets are
determined by a number of factors and parameters that are exogenous to
the model, such as the rate of arrival of public information, the amount of
nondiscretionary liquidity trading, and the length of the interval within
which each discretionary liquidity trader trades. As we noted, empirical
observations suggest that the daily patterns in trading volume and returns
are quite profound. In particular, there is heavier trading at the beginning
and end of the trading day than there is in the middle of the day, and the
returns and price changes are more variable.
There are a few hypotheses that, combined with our results, may explain
the concentration of trading at the open and the close. The open and close
are distinguished by the fact that they fall just after and just before the
exchange is closed: that is, after and before a period of time in which it
is difficult or impossible to trade. This may cause an increase in (nondiscretionary) liquidity trading at the open and close. As a result, discretionary
liquidity trading (as well as informed trading) will also be concentrated
in these periods, as implied by our results. In this case the forces we have
identified for concentration would be intensified.
The concentration of trading at the end of the trading day may also be
due to the settlement rules that are followed by many exchanges. Under
these rules all trades undertaken on a particular day are actually settled
by the close several days later. While delivery depends on the day in which
the transaction takes place, the exact time within a day in which the trade
occurs has no effect on delivery. This suggests that the interval within
which many discretionary liquidity traders must trade terminates at the
close of a trading day, (i.e., that for many liquidity traders T' is the close
of a trading day). Since T', the time at which liquidity demands are realized,
may vary across traders, there will be a tendency for trading to be concentrated at the close, when there is the most overlap among the intervals
available to different liquidity traders. (See Section 5.1 for an intuitive
discussion of this in the context of a related example.)
Note that the model of Section 4, in which discretionary liquidity traders
can allocate their trades over different periods, predicts that trading will
be concentrated in “earlier” trading periods (i.e., in periods closer to the
time in which the liquidity demand is realized). For example, if many
discretionary liquidity traders realize their liquidity demands after the
market closes, then our model predicts that they will satisfy them as soon as the market opens the next day. If, on the other hand, liquidity demands
are realized late in the trading day, then we will observe heavy trading by
discretionary liquidity traders and informed traders near the close of the
market.
Our analysis may also shed some light on the finding discussed in French
and Roll (1986) that the variance of returns over nontrading periods is
much lower than the variance of returns over trading periods. If the liquiditytrading volume is higher at the end of the trading day, then more
informed traders will trade at this time. As a result, the prices quoted at
the end of the trading day will reflect more of the information that will be
released publicly during the following nontrading hours (see Hypothesis
2 in Section 6). While this effect may explain some of these findings, it is
probably not sufficiently strong to account for the striking differences in
variances reported in French and Roll (1986).
It is interesting to ask whether our results can account for the actual
magnitudes of the observed patterns. A satisfactory answer to this question
requires a serious empirical investigation, something we will not attempt
here. However, casual calculations suggest that the predictions from the
model may accord well with the observed magnitudes. For example, consider again the Exxon data presented in Table 1. Suppose that there are
four informed traders in period 1 (10 A.M. to 12 noon), one informed trader
in period 2 (12 noon to 2 P.M.), and three informed traders in period 3 (2
P.M. to 4 P.M.). These values are roughly consistent with the pattern of
trading volume. Suppose also that φ = 0; that is, informed traders in period
Finally, let σδ2 = 0.115661, the average
t have perfect information about
of the variance of the price changes in the three periods. Then we can
calculate the variance of price change in each period as predicted by our
model using Equation (l6), modified to include σδ. (In doing this calculation we ignore the overnight period and assume that the third period of
one day immediately precedes the first period of the next.) These values are quite close to the observed values (0.34959, 0.28371,
0.37984).17 The foregoing should in no way be construed as a test of the 17 We have in fact searched over a...
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 Spring '12
 Svendsson

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