Department of Economics and Related Studies Financial Market Microstructure. Topic 1 : Overview and Fixed Cost Models of Spreads

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1 Session Department of Economics and Related Studies Financial Market Microstructure Topic 1 : Overview and Fixed Cost Models of Spreads 1 Introduction 1.1 Some background Most of what is taught in the MScs about asset pricing does not take into account the institutional arrangements that produce the prices and rates of return that are studied. Part of this is a timeless perspective - units of time are not very important. Prices that are traded are not really continuous, as we (implicitly) assume - they are often measured in fixed units such as eighths in US stock markets, ticks in stock markets in general and so on. Trading itself is not continuous and evenly spaced - there are actually markets that open and close, have days off for public holidays and weekends - these are often ignored. In Eqypt, for example, the stock market opens on a Sunday and not on a Friday, Datastream does not notice this. Also some assets are thinly traded and may go for long periods without trades. The actual process of trading can affect prices eg order driven in Euronext, quote driven in NYSE and Taiwan. A number of potential trading prices can co-exist - bid and ask, buying and selling prices with a spread between them can affect the serial correlation in prices and returns. Over what period of time between observations of prices or returns do these issues matter - less for long horizons, essential for short. But newer arguments suggest that microstructure effects might be long-lasting eg the effect of order flow on exchange rates; information effects as opposed to pricing errors. The existence of multiple equilibria might mean that the choice of equilibrium depends on microstructure parameters. 1

2 2 Market Efficiency Oneissuethatwillarisefrequentlyinthemodelsthatwelookatisthe question of whether a financial market is efficient. The classic reference on this is Fama s survey in 1970 where he wrote: A market in which prices always fully reflect available information in called efficient. One way of assessing this is to ask whether hypothetical trading based on a specific information set would earn superior returns. A set of information sets and definitions referred to by Fama is: Weak-form Efficiency: The information set includes only past prices themselves. Semi-strong Efficiency: The information set includes all information known to all market participants (publicly available information eg macro data series, other prices and returns). Strong-form Efficiency: The information set includes all information known to any market participant (private information). Often in the models that we will look at we will examine the question of whether the behaviour that is implied by the models concerned implies market efficiency and of what type. Given the nature of the data that are examined and the processes of trading that are modelled, there may be issues of timing or how the accumulation of information is reflected in prices. 3 The Canonical Model of a Dealer Market with Fixed Costs 3.1 Roll Model Structure This initial model lays out some of the basic of microstructure theory. The Roll (1984) model appears in a number of guises throughout the course. We assume that markets are efficient in the sense that prices reflect all available information. The efficient price is m t which can be thourght of as reflectingallavailableinformationandbethepricethat would hold in the absence of any transactions costs. We assume that is therefore moves through time as: m t = m t 1 + u t (1) where u t is a random error or innovation term which will reflect the innovation in expectations in an efficient market. Trading in this market is assumed to operate through dealers who post bid (b t ) and ask (a t ) 2

3 prices. Buyers buy at the price a t and sellers receive the price b t. The cost of a transaction is c per transaction. So the bid and ask prices are: a t = m t + c (2) b t = m t c (3) So the prices that we observe trading to take place at are p t which is given by: p t = m t + cq t (4) where q t =+1for a buyer-initiated trade, ie a buy at the ask and 1 for a seller initiated trade, ie a sell at the bid. We next assume that the innovation in expectations, u t has a constant variance σ 2 u, that buys and sells are equally likely and that the indicator variable q t is independent of it s past values and of u t.sowhat can we say about the properties of the observed price level p t?wemodel the change in the price, so: p t = p t p t 1 = cq t 1 + cq t + u t (5) and we can obtain the variance of the change in the price as: Var( p t )=2c 2 + σ 2 u (6) and the covariance of the change of the price with it s immeadiate past value: Cov( p t, p t 1 )= c 2 (7) The correlation is, therefore: Corr( p t, p t 1 )= c2 2c 2 + σ 2 u (8) The covariance with longer lags of price changes is zero: Cov( p t, p t k )=0,k >1 (9) Thus the change in the price is volatile and negatively serially correlated because of this particular microstructure effect ie because of the bid/ask bounce. Intuitively this happens because the trading price is either at the bid or ask (for a fixed m t ). So if the price is currently at the ask, the change in price to today is either 0 or 2c. The change to the next period is then either 0 or 2c. The opposite is true if the current price is at the bid, so the serial correlation of price changes must be negative. If the transaction cost c rises then the variance of the change in the price goes up. The extent of the impact on the degree of serial correlation 3

4 depends on the size of the transaction cost relative to the variance of the innovation in expectations. There is no higher order serial correlation whatever the level of the transaction cost. These expressions imply, furthermore, that a measure of c, or the implied bid-ask spread in this model 2c, can be calculated from the observed behaviour of prices as: c = 2p Cov( p t, p t 1 ) (10) and the variance of the innovation in expectations as: σ 2 u = Var( p t )+2.Cov( p t, p t 1 ) (11) ThismodelofRollthusprovidesuswithawayofestimatingthe costs of transactions from observed transactions prices in the absence of bid and ask price data. 3.2 Empirical Evidence Does the Roll model work? Hasbrouck (2006) presents the following data: for the firm CBL on July there were 821 NYSE trades. The estimated first order autocovariance of the price change is which implies an estimate of c =0.005($/share) and a spread of 2c = 0.01($/share). In this case the bid and ask prices exist. The average NYSE spread is 0.022($/share) so the Roll estimate looks too low. What would make these calculations wrong? There is always potential error in the assumptions underlying the model and any sampling error in the data. Also the real costs charged may be different to those quoted. Large customers may be able to negotiate lower rates and so there may be variation in actutal costs paid. One way of calculating the effective spread is to observe that trade prices are, on the NYSE, about ($/share) away from the midpoint of bid and ask quotes. The effective spread is therefore ($/share) which is closer to the Roll estimate. A problem observed with some of the inital estimates presented by Roll and by others is that price changes are estimated to be positively serially correlated rather than negatively, as predicted by the model. There may, of course, be other factors as work which might be the cause of the serial correlation and we will look at some of them in due course. The argument presented by Harris (1990) is based on the statistical properties of the estimated first-order covariance. Harris suggests that the Roll estimates are seriously biased by the degree of measurement error. Through the use of simulations, Harris establishes that, allowing for this noise or measurement error, the Roll calculations turn out to not be too bad. Many generalisations of the Roll model have been developed and 4

5 we will return to them. The first is due to Glosten and Milgrom (1985) and allows c to be endogenous and related to m t. We will examine this model when we look at the first set of asymmetric information models in a couple of weeks. A simple generalisation of the Roll model is provided by Choi et al (1988). They allow for serial correlation in transaction type. So they allow for the conditional probability of of a transaction at the bid following one at the bid to differ from 0.5. They also make the serial dependence the same for bids and asks. So if the probability that the transaction is at bid, given that it was at the bid in the previous period is δ thentheautocovariancebetweenthepricechangeinperiodtand t-1 can be shown to be Cov( p t, p t 1 )= (2c) 2 (1 δ) 2 (12) where this covariance is the same as that in equation (7) when δ =0.5. The implied bid-ask spread is then 2c =[ 2p Cov( p t, p t 1 )]/(1 δ) (13) So if there were positive serial correlation in transaction type with δ> 0.5 then the bid-ask spread calculated by equation (10) would be a downward biased estimate of the true spread. Choi et al present two estimates of δ based on data on options traded on the Chicago Board Options Exchange (CBOE) in the late 1970 s. The serial covariance of returns is estimated to with a standard error of So therefore the first order autocovariance of returns is found to be significantly negative. The estimate of δ is with a standard error of and therefore the estimate of the spread from equation ( 13) of 15.79% with a standard error of making it not very well determined. Again, bid and ask pricescanbeobservedinthisdatasetandtheaveragespreadis17.89%. The lower estimate provided by the model may be due to the influence of adverse selection effects on the observed spread which we will discuss later in this course. 5

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