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

We also use superscript parameters accordingly the

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 (35) 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 done, define (37) An estimate of λ can be obtained by regressing the observations of for 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 of 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 observations. 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 institutional traders. 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 is concentrated. • 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...
View Full Document

Ask a homework question - tutors are online