Market Microstructure: A Survey of Microfoundations, Empirical Results, and Policy Implications

Market Microstructure:
A Survey of Microfoundations, Empirical Results, and Policy
Implications
Bruno Biais, Larry Glosten and Chester Spatt*
Abstract
We survey the literature analyzing the price formation and trading process, and the conse-
quences of market organization for price discovery and welfare. We o er a synthesis of the the-
oretical microfoundations and empirical approaches. Within this framework, we confront adverse
selection, inventory costs and market power theories to the evidence on transactions costs and price
impact. Building on these results, we proceed to an equilibrium analysis of policy issues. We re-
view the extent to which market frictions can be mitigated by such features of market design as the
degree of transparency, the use of call auctions, the pricing grid, and the regulation of competition
between liquidity suppliers or exchanges.
*Biais is from Toulouse University, Glosten is from Columbia University, and Spatt is from
Carnegie Mellon University. We are grateful for helpful comments from Peter Bossaerts, Cather-
ine Casamatta, Thierry Foucault, Ravi Jagannathan, Maureen O'Hara, Christine Parlour, Patrik
Sandas and Avanidhar Subrahmanyam.
1

---

The Microstructure of Stock Markets
Mark Garman (1976) quite aptly coined the phrase \market microstructure" as the title of an
article about market making and inventory costs. The phrase became a descriptive title for the
investigation of the economic forces a ecting trades, quotes and prices. Our review covers not only
what research has had to say about the nature of transaction prices, but also the broader literature
on the interrelation between institutional structure, strategic behavior, prices and welfare.
In perfect markets, Walrasian equilibrium prices re ect the competitive demand curves of all
potential investors. While the determination of these fundamental equilibrium valuations is the fo-
cus of (most) asset pricing, market microstructure studies how, in the short term, transaction prices
converge to (or deviate from) long{term equilibrium values. Walras himself was concerned about
the convergence to equilibrium prices, through a t^
atonnement process. One of the rst descriptions
of the microstructure of a nancial market can be found in the Elements d'Economie Politique Pure
(1874), where he describes the workings of the Paris Bourse. Walras's eld observations contributed
to the genesis of his formalization of how supply and demand are expressed and markets clear.1
Market microstructure o ers a unique opportunity to confront directly microeconomic theory with
the actual workings of markets. This facilitates both tests of economic models and the development
of policy prescriptions.
Short{term deviations between transaction prices and long{term fundamental values arise be-
cause of frictions re ecting order{handling costs, as well as asymmetric information or strategic
behavior. A potential source of market power stems from the delegation of trade execution to
-
nancial intermediaries. Delegation arises because most potential investors cannot spend their time
monitoring the market and placing and revising supply and demand curves for
nancial assets.
Only a small subset of all economic agents become full{time traders and stand ready to accom-
modate the trading needs of the rest of the population. This raises the possibility that these key
liquidity suppliers behave strategically. The organization of
nancial markets de nes the rules of
the game played by investors and liquidity suppliers. These rules a ect the way in which prices
are formed and trades determined, as well as the scope for asymmetric information or strategic
1Walker (1987) o ers a historical perspective on this aspect of the genesis of general equilibrium theory.
2

---

behavior, and thus the frictions and transactions costs arising in the trading process.
The resources devoted to the trading process and the magnitude of transaction costs incurred
by investors both illustrate the importance of market microstructure. While the cost of transacting
could seem small, the volume of transactions makes the overall economic e ect non-trivial. For
example, in 2002 and 2003, roughly 360 billion shares traded on the NYSE alone. A transaction
cost charge of only ve cents implies a corresponding ow of 18 billion dollars. This represents an
important friction with respect to the allocation of capital.2 Large transaction costs increase the
cost of capital for corporations and reduce the e ciency of portfolio allocation for investors, thus
lowering economic e ciency and welfare.
The discussions of a number of security market issues have been markedly informed by the
microstructure literature. The NASDAQ collusion case arose as a consequence of the empirical mi-
crostructure study of Christie and Schultz (1994). Its resolution involved very substantial changes
in the structure of the market. This outcome resulted from a number of microstructure analy-
ses performed on behalf of both sides of the debate. The e ects of decimalization, payment for
order
ow, transparency, and the respective roles of specialists,
oors and electronic limit order
markets are additional examples of issues engaging regulators, the nancial services industry and
microstructure researchers.
To provide a uni ed perspective we survey the theoretical literature within the framework of
a simple synthetic model of the market for a risky asset with N competing market makers.3 We
also discuss which theoretical predictions have been tested, and to what extent they have been
rejected or found consistent with the data, and we rely on the theoretical analyses to o er an
interpretation for empirical
ndings. We thus show how the market microstructure literature,
building upon
rst economic principles, provides a tool to analyze traders' behavior and market
design, and o ers a rationale for a large array of stylized facts and empirical ndings. Our endeavor
to integrate the theoretical and empirical sides of the literature di ers from O'Hara (1997), whose
book surveys several theoretical models.
Madhavan (2000) o ers an interesting survey of the
2In particular, the volume of activity is very sensitive to the level of transactions costs, as illustrated by the
dramatic increase in turnover during the last 25 years. While this increase is partly due to phenomena which are
outside the scope of market microstructure, such as the development of derivative trading, it also re ects the decline
in trading costs that resulted from the deregulation of commissions, improvements in trading technology, and the
increase in the competitiveness and openness of exchanges.
3For the sake of brevity we only describe the assumptions and results, omitting the proofs. The latter are available
upon request for the interested reader.
3

---

microstructure literature, building on an empirical speci cation in the line of Hasbrouck (1988).
Our focus di ers from his, as we emphasize the microfoundations of the literature, and the scope for
strategic behavior. Taking this approach enables us to o er an equilibrium{based analysis of policy
and market design issues. We concentrate on the portion of the literature that addresses price
formation and market design, while not addressing other important issues such as the interactions
between market microstructure and corporate nance or asset pricing.4
Section 1 surveys the
rst generation of the market microstructure literature, analyzing the
price impact of trades and the spread, assuming competitive suppliers of liquidity. Under this
assumption, the revenues of the agents supplying liquidity, corresponding to the spread, simply
re ect the costs they incur: order-handling costs (Roll, 1984), adverse{selection costs (Kyle, 1985,
Glosten and Milgrom, 1985, Glosten, 1994) and inventory costs (Stoll, 1978). While this literature
identi ed these costs theoretically, it also developed empirical methodologies to analyze data on
transaction prices and quantities and estimated trading costs, through the relation between trades
and prices and the bid-ask spread (Roll, 1984, Glosten and Harris, 1988, and Hasbrouck, 1988).
This literature has shown that trades have both a transitory and a permanent impact on prices.
While the former can be traced back to order-handling and inventory costs, the latter re ects
information. Furthermore, as data on inventories became available, empirical studies of specialists'
or traders' inventories examined the relevance of the inventory paradigm. While this literature
has shown that inventory considerations have an impact on the trades of liquidity suppliers, the
empirical signi cance of the impact of inventories on the positioning of their quotes is less clear.5
In Section 2 the competitive assumption is relaxed to discuss the case in which the supply of
liquidity is provided by strategic agents bidding actively in the market. Their market power can
lead to a relative lack of liquidity, as shown theoretically by Kyle (1989), Bernhardt and Hughson
(1997) and Biais, Martimort and Rochet (2000), and empirically by Christie and Schultz (1994) and
4Like a large fraction of the market microstructure literature, the present survey is devoted to the analysis of stock
markets. The analysis of other markets (e.g., derivatives, foreign exchange, or energy markets), and their comparison
with stock markets is an important avenue of research. Evans and Lyons (2002) and Lyons (1995) analyze the foreign
exchange market, Biais and Hillion (1994) study options markets, Green, Holli eld and Sch•
urho
(2003) and Harris
and Piwowar (2003) examine the municipal bond market and Hotchkiss and Ronen (2002) consider the corporate
bond market.
5We also discuss how the rst generation of the market microstructure literature conceptualized liquidity in
nancial markets as re ecting the incentives of the traders to cluster to bene t from the additional liquidity they
provide to one another (Admati and P eiderer (1988b) and Pagano (1989)).
4

---

Christie, Harris and Schultz (1994). As the focus of the market microstructure literature shifted
from competitive to strategic liquidity suppliers, empirical studies went beyond the analyses of
transactions prices and quantities. We survey the insights o ered by the literature on quotes and
order placement strategies.
Building on the concepts and insights presented in the previous sections, as well as on recent
theoretical, empirical and experimental studies, Section 3 discusses market design. The literature
suggests that call auctions can facilitate gains from trade, enhance liquidity by concentrating trades
at one point in time and foster price discovery; however, for large trades, empirical and theoretical
analyses suggest that the continuous market also o ers a useful trading venue. The literature also
points to the bene ts of allowing investors to compete to supply liquidity by placing limit orders,
to the adverse{selection problems generated by asymmetric access to the marketplace (e.g., Rock,
1990), and to the usefulness of repeated trading relationships to mitigate adverse selection. Fur-
thermore, empirical studies show that while market fragmentation can reduce competition within
each of the market centers, it can enhance competition across exchanges. Market microstructure
studies have also identi ed tradeo s associated with alternative levels of market transparency and
the size of the pricing grid.
Section 4 o ers a brief conclusion and sketches some avenues for further research.
1
Competitive market makers and the cost of trades
In the
rst part of this section, we analyze, within a simple synthetic model, three sources of
market frictions: order-handling costs, inventory costs, and adverse selection. In the second part of
the section, we survey empirical analyses testing and estimating the models.
1.1
Theoretical analyses
Consider the market for a risky asset. Denote by
the expectation of the nal (or fundamental)
value, v. There are N liquidity suppliers. Denote by Ui the utility function, Hi the information set,
Ci the cash endowment, and Ii the risky asset endowment of liquidity supplier i.
Even with competitive market makers, transaction prices and trading outcomes re ect
ne
details of the structure of the market, such as the sequencing of moves or the price formation
rule. We will
rst consider the case in which the market order Q is placed and then equilibrium
achieved in a uniform{price auction. As discussed more precisely below, this trading mechanism is
5

---

similar to the call auction used to set opening prices in electronic limit order books such as Eurex
(in Frankfurt) or Euronext (in Amsterdam, Brussels and Paris). In this uniform{price auction,
liquidity supplier i optimally designs her limit order schedule by choosing, for each possible price
p, the quantity she o ers or demands: qi(p).
M axqi(p)EUi(Ci + Iiv + (v
p)qi(p)jHi);8p:
(1)
The equilibrium price is set by the market{clearing condition:
Q +
qi(p) = 0:
(2)
i X
=1;:::;N
Second, we will consider the alternative case in which limit orders are posted rst, and then hit
by a market order. In this context we will focus on discriminatory{price auctions. This is similar
to the workings of limit order books during the trading day.
1.1.1
Order{handling costs and the bid{ask bounce
In the line of Roll (1984) suppose the N market makers are risk neutral and incur an identical
cost c q2 to trade q shares. This re ects order{handling costs (but not other components of the
2
spread, re ecting inventory costs, adverse selection, or market power, analyzed below). Suppose a
market order to buy Q shares has been placed by an uninformed liquidity trader. In our simple
uniform{price auction model ((1) and (2)), the competitive market makers each sell Q shares at
N
the ask price:
c
A =
+ (
)Q;
(3)
N
re ecting their marginal cost. Similarly, if the liquidity trader had placed a sell order, the bid price
would have been:
c
B =
(
)Q:
(4)
N
Correspondingly, the spread is: 2 c Q: Generalizing this simple model i) to allow the fundamental
N
value to follow a random walk, and ii) assuming the market orders are i.i.d., there is negative serial
autocorrelation in transaction price changes (or returns), due to the bouncing of transaction prices
between the bid and the ask quote.
6

---

1.1.2
Inventory
Now suppose the market makers are risk averse, as
rst analyzed by Stoll (1978) and by Ho and
Stoll (1981 and 1983). To simplify the analysis we will hereafter focus on CARA utility functions
and jointly normally{distributed random variables. Denote the constant absolute risk aversion
index of the market makers
,
2 the variance of the nal cash ow of the asset (V (v)), and I
the average inventory position of the market makers (I = PNi=1Ii=N). Again applying our simple
uniform{price auction model ((1) and (2)), when the liquidity trader submits a market order to
buy Q shares, the ask price is set as the marginal valuation of the shares by the competitive market
makers:
c +
2
A = [
2I] + (
)Q:
(5)
N
Symmetrically, the bid price is:
c +
2
B = [
2I]
(
)Q:
(6)
N
The midpoint of the spread (m) is equal to the fundamental value of the asset ( ) minus a risk
premium compensating the market makers for the risk of holding their initial inventory (
2I).
Market makers with very long positions are reluctant to add additional inventory and relatively
inclined towards selling. Consequently, their ask and bid prices will be relatively low. Similarly,
market makers with very short inventory positions will tend to post relatively higher quotes and will
tend to buy. Thus, market makers' inventories will exhibit mean reversion. Because of the central
role of inventory considerations in this analysis, it is often referred to as the inventory paradigm.
In this model, the spread re ects the risk{bearing cost incurred by market makers building up
positions to accommodate the public order ow. The price impact of trades increases in trade size,
as does the risk aversion of the market makers
and the variance of the value
2:
While this analysis, in the line of the work of Stoll (1978), is cast in a mean-variance framework in
which the link between prices and inventory is linear, under alternative parameterizations inventory
e ects can be nonlinear. For example, the impact of inventory on prices could be relatively strong
for extreme inventory positions. Amihud and Mendelson (1980) analyze an alternative model in
which dealers are risk neutral, and yet set prices to manage their inventory positions, because they
face constraints on the maximum inventory they can hold. In this dynamic model mean reversion
in inventories also arises, along with a nonlinear impact of inventory on pricing.
While individuals are indeed likely to exhibit risk aversion, it is less obvious why the banks,
7

---

securities houses and other nancial institutions employing dealers would be averse to diversi able
risk. To speak to this issue it could be fruitful to analyze theoretically the internal organization of
these nancial institutions. For example, suppose the dealers need to exert costly but unobservable
e ort to be e cient and take pro table inventory positions. To incentivize them to exert e ort, it is
necessary to compensate them based on the pro ts they make. In this context, even if diversi able
risk does not enter the objective function of the nancial institution, it plays a role in the objective
function of an individual dealer quoting bid and ask prices.
1.1.3
Adverse selection
Now consider the case in which the market order is placed by an investor trading both for liquidity
and informational motives. Considering informed investors is in the line of Bagehot (1971), Gross-
man and Stiglitz (1980), Kyle (1985), and Glosten and Milgrom (1985). To study the consequences
of adverse selection, while avoiding the unpalatable assumption of exogenous noise traders,6 and
still building on the insights of the inventory paradigm, we now extend the simple model introduced
above to the asymmetric information case.7
Suppose the market order is placed by a strategic, risk{averse agent with CARA utility. Denote
her risk aversion parameter , which is potentially di erent from the market maker's risk aversion,
. She is endowed with L shares of the risky asset, and has observed a signal s on the nal value
v. Speci cally, v =
+ s + ; where
is a constant, E(s) = 0; E( ) = 0, and
2 now denotes the
variance of . The market makers do not know exactly the inventory shock of the informed trader.
From their viewpoint L is a random variable.8
The informed agent chooses the size of her market order Q, anticipating rationally its impact
on the price. Once this order has been placed, the competitive liquidity suppliers place schedules
of limit orders, taking into account the information content of the market order. This order re ects
both the signal (s) and the risk{sharing need (L) of the informed agent. In our simple normal
6The exogenous noise trading assumption raises the issue of why there exist noise traders willing to lose money. It
also makes it impossible to conduct any welfare analysis or to compare di erent market structures, since it prevents
accounting for the impact of the market structure on noise trading. Glosten (1989) and Spiegel and Subrahmanyam
(1992) endogenize liquidity trading resulting from rational risk{sharing motives.
7Subrahmanyam (1991) extends the analysis of Kyle (1985) to the case of risk{averse market makers posting
reservation quotes.
8We maintain the assumption, which greatly facilitates the algebraic calculations, that s; ; and L are jointly
normal and independent.
8

---

distribution{exponential utility context, the information revealed by the market order is equivalent
to that contained by the summary statistics:
= s
2L.
re ects the valuation of the strategic
informed trader for the asset, which is increasing in her private signal, and decreasing in her
inventory. Denote:
V (s)
=
:
V (s) + (
2)2V (L)
quanti es the relative weight of the noise and signal in the summary statistic .
also measures
the magnitude of the adverse-selection problem. For example,
= 0 corresponds to the case in
which there is no private information.
If
< 1 ; then, in our uniform{price auction, there exists a perfect Bayesian equilibrium where
2
the trade of the informed agent (Q) is a ne and increasing in
and the equilibrium price (P ) and
the updated conditional expectation of the asset value are a ne in the informed trade (Q). More
precisely,
E(vjQ) = [ m + (1
) ] + (2 +
2)Q;
(7)
(
m) +
Q =
;
(8)
2 +
2
and:
P = m + Q;
(9)
where,
V (v
m =
j )I;
(10)
1
and:
c + V (vj ) +
2
= N
N
:
(11)
1
2
When
= 0; i.e., there is no private information, this simpli es to the above presented Roll/Ho
and Stoll model. Symmetrically, in the case where market makers are risk neutral ( = 0), and there
is no order{handling cost (c = 0), we obtain a speci cation similar to Kyle (1985), where prices are
equal to updated expectations of the value of the asset, conditional on the order ow. Buy orders
9

---

convey good news and drive ask prices up, while sell orders convey bad news and push bid prices
down. In the general case where
> 0;
> 0 and c > 0; the informational component of the spread
is added to those re ecting risk aversion and order-handling costs. The larger the size of the order,
the larger its impact on prices. The strategic insider is aware of this e ect, and limits the size of the
trade to limit its impact.9 This provides a theoretical framework within which to analyze liquidity:
when information asymmetries are severe, market makers have limited risk{bearing ability or when
order{handling costs are large, trades have a strong impact on prices, which can be interpreted as
a form of illiquidity.
Equivalence with a call auction
In equilibrium, there is a one{to{one mapping between the
summary statistic , the price p, and the informed demand Q. Hence, the game is strategically
equivalent to a call auction, where the informed trader and the liquidity suppliers would move
simultaneously. Since the liquidity suppliers express their demand as a function of the price, they
can include the price in their information set, which is equivalent to conditioning on Q. Thus the
equilibrium above is relevant to analyze prices and trades in a call auction. This trading mechanism
is used to set opening prices on Euronext or Xetra, and to set closing prices on Euronext. While
conditioning on Q in a sequential game was introduced by Kyle (1985) and Glosten and Milgrom
(1985), conditioning on p in a simultaneous{move game was introduced by Grossman (1976) and
Grossman and Stiglitz (1980).
Single arrival models versus batch arrival models
The analysis presented above, similar
to Glosten and Milgrom (1985), is cast in the context of a \single arrival" model, where market
orders from individuals arrive at the market center individually, and the terms of trade can change
for each arriving market order. Alternatively, in \batch arrival" models, as in Kyle (1985), market
orders are aggregated, and the net order ow arrives at the market center. The signed quantity to
be traded by one or more informed traders is linear in the signal:
s, while the noise trade is a
random variable u. Thus, the aggregated net trade is Q = s + u. As in the model above, the price
associated with a signed trade of Q is given by equation (9). Equilibrium consists of a speci cation
of
and
. As above, the signal available to the dealers is of the form \s plus noise." In the
above model the noise is the unknown hedging demand, while in Kyle (1985) it is the exogenous
9An additional way for informed agents to limit part of their price impact is to sell information to other investors,
as analyzed by Admati and P eiderer (1986, 1988a, 1990), and Biais and Germain (2002).
10

---