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2
WHAT IS LIQUIDITY?
A market with low “transaction costs” including execution price, uncertainty and speed
This may mean different things depending upon the volume to be traded and impatience of the trader.
3
THREE MEASURES:
Bid Ask Spread– measures costs for small trades
Depth– quoted depth for small trades– depth with some price deterioration
Price Impact of a Trade– how much prices move in response to a
large trade
5
HOW DO THESE MEASURES OF LIQUIDITY VARY OVER TIME AND CAN THEY BE PREDICTED? BRIEFLY -THE ANSWER FIRST!! ACROSS ASSETS – MORE
TRANSACTIONS AND MORE VOLUME MEANS MORE LIQUIDITY.
HOWEVER – OVER TIME, MARKETS BECOME LESS LIQUID WHEN THEY ARE MORE ACTIVE!!!
6
WHY SHOULD EXECUTION BE WORSE WHEN THE MARKET IS ACTIVE?
Because the market is more active when there is information flowing.
When there is information, traders watch trades (and each other) to learn the information as quickly as possible
Often called “Price Discovery”
7
MICROSTRUCTURE THEORY
Inventory models– More trades make inventories easier to
manage– lower transaction costs and more liquidity
Asymmetric Information models– More informed traders increase adverse
selection costs - greater spreads and price impacts
8
ASYMMETRIC INFORMATION MODELS Glosten and Milgrom(1985) following
Bagehot(1971) and Copeland and Galai(1983)
A fraction of the traders have superior information about the value of the asset but they are otherwise indistinguishable.
9
MARKET MAKER INFERENCE PROBLEM: If the next trader is a buyer, this raises
my probability that the news is good. Knowing all the probabilities I can calculate bid and ask prices:
Over time, the specialist and the market ultimately learn the information and prices reflect this.
askPnewbuyhistorypastValueE )(
10
Easley and O’Hara(1992)
Three possible events- Good news, Bad news and no news
Three possible actions by traders- Buy, Sell, No Trade
Same updating strategy is used
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BEGINNING OF DAY
P(INFORMATION)=P(GOOD NEWS)=
P(AGENT IS INFORMED)=P(UNINFORMED WILL BE BUYER)=
P(UNINFORMED WILL TRADE)=
END OF DAY
12
Easley Kiefer and O’Hara
Empirically estimated these probabilities Econometrics involves simply matching
the proportions of buys, sells and non-trades to those observed.
Does not use (or need) prices, quantities or sequencing of trades
15
50.00
50.05
50.10
50.15
50.20
50.25
50.30
2 4 6 8 10 12 14
ASK1ASK_EKO
ASK2ASK3
ASK4
ASKING QUOTES WITH VARIOUS FRACTIONSOF INFORMED TRADERS
16
50.00
50.05
50.10
50.15
50.20
50.25
50.30
2 4 6 8 10 12 14
EVAEVANEVA2N
EVA3NEVA4NEVA5N
ASK QUOTES AFTER A SEQUENCE OF BUYSWITH INTERVENING NONTRADES
17
LIQUIDITY IMPLICATIONS
When the proportion of informed traders is high, the market is less liquid in all dimensions
When information flows, there are more informed traders, as they rush to trade ahead of price movements
For specific public news events, this could approach 100%
18
INFORMED TRADERS
What is an informed trader? – Information about true value– Information about fundamentals– Information about quantities– Information about who is informed
19
PRICE IMPACTS OF TRADES
In real settings where traders have a choice about when to trade, how to trade and how much to trade– Their choices may indicate whether they
have information– Large trades and rapid trades and trades
by big players all have greater price impacts
20
Econometric Tools
Data are irregularly spaced in time The timing of trades is informative Need to model jointly the time and
characteristics of a trade This is called a marked point process Will use Engle and Russell(1998)
Autoregressive Conditional Duration (ACD)
21
STATISTICAL MODELS
There are two kinds of random variables:– Arrival Times of events such as trades– Characteristics of events called Marks
which further describe the events Let x denote the time between trades
called durations and y be a vector of marks
Data: }N,...1i),y,x{( ii
22
A MARKED POINT PROCESS
Joint density conditional on the past:
can always be written:
);y,xy,x(f~)y,x( i1i1iii1iii
F
);y,x,xy(q);y,xx(g
);y,xy,x(f
i21i1iiii11i1ii
i1i1iii
23
THE CONDITIONAL INTENSITY PROCESS The conditional intensity is the
probability of an event at time t+t given past arrival times and the number of events.( , ( ); ,..., )
( ( ) ( ) ( ), ,..., )
( )
( )lim
t N t t t
P N t t N t N t t t
t
N t
t
N t
1
0
1
24
THE ACD MODEL
The statistical specification is:
where is the conditional duration and is an i.i.d. random variable with non-negative support
(i)
i i i i it t E x t t ( , ..., ; ) [ , ..., ]1 1 1 1
(ii) xi i i
25
TYPES OF ACD MODELS
Specifications of the conditional duration:
Specifications of the disturbances– Exponential
– Weibul
– Generalized Gamma
– Non-parametric
iiii
jijjiji
1i1ii
z,y,x
x
x
26
MAXIMUM LIKELIHOOD ESTIMATION For the exponential disturbance
which is so closely related to GARCH that often theorems and software designed for GARCH can be used for ACD. It is a QML estimator.
i i
ii
xlogL
27
EMPIRICAL EVIDENCE
Dufour and Engle(2000), “Time and the Price Impact of a Trade”, Journal of Finance, forthcoming
Engle, Robert and Jeff Russell,(1998) “Autoregressive Conditional Duration: A New Model for Irregularly Spaced Data, Econometrica
Engle, Robert,(2000), “The Econometrics of Ultra-High Frequency Data”, Econometrica
Engle and Lunde, “Trades and Quotes - A Bivariate Point Process”
Russell and Engle, “Econometric analysis of discrete-valued,
irregularly-spaced, financial transactions data”
29
APPROACH
Extend Hasbrouck’s Vector Autoregressive measurement of price impact of trades
Measure effect of time between trades on price impact
Use ACD to model stochastic process of trade arrivals
30
DATA:
TORQ dataset -transactions on 18 stocks for 3 months from Nov. 1990-Jan 1991. These are the actively traded stocks.
31
DEFINITIONS
PRICE is midquote when a trade arrives(actually use 5 seconds before a
trade).
R is the log change in PRICE
T is the time between transactions
X = 1 if transaction price> midquote, i.e. BUY
X= -1 if transaction price < midquote, SELL
X= 0 if transaction price = midquote
V is the number of shares in a transaction
32
CORRELATIONS
[ABS(R), T(-1)] <0, FOR 16
[SPREAD, T(-1) ]< 0, FOR ALL 18
[ABS(R), V(-1)] >0 , FOR ALL 18
33
HASBROUCK MODEL (1991)GENERALIZED FOR TIME EFFECT
Vector Autoregression of trade directions and returns
Use to calculate the long run effect of trades on prices as a function of time between trades
.vx ))Tln((xDrcx
vx ))Tln((xDrar
t,2
5
1iitit
xi
xi1t1t
xopen
5
1iitit
t,1
5
0iitit
ri
ritt
ropen
5
1iitit
34
RESULTS FOR RETURN EQUATION: o > 0 for all 18, all very significant
– Buys raise prices o < 0 for 17, 13 significant
– Buys raise prices more when durations are short H: all = 0; rejected for 13
– Time Matters H: ;
• rejected for 13,• negative for 16
05
1i
ri
35
for 18 , all very significant,
– serial correlation in trade direction for 15, significantly negative for 10,
– short durations increase autocorrelation rejected for 11
rejected for 12, 11 negative– time matters for trade dynamics
x5
x10 ...0:H
0:H5
1i
xi0
0x1
0x1
RESULTS FOR TRADE EQN.
36
INTRODUCING OTHER INTERACTIONS
H: all =0; rejected for 8 of 18 stocks. Volume and Spread are very significant
iti,3i,2iti,1iit
t
5
0iitittopen
5
1iitit
Sprd)Vln()Tlog(b
XbDRR
37
WACD estimation for FNM and IBM
112211
~~ ttttt DTT
a n d
.0, ~
exp~~ 1
t
t
tt
t
t forT
TTg
D t i s a d u m m y v a r ia b le fo r th e f i r s to b s e rv a t io n o f th e t r a d in g d a y .
F N M IB M
C o e f f . C o e f f .( T - S t a t . ) ( T - S t a t . )
0 .0 0 7 2 0 .0 0 4 8( 8 .6 1 ) ( 1 0 .5 7 )
0 .1 2 6 2 0 .0 8 0 4( 1 8 .6 0 ) ( 1 8 .5 6 )
-0 .0 8 0 3 -0 .0 3 3 4( - 1 1 .5 8 ) ( - 7 .5 2 )
0 .9 4 4 5 0 .9 4 5 7( 3 6 7 .1 8 ) ( 5 6 6 .6 0 )
0 .8 9 6 2 0 .8 8 4 5( 2 1 3 .1 0 ) ( 2 9 2 .9 6 )
D n e w d a y -0 .0 9 1 2 -0 .1 8 0 6( - 3 .1 2 ) ( - 6 .8 4 )
(1 + 1 / a 1 .0 5 5 1 .0 6 2
L ik e lih o o d - 2 6 9 4 3 .6 - 5 2 7 1 8 .4a T h e c o n d i t io n fo r s ta t io n a r i ty (1 + 1 / )* ( + w h e re () i sth e g a m m a fu n c t io n , i s s a t i s f ie d fo r b o ths to c k s .
38
CALCULATE IMPULSE RESPONSES OF A TRADE. WITH DURATIONS FIXED AT A
PARTICULAR VALUE WITH DURATIONS EVOLVING
JOINTLY MEASURED IN CALENDAR TIME
RATHER THAN TRANSACTION TIME Latter two require stochastic simulation
of the ACD
39
Cumulative percentage quote revision after an
unexpected buy
0
0.02
0.04
0.06
0.08
1 3 5 7 9 11 13 15 17 19 21
1/17/91
12/24/90
Transaction Time (t)
40
Cumulative percentage quote revision after an unexpected buy
0
0 .02
0 .04
0 .06
0 .080
:00
02:0
5
04:1
0
06:1
5
08:2
0
10:2
5
12:3
0
14:3
5
16:4
0
18:4
5
20:
50
Calendar time (min:sec)
1/17/91
12/24/90
41
SUMMARY The price impacts, the spreads, the
speed of quote revisions, and the volatility all respond to information
Econometric measures of information – high shares per trade– short duration between trades– wide spreads