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Chapter 4 Market microstructure

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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



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          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



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     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


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          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



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                                                                             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



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         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

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                                                                                    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.




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     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?




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