http weber ucsd edumbacciengle 1 EFFICIENT MARKET HYPOTHESIS

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EFFICIENT MARKET HYPOTHESIS In its simplest form asserts that excess returns are unpredictable - possibly even by agents with special information Is this true for long horizons? It is probably not true at short horizons Microstructure theory discusses the transition to efficiency http: //weber. ucsd. edu/~mbacci/engle/ 2

Why Don’t Informed Traders Make Easy Profits? Only by trading can they profit If others watch their trades, prices will move to reduce the profit When informed traders are buying, sellers will require higher prices until the advantage is gone. Trades carry information about prices http: //weber. ucsd. edu/~mbacci/engle/ 3

TRANSITION TO EFFICIENCY Glosten-Milgrom(1985), Easley and O’Hara(1987), Easley and O’Hara(1992), Copeland Galai(1983) and Kyle(1985) Two indistinguishable classes of traders - informed and uninformed When there is good news, informed traders will buy while the rest will be buyers and sellers. When there are more buyers than sellers, there is some probability that this is due to information traders – hence prices are increased by sophisticated market makers. http: //weber. ucsd. edu/~mbacci/engle/ 4

CONSEQUENCES Informed traders make temporary excess profits at the expense of uninformed traders. The higher the proportion of informed traders, the faster prices adjust to trades, wider is the bid ask spread and lower are the profits per informed trader. http: //weber. ucsd. edu/~mbacci/engle/ 5

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 http: //weber. ucsd. edu/~mbacci/engle/ 6

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Easley Kiefer and O’Hara Empirically estimated these probabilities Econometrics involves simply matching the proportions of buys, sells and nontrades to those observed. Does not use (or need) prices, quantities or sequencing of trades http: //weber. ucsd. edu/~mbacci/engle/ 8

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INFORMED TRADERS What is an informed trader? Information about true value fundamentals quantities who is informed Temporary profits from trading but ultimately will be incorporated into prices http: //weber. ucsd. edu/~mbacci/engle/ 13

HOW FAST IS THIS TRANSITION? Could be decades in emerging markets Could be seconds in big liquid markets Speed depends on market characteristics and on the ability of the market to distinguish between informed and uninformed traders Transparency is a factor http: //weber. ucsd. edu/~mbacci/engle/ 14

HOW CAN THE MARKET DETECT INFORMED TRADERS? When traders are informed, they are more likely to be in a hurry(short durations) When traders are informed, they prefer to trade large volumes. When bid ask spreads are wide, it is likely that the proportion of informed traders is high as market makers protect themselves http: //weber. ucsd. edu/~mbacci/engle/ 15

EMPIRICAL EVIDENCE 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 Dufour and Engle(2000), “Time and the Price Impact of a Trade”, Journal of Finance, forthcoming Engle and Lunde, “Trades and Quotes - A Bivariate Point Process” Russell and Engle, “Econometric analysis of discrete-valued, irregularly-spaced, financial transactions data” http: //weber. ucsd. edu/~mbacci/engle/ 16

APPROACH Model the time to the next price change as a random duration This is a model of volatility (its inverse) Model is a point process with dependence and deterministic diurnal effects NEW ECONOMETRICS REQUIRED http: //weber. ucsd. edu/~mbacci/engle/ 17

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Econometric Tools Data are irregularly spaced in time The timing of trades is informative Will use Engle and Russell(1998) Autoregressive Conditional Duration (ACD) http: //weber. ucsd. edu/~mbacci/engle/ 19

THE CONDITIONAL INTENSITY PROCESS The conditional intensity is the probability that the next event occurs at time t+ t given past arrival times and the number of events. http: //weber. ucsd. edu/~mbacci/engle/ 20

THE ACD MODEL The statistical specification is: where xi is the duration=ti-ti-1, is the conditional duration and is an i. i. d. random variable with non-negative support http: //weber. ucsd. edu/~mbacci/engle/ 21

TYPES OF ACD MODELS Specifications of the conditional duration: Specifications of the disturbances Exponential Weibul Generalized Gamma Non-parametric http: //weber. ucsd. edu/~mbacci/engle/ 22

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. http: //weber. ucsd. edu/~mbacci/engle/ 23

MODELING PRICE DURATIONS WITH IBM PRICE DURATION DATA ESTIMATE ACD(2, 2) ADD IN PREDETERMINED VARIABLES REPRESENTING STATE OF THE MARKET Key predictors are transactions/time, volume/transaction, spread http: //weber. ucsd. edu/~mbacci/engle/ 24

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EMPIRICAL EVIDENCE 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 Dufour and Engle(2000), “Time and the Price Impact of a Trade”, Journal of Finance, forthcoming Engle and Lunde, “Trades and Quotes - A Bivariate Point Process” Russell and Engle, “Econometric analysis of discrete-valued, irregularly-spaced, financial transactions data” http: //weber. ucsd. edu/~mbacci/engle/ 26

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: http: //weber. ucsd. edu/~mbacci/engle/ 27

A MARKED POINT PROCESS Joint density conditional on the past: can always be written: http: //weber. ucsd. edu/~mbacci/engle/ 28

MODELING VOLATILITY WITH TRANSACTION DATA Model the change in midquote from one transaction to the next conditional on the duration. Build GARCH model of volatility per unit of calendar time conditional on the duration. Find that short durations and wide spreads predict higher volatilities in the future http: //weber. ucsd. edu/~mbacci/engle/ 29

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EMPIRICAL EVIDENCE 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 Dufour and Engle(2000), “Time and the Price Impact of a Trade”, Journal of Finance, forthcoming Engle and Lunde, “Trades and Quotes - A Bivariate Point Process” Russell and Engle, “Econometric analysis of discrete-valued, irregularly-spaced, financial transactions data” http: //weber. ucsd. edu/~mbacci/engle/ 31

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 http: //weber. ucsd. edu/~mbacci/engle/ 32

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SUMMARY The price impacts, the spreads, the speed of quote revisions, and the volatility all respond to information variables TRANSITION IS FASTER WHEN THERE IS INFORMATION ARRIVING Econometric measures of information high shares per trade short duration between trades sustained wide spreads http: //weber. ucsd. edu/~mbacci/engle/ 35

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EMPIRICAL EVIDENCE 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 Dufour and Engle(2000), “Time and the Price Impact of a Trade”, Journal of Finance, forthcoming Engle and Lunde, “Trades and Quotes - A Bivariate Point Process” Russell and Engle, “Econometric analysis of discrete-valued, irregularly-spaced, financial transactions data” http: //weber. ucsd. edu/~mbacci/engle/ 37

Jeffrey R. Russell Robert F. Engle University of Chicago University of California, San Diego Graduate School of Business http: //gsbwww. uchicago. edu/fac/jeffrey. russell/research/ http: //weber. ucsd. edu/~mbacci/engle/ 38

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Goal: Develop an econometric model for discrete-valued, irregularly-spaced time series data. Method: Propose a class of models for the joint distribution of the arrival times of the data and the associated price changes. Questions: Are returns predictable in the short or long run? How long is the long run? What factors influence this adjustment rate? http: //weber. ucsd. edu/~mbacci/engle/ 40

Hausman, Lo and Mac. Kinlay Estimate Ordered Probit Model, JFE(1992) States are different price processes Independent variables Time between trades Bid Ask Spread Volume SP 500 futures returns over 5 minutes Buy-Sell indicator Lagged dependent variable http: //weber. ucsd. edu/~mbacci/engle/ 41

A Little Notation Let ti be the arrival time of the ith transaction where t 0<t 1<t 2… A sequence of strictly increasing random variables is called a simple point process. N(t) denotes the associated counting process. Let pi denote the price associated with the ith transaction and let yi=pi-pi-1 denote the price change associated with the ith transaction. Since the price changes are discrete we define yi to take k unique values. That is yi is a multinomial random variable. The bivariate process (yi, ti), is called a marked point process. http: //weber. ucsd. edu/~mbacci/engle/ 42

We take the following conditional joint distribution of the arrival time ti and the mark yi as the general object of interest: In the spirit of Engle (2000) we decompose the joint distribution into the product of the conditional and the marginal distribution: Engle and Russell (1998) http: //weber. ucsd. edu/~mbacci/engle/ 43

SPECIFYING THE PROBABILITY STRUCTURE Let be a kx 1 vector which has a 1 in only one place indicating the current state Let be the conditional probability of all the states in period i. A standard Markov chain assumes Instead we want modifiers of P http: //weber. ucsd. edu/~mbacci/engle/ 44

RESTRICTIONS For P to be a transition matrix It must have non negative elements All columns must sum to one To impose these constraints, parameterize P as an inverse logistic function of its determinants http: //weber. ucsd. edu/~mbacci/engle/ 45

THE PARAMETERIZATION For each time period t, express the probability of state i relative to a base state k as: Which implies that: http: //weber. ucsd. edu/~mbacci/engle/ 46

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MORE GENERALLY Let matrices have time subscripts and allow other lagged variables: The ACM likelihood is simply a multinomial for each observation conditional on the past http: //weber. ucsd. edu/~mbacci/engle/ 48

THE FULL LIKELIHOOD The sum of the ACD and ACM log likelihood is http: //weber. ucsd. edu/~mbacci/engle/ 49

Even more generally, we define the Autoregressive Conditional Multinomial (ACM) model as: Where is the inverse logistic function. Zi might contain ti, a constant term, a deterministic function of time, or perhaps other weakly exogenous variables. We call this an ACM(p, q, r) model. http: //weber. ucsd. edu/~mbacci/engle/ 50

The data: 58, 944 transactions of IBM stock over the 3 months of Nov. 1990 - Jan. 1991 on the consolidated market. (TORQ) 98. 6% of the price changes took one of 5 different values. http: //weber. ucsd. edu/~mbacci/engle/ 51

We therefore consider a 5 state model defined as It is interesting to consider the sample cross correlogram of the state vector xi. http: //weber. ucsd. edu/~mbacci/engle/ 52

Sample cross correlations of x up 2 up 1 down 2 http: //weber. ucsd. edu/~mbacci/engle/ 53

Parameters are estimated using the joint distribution of arrival times and price changes. Initially, we consider simple parameterizations in which the information set for the joint likelihood consists of the filtration of past arrival times and past price changes. http: //weber. ucsd. edu/~mbacci/engle/ 54

ACM(p, q, r) specification: Where and gj are symmetric. ACD(s, t) Engle and Russell (1998) specifies the conditional probability of the ith event arrival at time ti+t by where http: //weber. ucsd. edu/~mbacci/engle/ 55

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Simulations We perform simulations with spreads, volume, and transaction rates all set to their median value and examine the long run price impact of two consecutive trades that push the price down 1 ticks each. We then perform simulations with spreads, volume and transaction rates set to their 95 percentile values, one at a time, for the initial two trades and then reset them to their median values for the remainder of the simulation. http: //weber. ucsd. edu/~mbacci/engle/ 57

Price impact of 2 consecutive trades each pushing the price down by 1 tick. http: //weber. ucsd. edu/~mbacci/engle/ 58

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Conclusions 1. Both the realized and the expected duration impact the distribution of the price changes for the data studied. 2. Transaction rates tend to be lower when price are falling. 3. Transaction rates tend to be higher when volatility is higher. 4. Simulations suggest that the long run price impact of a trade can be very sensitive to the volume but is less sensitive to the spread and the transaction rates. http: //weber. ucsd. edu/~mbacci/engle/ 60