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Robert Engle UCSD and NYU July 2000

Forecasting Market Liquidity Using Transactions Data with the ACD Model. Robert Engle UCSD and NYU July 2000. WHAT IS LIQUIDITY?. A market with low “transaction costs” including execution price, uncertainty and speed

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Robert Engle UCSD and NYU July 2000

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  1. Forecasting Market Liquidity Using Transactions Data with the ACD Model Robert Engle UCSD and NYU July 2000

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

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

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

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

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

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

  8. MARKET MAKER INFERENCE PROBLEM: • 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: • Over time, the specialist and the market ultimately learn the information and prices reflect this.

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

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

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

  12. INFORMED TRADERS • What is an informed trader? • Information about true value • Information about fundamentals • Information about quantities • Information about who is informed

  13. PRICE IMPACTS OF TRADES • 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

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

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

  16. A MARKED POINT PROCESS • Joint density conditional on the past: • can always be written:

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

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

  19. TYPES OF ACD MODELS • Specifications of the conditional duration: • Specifications of the disturbances • Exponential • Weibul • Generalized Gamma • Non-parametric

  20. MAXIMUM LIKELIHOOD ESTIMATION • For the exponential disturbance • 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.

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

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

  23. DATA: • TORQ dataset -transactions on 18 stocks for 3 months from Nov. 1990-Jan 1991. These are the actively traded stocks.

  24. 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

  25. CORRELATIONS

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

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

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

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

  30. WACD estimation for FNM and IBM

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

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

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

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