O`Hara, Maureen. Market Microstructure Theory.
Date: 3 February 2005
Commentary: This book provides a detailed survey, discussion, and comparison of mathematical models of securities markets through the mid-1990s. Topics include market makers, dealers, specialists, informed and uninformed traders, trader strategies, timing and signaling, volume considerations, market structure & policy, liquidity, trader anonymity, block-trading markets, and many other topics.
Raw Notes: Chapter 1 provides
an introduction to markets and market making. Chapter 2 summarizes the early
inventory models of market behavior. The following are my raw notes from
chapters 3-9.
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Origin
- Bagehot (1971) noted distinction in market gains & trading gains.
- Implied bid-ask spread without assumption of transaction costs.
- Market maker knows some traders better informed
Copeland & Galai (1983)
- one-period model of market maker’s pricing problem
o heterogeneous traders
o risk neutral dealer sets prices to max profit
- market makers looses to informed traders
o easy to quantify in one-trade world
- multiple rounds does not imply a repeated Copeland-Galai model
Glosten & Milgrom (1985) “trades as signals”
- sequential trade framework, where asymmetric information implies a spread
o market makers & traders are risk neutral and competitive
o negates inventory-carrying effects via
§ risk neutrality
§ unlimited capacity
§ no bankruptcy
§ short time horizon
- informed traders (Ti) have information of V
- uninformed traders (Tu) don’t speculate
- specialist, assuming competition & risk neutrality, sets prices so E[profit] equals zero
- specialists update beliefs & prices according to Bayes Theorem
- results
o spread arises independent of exogenous transaction or inventory costs (same as C & G)
§ C & G said spread balances gains & losses
§ Here, buy causes market maker to raise price
Easley & O’Hara (1987)
- Also sequential trade framework
- Differences
o Different trade sizes
§ Introduces trader strategy
o Existence of “new” information not assumed
§ 1st, new info?
§ 2nd, what is it?
- Ti prefer large trades
o large trades imply informed trades to market maker
o ∆p = ƒ(size)
- Can’t have multiple bids
Issues with these sequential trade models
- assumes Ti/T is constant
- assumes no strategic behavior by informed traders to disguise information
Focus: strategy regarding
- Timing of trades
- Trade size
- Explicit link to rational expectations
Kyle (1984 competitive Ti, 1985 monopoly Ti)
- Begin with one-period batch-clearing model
o Market maker sets market-clearing price
o Uninformed “noise” traders
§ Non-speculative
§ Trade volume (μ) is normally distributed
o Informed traders
§ Do not know Tu demand
§ Unlike rat exp, Ti cannot condition on Tu trade quantity
o Equilibrium derived from MM and Ti strategies
§ Given x + μ, MM set p, where x = informed volume & μ = uninformed volume
§ Ti π = x(v – p)
§ MM price satisfies P(x + μ) = E[v | x + μ]
§ Ti uses variance of μ to “hide” trades from MM
§ Limit informed trade size
- Sequential auction in N rounds per day
o N→ ∞ Þ continuous auction
o Large trades early imply worse prices later
o Strategy
§ Profit from continuous trading, not mixed strategy
§ Vary size to “hide” from MM
o Back (1992) closed-form solution
§ finds an increase in liquidity leads to more informed trade, greater volatility, and more information transmitted
o Issues:
§ Don’t capture evolution of prices (quotes) as do sequential trade models
§ No limit orders for trade size flexibility
- Multiple Ti
o Profit = fn( cost of becoming informed )
Blume & Easley (1990 trading game to get rational expectations equilibrium)
- standard rational expectations concerned with properties of equilibrium
- microstructure concerned with how market structure & organization leads to equilibrium
- traders are risk averse
- salient pionts
o achieves rational expectations equilibrium
o traders earn return to information
o capture some features of actual markets
Admati-Pfleiderer (1988 – two types of uninformed liquidity traders)
- Previous models assume uninformed are noise traders
- Here, two types
o First, nondiscretionary liquidity (noise) traders – transact exogenously determined amounts
o Second, discretionary timing of trades – must satisfy liquidity demands by end-of-day.
- Market maker sets clearing price based on aggregate order flow.
- As with Kyle (1984),
o As # informed traders increases, order flow has less effect on prices.
- Also,
o As the variance of total uninformed trades increases, order flow has less effect on prices.
o Prices in deeper markets more resilient to order flow from informed trading
- As with Kyle,
o Amount of private info revealed
§ same across time periods
§ independent of total variance of liquidity trading
- Unlike previous models, A & P consider heterogeneously informed traders
o Reversing finding above… now prices in deeper markets (fewer informed traders) can be less resilient to informed trading because more information is revealed
Foster & Viswanathan (1990 – trade pattern when informed-trader advantage deteriorates across time)
- uses basic structure of continuous-auction Kyle (1985) model
- one trade period per day
- single, risk-neutral informed trader – gets private info signal every day
- noisy public signal at end-of-day
- informed traders have big information advantage on Monday
- a result
o if uninformed traders don’t time trades, the informed trader’s behavior is predicted by Kyle
o ability of uninformed traders to delay trades result in intraday patterns
Admati-Pfleiderer (1989 – security returns)
- previous models assume prices follow Martingale, so expected return is zero
- Martingale assumption desirable from perspective of market efficiency
- But, in Glosten & Milgrom, simple sequential trade model inadequate to look for patterns based on aggregation of trades
- A & P 1989 employ call market to analyze effects on return patterns from relative & absolute numbers of buys and sells
o Consider competitive & monopolistic market makers
o Again, traders are informed, discretionary liquidity, and nondiscretionary liquidity
- Equilibrium is unceretain
o Numerous plausible equilibria
o Outcome is economically plausible
o Outcomes not necessarily an equilibrium
o Why?
§ Equilibrium defined by equilibrium concept & game being played, but
§ Neither game nor concept is specified
In previous models (sequential trade network & batch trading models),
- prices equal conditional expected values
- prices adjust to new info, but at any time reflect all public information, but not private
Here, how do prices adjust over time?
Brown-Jennings (1989 – rational expectations with exogenously given random supply of asset)
- risky and risk-free asset
- initial endowment of risk-free asset
- after trading, risky asset pays liquidating dividend
- current prices do not impound all information
o traders who track prices know more than those who simply know current price
Grundy-McNichols (1989 – rational expectation with IID normal endowments of asset)
Kim-Verrechia (1991 – link between public information announcements and volume)
Two rational-expectations approaches to role of volume
- analyze the volume that emerges when traders with different information signals transact
o correlate volume with variables such as trader homogeneity
- information inherent in the volume statistics, and what traders learn from volumes
Wang (1994 – how factors such as dividend information affects price-volume relationship)
- some traders are better informed of risky assets’ dividend processes & investment opportunities
- less informed traders get noisy signal of dividends and no signal of opportunities
- volume is decreasing in informational asymmetry
Role of time not previously considered.
- In Kyle, trades are batched and cleared, so arrival is not important.
Diamond-Verrecchia (1987 – consider whether market short sale constraints affect the propensity to trade)
- sequential trade model
- changes in trade propensity introduce asymmetries into the speed of price adjustment
- assume traders in three categories
o no cost of short sales
o proceeds constrained
o prohibited from short selling
- trading day has T intervals
- trade determined by population parameters
(continued)
Easley-O’Hara (1992 –timing is related to existence of new information)
- traders learn from trade and lack of trade
- recall standard sequential trade framework Glosten-Milgrom (`85): event uncertainty does not arise because information event assumed to have occurred
- Here,
o consider variant of 1985 paper, where event occurred with some probability
o some traders receive signal, other do not
o uninformed are either liquidity traders, or have individual-specific trading rules
o trading day divided into discrete time intervals
o possible for no trades to occur in some time intervals, if no events
o informed traders always trade when price not at full-information level
- Contrast with Diamond-Verrecchia
o In D-V, absence of trade construed as bad news
Ch. 7: Market Viability and Stability
Sequential trade models (Glosten-Milgrom)
- market makers quote bid & ask prices
- single trade transacts at the quoted price
Strategic rational expectation models (Kyle)
- no bid/ask prices
- orders are batched together for market-clearing price
Common features:
- market makers set asset prices equal to asset’s conditional expected value
- only market orders, no limit orders, no book of unfilled orders
Issues
- how characteristics of trading mechanisms affects transmission of information into prices
o link between mechanism & stability & market performance (Post 1987)
- how order type affects market performance
Information and market viability
- Glosten (1989) explore how monopolistic specialists might create stability
- Madhavan (1992) suggest that call (order-driven) mechanics rather continuous (quote-driven) mechanics, with periodic clearing, can preclude failure
Order form and price behavior
- Rock (1991) considers interaction between market and limit orders and adverse selection
- Easley-O’Hara (1991) consider the effect of stop orders on market behavior
o Find prices converge exponentially to strong-form efficient value
Policy Issues in Market Structure
- Gennotte and Leland (1990) and Jacklin et al (1992)
o Post 1987 crash
o Rationality implies mechanism explain market behavior
o Relationship between unexpected price-contingent hedging and liquidity
o G-L: make a “price-pressure” argument in 2-period rational expectations argument
§ Uninformed traders
§ Supply-informed traders
§ Price informed traders
o JKP: focus of amount of hedging in sequential trade model
§ Inference problem: estimate the amount of hedge-based order flow
Trading mechanisms match trading desires of buyers & sellers, but involve provision of liquidity.
- focus: linkages b/w markets introduced by liquidity
o effects of fragmentation & scale of trading on markets
o alternative mechanisms: “upstairs market” and liquidity for large block trades
o effects of derivative instruments on price behavior
Nature of Liquidity
- liquidity market accommodate trading with the least effect on price
- Inter-temporal perspective on liquidity
o order flow (Kyle)
o small spreads
o low “costs-of-trading”
- Grossman-Miller (1988) consider “price of immediacy” model
o No private information
o Liquidity shocks and rebalancing
o Willingness to delay transactions command better price
Endogenous liquidity and Market performance
- Cross-sectional perspective on liquidity
o If number of traders affects liquidity, then the scale of trading may affect market performance.
- Pagano (1989) considers whether multiple markets can exist given that liquidity is an increasing function of scale
Block trades and Alternative Trading mechanisms
- In 1992, 50% of volume was in block trades
- Block trader (upstairs market maker) represents a syndication of buyers
o Burdett & O’Hara (1987) consider syndication strategy
o Sappi (1990, 92) consider lack of anonymity effect on traders; dynamic strategy
o Grossman (1990) consider information advantage of block trader over specialist
Information and Multiple market activity
- index volume exceeds underlying securities volume
- Subraharanyan (1991) provides variant of Kyle (1984) to consider where to trade: in an index or an individual stock
- Multiple market links have complex (often conflicting) effects on liquidity
Issues:
- Informed traders gain at expense of uninformed, but gains incorporate information into prices
o Implies costs to some groups of traders
o Robustness might override social welfare issues
Market Transparency
- Madhavan (1992) compares quote-driven (NASDAQ) versus order driven
- Pagano-Roell (1993) compare batch, dealer, continuous, and transparent markets
o Considers how transparency affects losses of uninformed traders
o Finds that uninformed traders do better in transparent markets
Trader Anonimity
- Standard analyses: orders arrive from unspecified sources, market makers see flow
- But,
o Market makers know future flow from book
o Future traders know direction of trade for particular entries to occur
o Brokers: who submits & future intentions?
- Forster & George (1992) extend Kyle (1985)
o analyze equilibrium when a subset has greater information on uninformed trades
o find that trader information has real effects