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Chapter 4: Market microstructure Chapter 4: Market microstructure Essential reading Barclay, M.J. and J.B. Warner ‘Stealth Trading and Volatility: Which Trades Move Prices?’ Journal of Financial Economics, 34: 281–305, 1993. Glosten, L.R. and P.R. Milgrom ‘Bid, Ask, and Transaction Prices in a Specialist Market with Heterogeneous’ly Informed Agents’, Journal of Financial Economics 14: 71–100, 1985. Further reading Madhavan, A. ‘Market Microstructure: A Survey’, Journal of Financial Markets 3: 205–258, 2000. Kyle, A.S. ‘Continuous Auctions and Insider Trading’, Econometrica 53, 1315–1335, 1985. Introduction This chapter looks more closely at market microstructure, which is deﬁned broadly as the process by which latent demand for trading of a security transforms into actual transaction prices and volumes. This means that the literature is interested in how traders who can beneﬁt from participating in the market, actually behaves in a given market environment, and how this behaviour leads to actual transactions. There is a considerable interest in this area as there is increasing evidence that the way in which we design markets has a huge impact on the way transactions are carried out. Participating in trading has, moreover, become increasingly popular among ordinary people. It is currently possible to trade actively in stocks and bonds from your own home computer. Your order will be collected and executed (often completely electronically) against other orders that arrive around the same time. A transaction is then carried out and settled automatically against your bank account. What sort of issues does the market microstructure literature look at? Of particular importance are two areas. The ﬁrst is the way in which so called informed traders interact with so called uninformed traders. The second is the way in which the market structure can be designed such as to minimize the adverse effects of the conﬂict between informed and uninformed traders. In this chapter, we will not go very deeply into these issues however, but rather provide an introduction to this ﬁeld. Market microstructure effects on transaction prices An early observation is that buy transactions tend to be transacted at slightly higher prices than bid transactions, that is, buy orders are executed near the ask price and sell orders near the bid price. The bid-ask spread, therefore, induces a price process that has negative autocovariance (negative autocovariance implies that high returns tend to be followed by low returns and vice versa) even if no new information arrives that causes the traders to revise their price expectations. To see this, consider the case that each incoming order is equally likely to be a buy order as a sell order. The buy order is executed at the ask price pA, and the sell order is executed at the bid price pB, and the ‘fundamental’ price lies between these prices. The bid-ask spread is S = pA – pB. Conditional on a current transaction being at the ask 29 Investment management price, the return between the current price and the price of the next transaction is either 0 or –S/pA and the corresponding return for the previous transaction was either 0 or +S/pB. Conditional on a current transaction being at the bid price, the return between the current price and the price of the next transaction is either 0 or +S/pB, and the corresponding return for the previous transaction was either 0 or –S/pA . If we think of all outcomes as equally likely, we get the following table of ‘transition’ probabilities from the return of the price process as new transactions are made. The last three entries in the top row represent the returns between the current price and that of the next transaction, and the last three entries in the left column, the return between the previous transaction price and the current transaction price. Transition: -S/p 0 +S/p A B probabilities -S/pA 0 0.125 0.125 0 0.125 0.25 0.125 S/pB 0.125 0.125 0 The autocovariance is Autocovariance = E(Future Return)(Past Return) – E(Future Return) E(Past Return) 2 S = 0.25 – –0 pApB S2 =– 4pApB The price process of stocks contains, therefore, negative autocovariance that is increasing in the bid-ask spread of the stock. The bid-ask spread The next problem is to explain why there is a bid-ask spread in the market in the ﬁrst place. Why doesn’t competition between traders push the transactions prices of both buy and sell order towards the same level? There are two answers to this question, both of which are based on the market maker framework which underpins much of the market microstructure literature. A market maker market is one in which there is a trader who is ‘special’ in that his role is primarily to provide liquidity to incoming traders when there are temporarily too many buyers or sellers in the market. Traders who arrive deal directly or indirectly with the market maker, and the market maker’s primary role is to set prices at which the job of clearing the market is done as efﬁciently as possible. The market maker is normally assumed to operate in a competitive framework so is not able to capture monopoly proﬁts. Inventory risk The ﬁrst story in explaining the bid-ask spread relates to inventory costs associated with the excess inventory (positive or negative) of risky stock necessary to be carried by the market maker in order to clear the market. For instance, a buyer might wish to sell 50,000 shares in a stock when there is no buyer present. The market maker makes the transaction in the hope that a buyer comes around soon, but there is a risk that this will not happen. If it does not, the market maker is sitting on a non-diversiﬁed holding of a stock with uncertain value. The market maker, consequently, demands a price discount from the seller as compensation for this risk. In practice, this means 30 Chapter 4: Market microstructure that when you buy from the market maker, you expect to pay the fair price plus a premium which gives you the price you pay - the ask price. Similarly, when you sell, you expect to receive the fair price minus a discount which gives you the price you receive - the bid price. In some markets where there is a panel of dealers active for a broad range of stocks (such as the NASDAQ market and the London market prior to 1997), variations in inventory across dealers lead to variations in their quotes of bid and ask prices. In these markets we might observe that the dealer who has the most competitive quote on the bid side might not have the most competitive quote on the ask side. The reason is that the one who has the most attractive bid price is attempting to attract sellers who can ﬁll a temporary short position of the dealer, and the one who has the most attractive ask price is attempting to attract buyers who can ofﬂoad a temporary long position of the dealer. Adverse selection – the Glosten-Milgrom model If traders have different information there is scope for adverse selection which we will illustrate in the following example. Suppose you want to trade a stock with payoff x. You think there is equal chance the payoff x is 1 or 0, so you are in principle willing to trade at a price p between 0 and 1 (if you are risk averse and buying the stock you’d like to trade at a price less than one half, and if you are selling you’d like to trade at a price greater than one half). If your trading partner knows for sure whether x equals 1 or 0 you would, however, be better off not trading at all. The reason is as follows. If the true payoff is 1, you know that your trading partner would always turn down a sell transaction at any price strictly lower than 1. The only time he trades is if he’s buying, in which case he makes a trading gain and you make a corresponding trading loss of 1-p per unit. Similarly, if the true payoff is 0, your trading partner would turn down any buy transaction at a price strictly greater than 0. The only time he trades is if he’s selling, in which case he makes a trading gain and you make a corresponding trading loss of p-0 per unit traded. Consequently, if you trade you make an expected loss regardless of what the transaction price p is. You would be better off not trading at all. This is called adverse selection – referring to the fact that you would tend to select a trading counterparty with adverse information. The market maker faces the same problem if there are informed traders (so called insiders) among the buyers and sellers who approach the market. If insiders operate, they tend to bunch together on the same side of the market – if they have more optimistic information than the average investors they bunch together on the buy side, and if they have more pessimistic information they bunch together on the sell side. This poses a dilemma for the market maker, who is to clear the incoming order imbalance, as on the one side he provides uninformed traders who trade for liquidity reasons, and on the other he is vulnerable to the activity of insiders. The Glosten-Milgrom model attempts to take this effect into account when the market maker sets the bid-ask spread. The model assumes a sequential arrival sequence, where each trader is either a liquidity trader who is equally likely to buy or sell or an insider who will buy or sell depending on his information set. The amount traded is ﬁxed. The market maker ﬁgures out that whereas the liquidity traders are spread equally on both sides of the market, the insiders tend to go to one side only. The market maker will, therefore, become worried if consecutive buy or sell orders arrive, and will change his quotes accordingly. The Glosten-Milgrom model shows the optimal quote-setting strategy for a competitive market maker. Suppose the market maker thinks there is a probability p that the next trader is an insider and 1-p that the next trader is a liquidity trader. If the 31 Investment management next trader is a liquidity trader, he is equally likely to buy or sell. If the next trader is an insider, he buys for sure if the asset value is high and sells for sure if the asset value is low. Suppose the asset has a high value of 1 with probability one half and low value of 0 with probability also one half. What are the market maker’s bid and ask prices in this situation? The answer is given by revising the market maker’s beliefs contingent on selling at the ask or buying at the bid. If a buy order arrives so that the market maker sells at the ask, he knows that this might have happened through uninformed liquidity trading (with probability (1-p)/2) or it might have happened through insider trading (with probability p/2). By Bayes’ rule the probability that the asset value is low contingent on selling at the ask is Pr(Sell at Ask | High)Pr(Hi gh) Pr(High | Sell at Ask) = Pr(Sell at Ask | High)Pr(Hi gh) +Pr(Sell at Ask | Low)Pr(Low ) ((1 - p)/2 + p)/2 = ((1 - p)/2 + p)/2 + (1 - p)/4 1+ p = 2 Therefore, the market maker thinks the expected value of the asset, contingent on selling at the ask, equals 1+p 1 p 1+ p Expected (Value | Sell at Ask) = 1+ 0= 2 2 2 If the market maker acts competitively and is risk neutral (zero inventory risk), he quotes an ask price that is greater than the (unconditional) expected asset value of one half. The optimal ask price is (1+p)/2. Similarly, the optimal bid price is (1-p)/2. The whole Glosten-Milgrom model is essentially an exercise in revising beliefs using Bayes rule. This rule assumes that we have a prior probability distribution of events, then we make some observation that causes us to revise our beliefs, and we end up with a posterior probability distribution of events. In the Glosten-Milgrom model, the ‘observation’ is that a trader attempts to trade at the bid or the ask side. Given this observation, the market maker revises his beliefs about the probability distribution over the asset’s values, and the bid and the ask prices are determined according to the posterior probabilities rather than the prior probabilities. In effect, the market maker sets the bid and the ask prices in a ‘regret-free’ manner – i.e. the market maker does not regret making the ﬁrst trade at the ask or the bid as long as these prices are determined by the posterior probabilities. Bayes rule is given in general by the relationship Pr(B | A)Pr(A) Pr(A | B) = Pr(B) and this relationship is the key driving force in the formation of bid and ask prices in the Glosten-Milgrom model. Optimal insider trading – the Kyle model We know from the Glosten-Milgrom framework that the bid and the ask quotes respond to the relative arrival rates of buy and sell orders. In periods where these are fairly balanced, the market maker keeps his bid-ask spread tight to reﬂect the fact that insider trading is unlikely. In periods where there is an imbalance, the market maker responds by making the quotes biased upwards if there is a buy bias and downwards if there is a sell bias. This poses 32 Chapter 4: Market microstructure a dilemma for insiders. If an insider trades in small quantities he makes a large proﬁt per trade as prices remain fairly uninformative, but foregoes quantity-related proﬁts. If he trades in large quantities he makes a bigger impact on price which reveals more accurately the information of the insider, so he foregoes price-related proﬁts. The obvious question is how to balance the two. This question is posed in the Kyle model, which we sketch below. This model is much more complicated than the Glosten-Milgrom model as it involves more than the process of revising beliefs. It also contains the concept of equilibrium as there are two players – the insider who trades against the market maker, and the market maker who seeks to infer from the trading quantities the information of the insider. The insider’s trading strategy needs to be the optimal one given the market maker’s inference, and the market maker’s inference needs to reﬂect correctly the trading strategy of the insider. The original Kyle model assumes a normally distributed asset price x, which (irrational) noise traders trade in a quantity y which is also normally distributed. The assumption that asset prices are normal is of course unrealistic in the case of equities, as limited liability ensures that the value of equity can be at least zero. This assumption is, however, convenient in terms of algebra. The assumptions are 2 x ~ N (0 , ) 2 y ~ N (0 , ) where N denotes the normal distribution with the ﬁrst argument denoting the expectation and the second argument the variance. The insider trader trades a quantity z, so that the aggregate market order is the sum q = y + z, which is observable to the market maker. The market maker cannot observe y and z separately, so if he observes a large aggregate of buy orders he does not know whether this is caused by an unexpected large number of noisy buy orders, or by an unexpected large number of insider trades. The market maker observes the aggregate market order and determines the market clearing price p = E(x | q) which equals the expected asset price conditional on the market order q. A linear equilibrium consists of two functions z = bx p = dq where b and d are constants, such that z maximizes the insider’s proﬁts given the price function p = dq, and the price function p = E(x|q) given the proﬁt maximising trading strategy z = bx. We work out the price function ﬁrst. Suppose the insider uses a linear strategy bx. Then the aggregate order ﬂow is equal to bx plus a normally distributed error term (the demand by noise traders) which is independent of x. If we regress the asset value x on the aggregate order ﬂow q, therefore, we would obtain the relationship x = bq + y where the insider’s strategy b is simply the coefﬁcient in this regression. When forecasting x based on observations of q, the market maker ﬁnds the optimal forecast E ( x | q) = dq 33 Investment management where the regression coefﬁcient is given by the covariance between q and x over the variance of q. This can be found in basic econometrics books, but we also recall the beta-factor in the CAPM model which is deﬁned similarly as the covariance between the return on the asset and the return on the market over the variance of the return on the market. The beta-factor is also the coefﬁcient in a regression of asset returns on the index return (see Appendix 1 for a review of regression methods). Using this result, we ﬁnd that Cov (q, x ) Cov (bx + y, x ) bVar ( x ) b 2 d = = = 2 = 2 2 Var (q ) Var (bx + y ) b Var (x ) + Var ( y ) b + 2 where the ﬁrst equality gives us the expression of the coefﬁcient of the regression, the second equality follows by the deﬁnition of q = bx + y, the third equality follows from the fact that x and y are independent, so Cov(y,x) = 0, and the fact that Cov(x,x) = Var(x), and ﬁnally the last equality follows from our initial assumptions of the distributions of x and y. Therefore, the market maker’s response to aggregate demand is given by the function 2 b E ( x | q)= q b2 2 + 2 Now we turn to the insider’s problem. The insider observes x ﬁrst, then he decides his optimal trading quantity z. For each unit traded, the insider makes proﬁts ( x) = z ( x d ( y + z )) which depend on the asset value (x), the amount the insider decides to trade (z), and the amount the noise traders trade (y). The insider cannot observe the noise traders’ demand y, so he takes an expectation over all outcomes of y: E ( x ) = z (x dz ) where y now disappears as it has zero expectation. The insider is obviously interested in maximizing the expected proﬁt on his trading, so he seeks to maximize z(x-dz) with respect to the trading quantity z. This yields the ﬁrst order conditions 0=x 2dz or equivalently, x b2 2 + 2 z= = x = bx 2d 2b 2 where we have substituted for d from the expression above. The constant b is, therefore, give by b2 2 + 2 b= = 2b 2 where the ﬁrst equality follows directly from the expression above, and the second equality follows from the ﬁrst by multiplying both sides by the denominator (2b 2) to get 2b2 2 = b2 2 + r2. Subtracting b2 2 from both sides of this equation, we ﬁnd b2 2 = r2. Taking square roots on both sides, we ﬁnd b as the ratio of the standard deviation of noise trade (r) over the standard deviation of the asset value ( ). The full equilibrium is, therefore, given by z= x p= q 2 34 Chapter 4: Market microstructure The greater the ratio of the variance of noise trade to that of the asset value, therefore, the more aggressively the insider trades on the basis of his information. A greater ratio leads to a deeper market however, as the market maker’s prices respond less to the volume of demand. The stealth trading hypothesis The Kyle model demonstrates that insiders do not necessarily trade very aggressively to exploit their informational advantage. This is to some extent supported by empirical evidence. Barclay and Werner look at transaction data to explore the characteristics of the trades that tend to move prices the most. They ﬁnd that the very small trades and the very large trades do not move prices a lot. It is, in contrast, the average sized trades that tend to move prices. This suggests that insiders attempt to ‘hide’ their information when submitting their orders. This is called the ‘stealth trading hypothesis’. Why market microstructure matters to investment analysis The market microstructure area suggests that the prices of ﬁnancial assets may not only reﬂect the underlying ‘fundamental’ value of the asset, they may also contain components that are speciﬁc to the environment in which they are traded. We have discussed two such factors, one is that prices tend to become depressed when there is temporarily a lack of buyers in the market and that prices tend to become inﬂated when there is temporarily a lack of sellers. The other is that the bid-ask spread between buy and sell transactions may become large when there is a possibility that traders with superior information operate. Second, if you are a relatively unsophisticated trader with poor information, you are likely to incur speciﬁc costs of trading against more sophisticated traders, the so called adverse selection costs of trading. There is no obvious way to detect and protect yourself from sophisticated, well-informed traders, as these are likely to adopt techniques to hide their trading activity from the other market participants. This is, however, not necessarily an argument against participating in ﬁnancial market but it is an argument against trading very often. A strategy involving buying and holding a portfolio long term is, therefore, likely to be of beneﬁt unsophisticated traders. Activity 1. Explain the ‘stealth trading’ hypothesis. 2. Explain, in words, why the bid-ask spread tends to be greater when the likelihood of insider trading is greater. Learning outcomes After reading this chapter you should be able to: • describe how the bid-ask spread leads to negative autocorrelation in transaction prices • work out bid and ask quotes in the Glosten-Milgrom model • derive the optimal trading strategies of an insider, and the optimal price setting strategy of the market maker, in the Kyle model. 35 Investment management Sample examination questions 1. Suppose the ask price is 1% greater than the current price of 100p per share, and the bid price is 1% lower. If each transaction is equally likely to be a buy order as a sell order, what is the autocovariance of transaction prices? 36

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