Empirical Market Microstructure

1
Empirical Market Microstructure

• Rotman School Distinguished Lecture Series
• March 2008
• Ingrid M. Werner
• Martin and Andrew Murrer Professor of Finance
• Fisher College of Business, The Ohio State
  University

2
Empirical tests of MM models

• Dealer markets
• Theory of Dealer Markets
• Cross-sectional spreads
• Inventory management
• Interdealer trading
• Asymmetric Information/Strategic Trading
• Transaction Costs
• Intraday patterns
• Spread decomposition
• Order processing
• Inventory
• Asymmetric information
• Price process

3
The Inventory Control Hypothesis

• Objective
• To understand how market prices arise given the
  nature of order flow and the market-clearing
  protocol.
• Focus
• The liquidity provider
• Specialist
• Dealer
• Market Maker (MM)

4
Garman (1976)Bankruptcy Risk

• Can a market maker who posts bid and ask prices
  and faces random asynchronous arrival of buy and
  sell orders avoid bankruptcy?
• That is, can he/she avoid running out of cash
  and/or stock?
• How should he/she set bid and ask prices to
  maximize the chances of avoiding bankruptcy?
• Gamblers ruin problem
• Key insightA positive spread is necessary to
  avoid going bankrupt with probability one

5
Garman (1976)Bankruptcy Risk

• Key assumptions
• Single risk-neutral monopolistic dealer
• sets the bid price, pb, and ask price, pa (only
  once)
• receives orders
• clears trades
• holds stock and cash
• Maximizes expected profits, tries to avoid
  bankruptcy
• Order-arrival processes
• one unit of stock
• Poisson arrivals
• Sells (?a(pa), ?a(pa) 0)
• Buys (?b(pb), ?b(pb) 0)
• Waiting time between order arrivals is
  exponentially distributed
• Buy and sell orders are driven by independent
  processes
• No herding or information driven trading
• Black-box, only depends on price, p

6
Garman (1976)Bankruptcy Risk

• Key insights
• Order arrivals will affect both the inventory of
  stock and cash
• Let Ic(0) be the initial inventory of cash and
  Is(0) be the inventory of stock.
• Let R(t) (Q(t)) be the probability that the
  dealer will run out of stock (cash).

• Note that pa gt pb is required for ?apa gt ?bpb
  and ?alt ?b to hold
• The dealer has to post a positive spread to avoid
  failure with probability equals one.
• No matter what prices the dealer sets, he will
  fail with probability gt 0.

7
Garman (1976)Bankruptcy Risk

• How are prices set?
• Raise ask and buy orders slow down
• Raise bid and sell orders arrive more rapidly
• To achieve zero-drift in inventories of cash and
  stock, the dealer needs to set prices such that
  arrival rates are equated
• ?a(pe)?b(pe) ?e gt profits 0
• ?a ?b ? gt profits gt 0
• Shortcomings
• Dealer cannot change prices over time
• No link between prices and the inventory position
  of the dealer

Dealer seeks to maximize shaded area
?b(pb)
pa
pe
pb
?a(pa)
?
Arrival rate
?e
8
Amihud and Mendelson (1980) Inventory Management

• Generalizes Garman (1976) by modeling a profit
  maximizing, risk neutral monopolistic dealer who
  changes prices over time.
• Punt on the bankruptcy problem by assuming that
  inventory, I, is finite and bounded from below I
  in (-K, L), L lt 8.
• Translate the Poisson arrival process of Garman
  (1976) into a birth and death process
• This is a semi-Markov decision process where the
  state variable is the inventory of stock, Ij, at
  hand.
• The decisions are to set bid, pb(Ij), and ask,
  pa(Ij), prices.
• Dealer controls the arrival rates directly as a
  function of the state variable, Ij.
• Key insightsA positive spread arises due to
  dealer market power.Market prices will fluctuate
  in part due to dealer inventory control.

9
Amihud and Mendelson (1980)Inventory Management

• Optimal bid and ask prices are monotone
  decreasing functions of the dealers inventory
  position
• The dealer has a preferred inventory position, -K
  lt I lt L
• The preferred inventory position is a function of
  the variability of order arrival rates (cushion)
• Positive spread arises because of market power
• The spread is increasing in the distance between
  the dealers current inventory and his desired
  inventory
• The mid-quote is not always equal to the true
  value of the stock!
• The spread is wider than the spread that the
  Garman specialist would set.
• Competition would drive this spread to zero
• Empirically testable predictionsMarket prices
  will fluctuate in part because of inventory
  controlPrice effects of inventory imbalances are
  transient

A2
A1
I1 gt I2
B2
B1
10
Amihud and Mendelson (1980)Inventory Management
pa
?
pa
pb
?
pb
Inventorylevel
I
11
Stoll (1978)Inventory Risk

• Dealer as a supplier of immediacy.
• Dealers are regular risk-averse traders.
• A dealer is a trader who voluntarily alters his
  portfolio away from the optimal portfolio to
  accommodate other traders demands.
• Dealers require compensation for doing so.
• The compensation for risk is the bid-ask spread.
• Earlier work modeled risk-neutral traders (Amihud
  and Mendelson (1980) and Garman (1976)) and the
  spread was the result of monopoly power.
• Key insightThe spread is compensation for the
  risk the dealer takes on by tilting his portfolio
  away from the optimal portfolio

12
Stoll (1978)Inventory Risk

• Costs for providing immediacy
• Holding costs associated with suboptimal
  portfolio.
• Order-processing costs.
• Asymmetric information costs.
• Dealer is assumed to have exogenous beliefs about
  the true price of the asset, and its true rate of
  return.
• Returns are normally distributed.
• Utility is negative exponential gt CARA
• Dealer maximized terminal wealth.
• Sets prices for one transaction (buy or sell).
• Inventory is financed by borrowing/lending at the
  risk-free rate.
• Market for supplying liquidity services is
  competitive.

13
Stoll (1978)Inventory Risk

• Let Qi be the true value of a trade in stock i
  and Ci be the present dollar cost to the dealer
  of trading Qi
• Expanding both sides (Taylor series expansion),
  dropping terms of order higher than two, setting
  Rf 0, and simplifying the resulting expression
  for the cost to the dealer of trading per unit of
  Q is

14
Stoll (1978)Inventory Risk

• Where z is the dealers coefficient of relative
  risk aversion, Qp is the true dollar value of the
  dealers optimal inventory, sip is the covariance
  between the rate of return on stock i and the
  optimal portfolio and si2 is the variance of
  stock is return.
• So, the cost function depends on
• Dealer wealth and risk preferences
• The level of the dealers optimal inventory
• The size of the trade in stock i
• The variance of the stock and its covariance with
  the dealers optimal inventory.

15
Stoll (1978)Inventory Risk

• If the dealer quotes symmetric quantities on the
  bid and the offer, Qi, it is easy to show that
  the spread relative to the true price will be
• The spread is thus linear in trade size.
• The dealers inventory will affect where the bid
  and ask prices are placed, but not the spread.
• Empirically testable predictionSpread is
  linearly increasing in trade size and in the
  volatility of the stock

16
Ho and Stoll (1981)Dynamic Model

• Extends the intuition of Stoll (1978) to a
  multi-period framework in which both order flow
  (Poisson) and returns are stochastic.
• Dealers are risk-averse and maximize utility of
  terminal wealth.
• Model is solved using finite horizon dynamic
  programming to characterize the dealers optimal
  pricing policy.
• Characteristics of the solution
• The spread includes an adjustment for risk that
  depends on dealer risk aversion, the size of the
  transaction, and the risk of the stock.
• Transactions uncertainty per se does not affect
  the spread.
• In the limit there is only a risk-neutral
  (monopoly) spread.
• Dealers optimal pricing depends on the time
  horizon (dealer becomes less risk averse over
  time).
• The spread is independent of the inventory level.
• Key insightThe spread arises due to market
  power plus an adjustment for inventory risk plus
  an adjustment for the risk from a suboptimal
  asset allocation.

17
Ho and Stoll (1983)Multiple Dealers

• How do dealers decide on optimal prices in a
  setting with competition (e.g., Nasdaq, Forex,
  OTC markets)?
• Extension of Ho and Stoll (1981) to a setting
  with multiple competitive dealers that can trade
  with the public as well as with each other
  (interdealer trading).
• Public orders go to dealer with the best price,
  and are randomly allocated if several dealers
  quote the best price.
• The order size is fixed.
• Dealer wealth and inventories are public
  information.
• Inventory is more risky than if the dealer had an
  exclusive franchise.
• Each dealers strategy depends on the strategies
  of all other dealers. Need symmetry to
  facilitate solution.
• Key insight (English auction)Optimal strategy
  is for the dealer who is the most eager to sell
  (buy) to place his ask e above (bid e below) the
  second most eager dealer to sell (buy).The
  market spread depends on risk aversion, order
  size, and riskiness of the stock and on the
  distribution of inventories.

18
Ho and Stoll (1983)Multiple Dealers

• As in previous models, the inventory will play a
  key role.
• Inventories dictate the reservation values for
  each dealer, i.e., they determine the prices
  (pa1ar, pb1-br) at which the dealer is
  indifferent between trading and not trading.
• Since inventories are public information,
  everyone knows each others reservation values.
• It is possible to order dealers in terms of their
  eagerness to buy (lowest inventory) and to sell
  (highest inventory).

19
Ho and Stoll (1983)Multiple Dealers

• It is not necessarily optimal to quote
  reservation values.
• Suppose we order inventory levels (public
  information) from the lowest to the highest I1
  lt I2 lt lt IN-1 lt IN
• It follows from our reservation quotesb1 lt b2 lt
  lt bN-1 lt bNaN lt aN-1 lt lt a2 lt a1

Dealer N shades her ask by aN-1-aN -e
1a1
1a2
1aN-1-e
1aN-1
1aN
1-b1
1-b2
1-b2e
1-bN-1
1-bN
Dealer one shades his bid by b2-b1 -e
If you are the marginal dealer on either side,
set prices e away from the reservation quotes of
the second most desperate dealer..
20
Ho and Stoll (1983)Multiple Dealers

• There is no guarantee that the optimal policy we
  just derived will result in a market ask price
  that exceeds the bid!
• It depends on the support of the inventory
  distribution, and on the other parameters (A, s2,
  Q)
• Introduce a round of interdealer trading prior to
  customer order arrival

1a1
1a2
Dealer N shades her ask by aN-1-aN -e
1-b2e
1-b1
1-b2
1aN-1
1aN
1aN-1-e
Dealer one shades his bid by b2-b1 -e
1-bN-1
1-bN
Absent interdealer trading, optimal spread would
be negative, leavingroom for arbitrage by
customers...
21
Ho and Stoll (1983)Multiple Dealers

• Implications (Empirically testable)
• As long as there are more than 2 dealers,
  interdealer trading may occur.
• Dealers will use interdealer trades to reduce
  some of the discrepancies in inventories by
  trading with each other.
• They will then compete with each other for the
  arriving customer orders (second price auction)
• Quotes will be less spread out in the public
  market than if we do not allow interdealer
  trading
• Market spread is declining in the number of
  dealers
• Problems
• The assumption of full transparency of
  inventories is unrealistic!
• Dealers also need to know A, subjective s2, etc
• Model is static and order flow is naïve

22
Biais (1993)Incomplete Transparency/Fragmentation

• In practice, we cannot easily track dealer trades
  or when a particular dealer quotes get hit
  (fragmentation).
• Can the model of Ho and Stoll (1983) be relaxed
  to deal with incomplete transparency?
• How would dealers optimally set their quotes if
  they do not know each others inventories?
• Biais (1993) assumes that dealers do not know
  each others inventories, but they do know the
  distribution from which each dealers inventory
  is drawn.
• Quotes are sealed-bid Dutch auction
• Key insightsDealers will act strategically and
  shade their prices.The spread is wider than
  under full transparency.Competition will reduce
  the room for strategic behavior gt spreads
  narrow when there are more dealers.

23
Biais (1993)Incomplete Transparency/Fragmentation

• Game
• Traders decide whether or not to become a dealer
• Dealers receive inventories I in -R, R, iid
• Market order arrives, B/S with equal probability,
  
• Best quotes gets the order
• Final value of the asset is realized
• Solution is by backwards induction
• Lucky for us, it starts with Ho and Stoll (1981,
  1983) solution for reservation quotes.
• Difference is that the dealer does not know the
  reservation values of his/her competitors (since
  inventories are not public information)
• Dealer needs to figure out the probability that
  his ask (bid) price is lower (higher) than that
  of all other dealers (could get the trade)
• Bayes-Nash equilibrium concept

24
Biais (1993)Incomplete Transparency/Fragmentation

• Assume that the inventory distribution is
  uniform.
• Optimal bid (1-bi) and ask (1ai) quotes are

Dealers shade their quotes Shading is increasing
in A, s2, R Shading is decreasing in the
numberof dealers Dealer spreads are decreasing
in the number of dealers
Dealer will post an ask price as if his
inventory is Ii lt Ii
1/2R
-R
R
Ii
0
Ii
(Ii-(-R)) divided by N determines shading
25
Empirical Predictions Inventories

• Predictions from theory
• Arrival rate of orders is price elastic
• Quotes should reflect inventory position of
  dealers.
• The rate at which dealer trade inventory
  imbalances depends on
• risk aversion
• the number of dealers
• risk of the stock
• time
• There is a target inventory level and spreads
  widen as we move away from this target inventory
  level.
• The market spread should be increasing in the
  size of the customer trade
• The market spread should be increasing in the
  volatility of the stock
• The market spread should be decreasing in the
  number of dealers

26
Stoll (1978)Cost of Trading on Nasdaq
Order ProcessingCosts
Risk-aversion

• Sample of 2,508 stocks for 6 trading days
• Median dealers is 5
• Median spread is 3-4
• The number of dealers is increasing in liquidity
• Not all registered dealers are actively trading
• Empirical model for spreads (log-linear)
• Spreads are declining in dealers and liquidity!
• Spreads are increasing in proxy for adverse
  selection!

spread
Turnover
Risk
Dealers
Wealth
Volume
Avg. daily inventory change
Concentration ratio
CAPM
MM Residual
27
Stoll (1976)Nasdaq Dealer Inventory

• Start with our model of dealer spreads (Ho and
  Stoll (1978))
• Add order processing and information costs (ad
  hoq)
• Assume a lot of symmetry and perfect competition
• Let ?Q be the change in aggregate inventory
  (proxy order imbalance)
• Let P be the midquote and r the midquote return
• Use data on 5 days for 2,052 stocks

lt0 Suggests passive inventory adjustment rgt0 gt
?Q lt 0 stabilizing
lt0 Suggests mean Reversion gt 8-10 days to
reverse Q gt Inventory risk
Dealers get taken by informed traders
28
Hasbrouck and Sofianos (1993)Trades of NYSE
Specialists

• Inventory is sometimes negative (short positions)
• There is no obvious drift or divergence
• Patterns suggests rather tight inventory
  management
• The mean inventory is near zero
• Overnight positions are small Dealers tend to go
  home flat
• Liquid stock
• Large market capitalization

29
Hasbrouck and Sofianos (1993)Trades of NYSE
Specialists
Discrete jump Offsetting position in other
stock?Options/derivatives? Overseas
traded? Illiquid stock Small capitalization
Wandering inventory Offsetting position in other
stock?Options/derivatives? Overseas
traded? Illiquid stockSmall capitalization
30
Hasbrouck and Sofianos (1993)Trades of NYSE
Specialist

• Stationary? They have to be (at least mean
  reverting)
• Noisy data
• Misinterpreted
• Horizon not long enough
• How fast do specialists get rid of inventory
  positions? Slow

31
Madhavan and Sofianos (1993)Trades of NYSE
Specialists

• Why is the mean reversion so slow?
• Measurement issues?
• Study days with extreme price changes
• Evidence shows that specialists reverts large
  inventory shocks quickly
• 24/40 cases one day
• 36/49 cases by fourth day
• Hedging
• Evidence suggests not commonly used
• Correlated securities
• Correlation of inventories across stocks is on
  average positive for 41 out of the 50 specialists
  units
• Speculation
• Would mess up our estimates?

32
Hasbrouck and Sofianos (1993)Trades of NYSE
Specialists

• Are NYSE specialists profitable?
• On average, profits are negative
• Short and medium term profits are positive
• Long term profits are negative and very noisy
• Specialists make profits from the spread, but
  there is also some evidence of profitable
  speculation (informed trading)
• Prices, trades, and inventories
• Most of the quote dynamics are attributable to
  trades, with inventories contributing little
  explanatory power.
• Positions are not managed by adjustment of
  publicly quoted bids and offers.

• But, how is then inventory management done?
• Selective nonpublic quoting
• Interdealer trading
• Market specific rules that allow dealers to
  participate in trades without publicly signaling
  through their quotes (NYSE).

33
Madhavan and Smidt (1993)Inventories and Quotes
of NYSE Specialists

• Develop a structural model to estimate
• Mean reversion of inventories, ß
• ß -1 implies inventories reversed in one day
• Desired inventory level, Id
• Results
• ß is negative and significant for 8 out of 16
  stocks
• ß is on average -0.05 which implies a half life
  of 49 days (even slower than HS (1993))
• Desired inventory is positive and significant for
  12 out of 16 stocks!
• Bad news
• Structural model did not manage to eliminate the
  slow mean reversion
• Allow for shifts in desired inventory
• ß is negative and significant for 13 out of 16
  stocks
• ß is on average -0.134 which implies a half life
  of 7.3

34
Madhavan and Smidt (1993)Quotes and Inventories
of NYSE Specialists

• Half lives vary significantly across stocks.
• Midquote-updates are modeled as a function of
• Shocks to order imbalances ()
• Inventory adjustment (-)
• If there is a positive shock to (buy) order
  imbalances, midquotes increases gt Information?
• If inventory levels increase, midquotes decrease
• Thus, MS (1993) find a strong link between
  quotes and inventories

35
Madhavan and Sofianos (1998)NYSE Specialist
Trades

• How does dealer activity vary across stocks?
• Liquidity
• Off-exchange competition
• Tick size (tick/P high gt more specialist
  trading?)
• Specialist participation rate (SP) is defined as
  specialist purchases and sales, divided by total
  purchases and sales.
• Level SP(Liquidity (-), Off-exchange competition
  (-), Tick/P (-), )
• What affects specialist trading over time in an
  individual stock?
• Inventory
• Spread
• Trade size
• Momentum
• Signed SP(Inventory(-), Spread (-), Trade Size
  (), Momentum (-), )

36
Madhavan and Sofianos (1998)NYSE Specialist
Trades
37
Madhavan and Sofianos (1998)NYSE Specialist
Trades
38
Hansch, Naik, and Viswanathan (1998)Dealer
Inventories in London

• Study normalized inventories
• Over 50 of large trades are taken by dealer with
  extreme inventory
• Dealers posting at the BBO attract more than
  their expected share of order flow
• There is a strong (?) link between quotes and
  inventories

39
Hansch, Naik, and Viswanathan (1998)Dealer
Inventories in London

• Model mean reversion as a piece-wise linear
  regression
• There is considerable variation in the speed of
  mean reversion depending on how extreme the
  position is in the first place.
• Mean reversion is still relatively slow!
• One sigma shock
• Half-life 5 days (All)
• Half-life 3.5 days (Non-ADR)
• Five sigma shock
• Half-life 1.3 days (All)
• Half-life 1.2 days (Non-ADR)
• Problems
• Variable transformation
• Pre-arranged trades

40
Reiss and Werner (1998)London Interdealer Trading
41
Reiss and Werner (1998)London Interdealer Trading
42
Reiss and Werner (1998)London Interdealer Trading

• Does risk-sharing motivate interdealer trading
  (Ho and Stoll (1983))?
• Methodology
• Inventory cycles
• Prepositioned/Anticipated trades
• ID trading represents roughly 25 percent of
  volume
• Active inventory management compared to HNV
  (1998)
• One (FTSE) to two days (non-FTSE)
• ID trading conforms to Ho and Stolls (1983)
  hypotheses
• ID are used to reduce inventory imbalances
• Roughly 80 of ID trades are in the unwinding
  direction
• Roughly 65 of ID trades have both dealers
  unwinding
• Dealers in ID trades have extreme inventories
• Position taking is profitable, and profits are
  larger if customer trades are used to unwind the
  inventory

43
Additional Research on Dealer Inventories

• Naik and Yadav (2003) study London dealers
  trading multiple stocks and find that dealers do
  not seem to take a portfolio approach to their
  risk exposure.
• Lyons (1995) study one FOREX dealer and finds
  strong evidence of inventory control.
• Manaster and Mann (1996) study futures markets
  and find patterns consistent with inventory
  control.
• Chakravarty and Li (2003) study futures markets
  and find rapid mean reversion in the personal
  inventory of dual traders.
• Kavajez and Odders-White (2001) study NYSE
  specialists and find no evidence that specialists
  revise their price schedules in response to
  changes in their inventory.

44
Inventory Empirics Conclusion

• Spreads do seem to be consistent with models of
  dealer markets in the cross-section
• Mean reversion of inventories seems surprisingly
  slow in many markets
• Link between quotes and inventories is
  surprisingly weak
• Why is dealer inventory management so difficult
  to measure?
• Dealers have complex objectives
• Off-exchange trading
• Order preferencing, payment for order flow, soft
  dollars, etc

45
Dealer Market References

• Theory
• OHara, M., 1995, Market Microstructure Theory,
  Chapter 2.
• Hasbrouck, J., 2007, Empirical Market
  Microstructure, Chapter 11.
• Amihud, Y., and H. Mendelson, 1980, Dealership
  markets Market making with inventory, Journal of
  Financial Economics 8, 31-53.
• Biais, B., 1993, Price formation and equilibrium
  liquidity in fragmented and centralized markets,
  Journal of Finance 48, 157-185.
• Garman, M., 1976, Market microstructure, Journal
  of Financial Economics 3, 257-275.
• Ho, T., and H. Stoll, 1981, Optimal dealer
  pricing under transactions and return
  uncertainty, Journal of Financial Economics 9.
  47-73.
• Ho, T., and H. Stoll, 1983, The dynamics of
  dealer markets under competition, Journal of
  Finance 38, 1053-1074.
• OHara, M., and G. Oldfield, 1980, The
  microeconomics of market making, Journal of
  Financial and Quantitative Analysis 21, 361-376.
• Stoll, H., 1978, The supply of dealer services in
  securities markets, Journal of Finance 33,
  1133-1151.

46
Dealer Market References

• Empirical
• Bacidore, J. and G. Sofianos, 2002, Liquidity
  provision and specialist trading in NYSE-listed
  non-U.S. stocks, Journal of Financial Economics
  63, 133-158.
• Hansch, O., Naik, N., and S. Viswanathan, 1998,
  Do inventories matter in dealership markets?
  Evidence from the London Stock Exchange, Journal
  of Finance 53, 1623-1656.
• Hasbrouck, J., and G. Sofianos, 1993, The trades
  of market makers An empirical analysis of NYSE
  specialists, Journal of Finance 48, 1565-1593.
• Madhavan, A., and S. Smidt, 1993, An intraday
  analysis of daily changes in specialist
  inventories and quotations, Journal of Finance
  48, 1595-1628.
• Manaster, S., and S. Mann, 1996, Life in the
  pits competitive market making and inventory
  control, Review of Financial Studies 6, 953-975.
• Lyons, R., 1993, Test of microstructure
  hypotheses in the foreign exchange market,
  Journal of Financial Economics 39, 321-351.
• Reiss, P., and I.M. Werner, 1998, Does risk
  sharing motivate interdealer trading? Journal of
  Finance 53, 1657-1703.
• Stoll, H., 1976, Dealer inventory behavior An
  empirical investigation of Nasdaq stocks, Journal
  of Financial and Quantitative Analysis 11,
  359-380.