1 Robert Engle UCSD and NYU July 2000

2 WHAT IS LIQUIDITY? n A market with low “transaction costs” including execution price, uncertainty and speed n This may mean different things depending upon the volume to be traded and impatience of the trader.

3 THREE MEASURES: n Bid Ask Spread –measures costs for small trades n Depth –quoted depth for small trades –depth with some price deterioration n Price Impact of a Trade –how much prices move in response to a large trade

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5 HOW DO THESE MEASURES OF LIQUIDITY VARY OVER TIME AND CAN THEY BE PREDICTED? n BRIEFLY -THE ANSWER FIRST!! n ACROSS ASSETS – MORE TRANSACTIONS AND MORE VOLUME MEANS MORE LIQUIDITY. n HOWEVER – OVER TIME, MARKETS BECOME LESS LIQUID WHEN THEY ARE MORE ACTIVE!!!

6 WHY SHOULD EXECUTION BE WORSE WHEN THE MARKET IS ACTIVE? n Because the market is more active when there is information flowing. n When there is information, traders watch trades (and each other) to learn the information as quickly as possible n Often called “Price Discovery”

7 MICROSTRUCTURE THEORY n Inventory models –More trades make inventories easier to manage –lower transaction costs and more liquidity n Asymmetric Information models –More informed traders increase adverse selection costs - greater spreads and price impacts

8 ASYMMETRIC INFORMATION MODELS n Glosten and Milgrom(1985) following Bagehot(1971) and Copeland and Galai(1983) n A fraction of the traders have superior information about the value of the asset but they are otherwise indistinguishable.

9 MARKET MAKER INFERENCE PROBLEM: n If the next trader is a buyer, this raises my probability that the news is good. Knowing all the probabilities I can calculate bid and ask prices: n Over time, the specialist and the market ultimately learn the information and prices reflect this.

10 Easley and O’Hara(1992) n Three possible events- Good news, Bad news and no news n Three possible actions by traders- Buy, Sell, No Trade n Same updating strategy is used

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12 Easley Kiefer and O’Hara n Empirically estimated these probabilities n Econometrics involves simply matching the proportions of buys, sells and non- trades to those observed. n Does not use (or need) prices, quantities or sequencing of trades

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17 LIQUIDITY IMPLICATIONS n When the proportion of informed traders is high, the market is less liquid in all dimensions n When information flows, there are more informed traders, as they rush to trade ahead of price movements n For specific public news events, this could approach 100%

18 INFORMED TRADERS n What is an informed trader? –Information about true value –Information about fundamentals –Information about quantities –Information about who is informed

19 PRICE IMPACTS OF TRADES n In real settings where traders have a choice about when to trade, how to trade and how much to trade –Their choices may indicate whether they have information –Large trades and rapid trades and trades by big players all have greater price impacts

20 Econometric Tools n Data are irregularly spaced in time n The timing of trades is informative n Need to model jointly the time and characteristics of a trade n This is called a marked point process n Will use Engle and Russell(1998) Autoregressive Conditional Duration (ACD)

21 STATISTICAL MODELS n There are two kinds of random variables: –Arrival Times of events such as trades –Characteristics of events called Marks which further describe the events n Let x denote the time between trades called durations and y be a vector of marks n Data:

22 A MARKED POINT PROCESS n Joint density conditional on the past: n can always be written:

23 THE CONDITIONAL INTENSITY PROCESS n The conditional intensity is the probability of an event at time t+  t given past arrival times and the number of events.

24 THE ACD MODEL n The statistical specification is: n where  is the conditional duration and  is an i.i.d. random variable with non- negative support

25 TYPES OF ACD MODELS n Specifications of the conditional duration: n Specifications of the disturbances –Exponential –Weibul –Generalized Gamma –Non-parametric

26 MAXIMUM LIKELIHOOD ESTIMATION n For the exponential disturbance n which is so closely related to GARCH that often theorems and software designed for GARCH can be used for ACD. It is a QML estimator.

27 EMPIRICAL EVIDENCE n Dufour and Engle(2000), “Time and the Price Impact of a Trade”, Journal of Finance, forthcoming n Engle, Robert and Jeff Russell,(1998) “Autoregressive Conditional Duration: A New Model for Irregularly Spaced Data, Econometrica n Engle, Robert,(2000), “The Econometrics of Ultra-High Frequency Data”, Econometrica n Engle and Lunde, “Trades and Quotes - A Bivariate Point Process” n Russell and Engle, “Econometric analysis of discrete-valued, irregularly-spaced, financial transactions data ”

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29 APPROACH n Extend Hasbrouck’s Vector Autoregressive measurement of price impact of trades n Measure effect of time between trades on price impact n Use ACD to model stochastic process of trade arrivals

30 DATA: n TORQ dataset -transactions on 18 stocks for 3 months from Nov Jan These are the actively traded stocks.

31 DEFINITIONS PRICE is midquote when a trade arrives (actually use 5 seconds before a trade). R is the log change in PRICE T is the time between transactions X = 1 if transaction price> midquote, i.e. BUY X= -1 if transaction price < midquote, SELL X= 0 if transaction price = midquote V is the number of shares in a transaction

32 CORRELATIONS

33 HASBROUCK MODEL (1991) GENERALIZED FOR TIME EFFECT n Vector Autoregression of trade directions and returns n Use to calculate the long run effect of trades on prices as a function of time between trades

34 RESULTS FOR RETURN EQUATION: n  o > 0 for all 18, all very significant –Buys raise prices n  o < 0 for 17, 13 significant –Buys raise prices more when durations are short n H: all  = 0; rejected for 13 –Time Matters n H: ; rejected for 13, negative for 16

35 n for 18, all very significant, –serial correlation in trade direction n for 15, significantly negative for 10, –short durations increase autocorrelation n rejected for 11 n rejected for 12, 11 negative –time matters for trade dynamics RESULTS FOR TRADE EQN.

36 INTRODUCING OTHER INTERACTIONS n n H: all  =0;rejected for 8 of 18 stocks. n Volume and Spread are very significant

37 WACD estimation for FNM and IBM

38 CALCULATE IMPULSE RESPONSES OF A TRADE. n WITH DURATIONS FIXED AT A PARTICULAR VALUE n WITH DURATIONS EVOLVING JOINTLY n MEASURED IN CALENDAR TIME RATHER THAN TRANSACTION TIME n Latter two require stochastic simulation of the ACD

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41 SUMMARY n The price impacts, the spreads, the speed of quote revisions, and the volatility all respond to information n Econometric measures of information –high shares per trade –short duration between trades –wide spreads

42 CONCLUSIONS n MARKETS ARE LESS LIQUID WHEN THEY ARE MORE ACTIVE n TRANSITION TO FULL INFORMATION OR EFFICIENT PRICES IS FASTER WHEN THERE IS INFORMATION ARRIVING