a
of t&°;
—
DHD28
.M414
9*
ALFRED
P.
WORKING PAPER
SLOAN SCHOOL OF MANAGEMENT
TRANSACTIONAL RISK, MARKET CRASHES,
AND THE ROLE OF CIRCUIT BREAKERS
Bruce C. Greenwald*
Jeremy C. Stein**
First Draft:
March 1989
This Draft:
October 1990
WP # 3226-90-EFA
MASSACHUSETTS
TECHNOLOGY
50 MEMORIAL DRIVE
CAMBRIDGE, MASSACHUSETTS 02139
INSTITUTE OF
TRANSACTIONAL RISK, MARKET CRASHES,
AND THE ROLE OF CIRCUIT BREAKERS
Bruce C. Greenwald*
Jeremy C. Stein**
March 1989
First Draft:
October 1990
This Draft:
WP # 3226-90-EFA
Forthcoming, Journal of Business
*
**
Bell Communications Research
Sloan School of Management, M.I.T.
We thank Jim Gammill, Hank McMillan, Andre Perold, Robert Schwartz, Eric Sirri,
Larry Summers, an anonymous referee and seminar participants at the CFTC, the
SEC, the Federal Reserve and the Western Finance meetings for helpful comments.
Transactional Risk, Market Crashes, and the
Role of Circuit Breakers
Bruce
Greenwald*
C.
Jeremy
C.
First Draft:
Stein**
March 1989
This Draft: October 1990
Forthcoming, Journal of Business
*
**
Bell Communications Research
Sloan School of Management, M.I.T.
We thank Jim Gammill, Hank McMillan, Andre Perold, Robert Schwartz, Eric Sirri,
Larry Summers, an anonymous referee and seminar participants at the CFTC, the
SEC, the Federal Reserve and the Western Finance meetings for helpful comments.
s
Abstract
We develop a pair of models that illustrate how imperfections in
transactional mechanisms can lead to a market crash. Neither market orders nor
limit orders allow traders to condition their demands on the full information set
When volume shocks are sufficiently
needed to achieve a Walrasian outcome.
large, the deviations from Walrasian prices and allocations are large also.
Properly designed and implemented, circuit breakers may help to overcome some of
these informational problems, and thereby improve the market's ability to absorb
large volume shocks
I
.
Introduction
accounts
Many
of
market
stock
the
crash
October
of
point
1987
to
market microstructure factors as playing an important role in the dramatic
For example, Grossman and Miller (1988) write:
events of those few days.
".. .both markets had by then become highly illiquid and
virtually incapable of supplying immediacy at the low cost their
That illiquidity was evidenced in
users had come to expect
the spot market by (1) the virtual impossibility of executing
market sell orders at the bid quoted at the time of order entry,
and (2' the delays in executing and confirming trades on Monday
afternoon and again, after the opening on Tuesday." (p. 632)
.
.
.
(Greenwald and
In our interpretation of the Brady Task Force Report,
Stein (1988)), we also emphasized the breakdown of market-making as one of
the
characteristics
key
prevent
breakdown
can
working:
under more
attractive
However,
of
would
prevent
system
market-making
the
Walrasian
circumstances,
ordinary
opportunities,
if
normal
the
We
crash.
the
is
argued
that
adjustment
prices
from
failing,
mechanism
falling
value
of
from
perceiving
buyers,"
"value
type
this
too
buyers
far.
may
be
deterred from placing orders because they view the "transactional risk" as
extremely high- -they are very unsure as to the prices at which their orders
We concluded that such transactional risks may justify
will be executed.
the use
According to this view,
"circuit breakers."
of
circuit breakers
are not intended to prevent a rapid fundamental Walrasian price adjustment,
but rather to
facilitate
it,
by reducing transactional risks and thereby
encouraging value buyers to bring their demands to market.
This paper presents a pair of market microstructure models designed to
elaborate
upon
and
clarify
the
informal
arguments
made
in
our
earlier
paper.
The models appear to fit with many of the stylized facts about the
crash,
and
they
have
quite
specific
implementation of circuit breakers.
implications
for
the
design
and
-
2
-
The models are closely related to the one seen in Grossman and Miller.
Like Grossman and Miller,
is,
as
disseminated to the investing public (or "value buyers")
in two stages,
Because
whole.
a
receive the shock,
smaller
group
second stage,
of
they examine how an informationless supply shock
public
entire
the
after
delay,
a
immediately
prepared
to
first stage be temporarily absorbed by a
it must in the
competitive,
not
is
market
risk-averse,
does
Only
makers.
in
the
public buy some of the new supply
the
from the market makers.
There is one key respect in which the models here differ from Grossman
Their primary focus
however.
and Miller,
first stage
on the
is
of
this
transmission sequence, and their second stage is, by assumption, completely
Walrasian
in
and market makers
value buyers
nature:
effectively submit
complete demand curves to a hypothetical auctioneer, who then sets a market
Hence there
clearing price.
is
is
scope for transactional risk- -everyone
no
assured of receiving a price-quantity pair that they view as optimal.
In contrast,
price.
submit market
must
buyers
1
value
the second stage of the models here is less efficient:
Consequently,
that
orders
there
is
uncontingent
are
on
execution
the
transactional risk--there is a possibility
that these orders will be executed at an unattractive price level.
The main point being made here
first
stage
of
transmission
is
sequence
transactional risk in the second stage.
reluctant
to
come
to
market
to
feeds back to the market makers.
the
first
stage,
knowing
that
that
absorb
large volume
a
will
tend
As a result,
some
of
the
to
shock in
increase
the
the
value buyers will be
shock.
This
in
turn
They will shy away from large volumes in
such
difficult to unload to the public.
amounts
will
The end result
subsequently
is
a
be
very
"microstructure-
induced crash" --the outcome of the two- stage transmission sequence is very
different from what would happen in a hypothetical world where
buyers were able
to
meet
the
volume
shock instantaneously in
a
the value
Walrasian
fashion, without using the market-making mechanism as a temporary conduit.
-
context of our models,
In the
than
an
risk-bearers
of
economy.
the
in
informational
-
a
market crash is really nothing more
volume
the
This
imperfection- -the
conditioned on an
fact
among
shock
inefficiency
important variable,
primary purpose of
the
allocation
inefficient
3
can
market
that
namely
potential
the
traced
be
orders
to
cannot
execution price.
the
2
an
be
The
circuit breaker mechanism should thus be to improve
a
information available
market participants at the time
to
they submit
their orders.
In Sections
so,
we
assume
considered.
II
that
This
and III,
traders
use
assumption
consistent
with
the
buyers"
make
little
to
we
observed
use
develop our two simple models.
only market orders
makes
the
tendency
of
limit
of
--
limit
analysis
many
orders.
large
In
In doing
orders
are
not
and
is
tractable,
real
world
Section IV,
we
"value
use
our
first model to shed some light on the question of why limit orders do not
play
a
more
discuss the
important
role
in
market
stabilization.
In
Section
V,
we
implications of the models with respect to both the stylized
facts about the October 1987 crash, and to the design and implementation of
circuit-breaker trading mechanisms.
II.
Model #1
a)
Model Description
This model features
and
Section VI concludes.
"value
buyers,"
two
each
of
types of traders:
whom
has
competitive market makers
constant
utility with a risk aversion coefficient of one.
absolute
The
risk
aversion
market makers
are
"myopic maximizers" - -at each point in time, they only look one period ahead
in
changing
demands.
their
formulating
(This
substantive.)
anything
simplifies
timing
The
of
mathematics without
the
the
model
diagrammed
is
below:
Time
Time
1
Time
2
Competition among
market makers for
value buyer orders
leads to price = P 2
News about
fundamentals
Supply shock s of
risky asset hits
market, is absorbed
by n 1 market
Price = P a
makers.
emerges.
This
activates a random
number n 2 of value
buyers, each of
whom submits a
market order d.
Fundamentals
3
Liquidation of
asset, more news
about fundamentals
Anyone holding
asset gets
F - f2 + f 3
.
.
E,F = f,.
EjF = 0.
At time
the
1,
entire supply shock
information about
model)
it
is
important
This leads to a price P :
s.
(indeed,
s
it
is
.
Since ? 1 conveys
perfectly informative about
P lt
1
s
in
this
They submit market
arouses the attention of the value buyers.
orders at time
lower
group of n x risk-averse market makers must absorb the
based on the magnitude of the price decline at time l--the
the
larger
feature
of
is
the
the
model
reacting to the price signal
is
is
a
placed by
order
that
the
number
random variable.
interpretations that can be given to n 2
.
value
each
buyer.
buyers
value
of
An
n2
There are a variety of
The most literal one is that not
all value buyers are monitoring the market at all times,
so that a fraction
of them are "asleep" and miss the price signal at time
1.
it
may be
speed,
that not
all
buyers are able
to
place
their orders
and some are unable to get an order in before time
developed
in
the
next
section
expands
on
this
Alternatively,
idea,
2.
with equal
(The model
allowing
for
two
leads
to
separate times at which value buyer orders can be executed.)
The
uncertainty
surrounding
the
realization
of
n2
-
-
5
transactional risk for value buyers placing orders at time
is the realized n 2
execution price
here
the more total orders are placed,
,
P2
of
uncertainty
more
imply
s
distribution of n 2 is taken to be independent of
it
likely that a high
is
and the higher is the
should be pointed out that there is no assumption
values
large
that
It
.
The larger
1.
s
s.
about
However,
n 2 --the
in reality,
increase the conditional variance of n 2
does
.
This was certainly the case in October 1987, when larger order flows led to
purely mechanical problems
made
it
difficult
more
predict what proportion of orders placed at a
to
given time would be executed promptly.
magnitude of
s
that
telephone and computer backups)
(such as
If
relationship between the
this
and the variance of n 2 were incorporated into the model,
the
results would just be accentuated.
Time
3
introduced into the model only as
is
the equilibrium.
gets
payoff
a
about
News
F.
device for tying down
anybody holding a unit of the risky asset
At this time,
of
a
value
the
of
F
(i.e.
about
news
"fundamentals") arrives slowly over the course of time--F is represanted as
f2 +
f3
,
where
f2
is
learned at time
and f 3 is learned at time
2
These
3.
news innovations are taken to be normally distributed, with mean zero.
Gate
2
innovation has variance
a\
The
.
date
3
innovation
thought of as occurring over a longer interval of time)
is
The
(which may be
normalized to
have variance of unity.
b)
Solution for Non-Stochastic n ?
As a benchmark,
case where
n2
is
it
is
useful to first work through the model for the
non-stochastic,
model can be solved backwards.
holding a total supply of
(s
takes
and
At time
-
n 2 d)
2,
denoted by n 1m2
,
is
the
fixed value
n2
.
The
the market-makers will be left
initial supply shock,
--the
that has been absorbed by the value buyers.
for the market makers,
on
less any
The aggregate demand function
given by:
-
(1)
n^
-
- F,)
(£,F
77,
v
n,(f2
-
{F)
P2
-
6
)
Setting this demand equal to the supply that is held by the market makers
leads to the price that emerges at time
(2)
2:
2—
P, - f, +
The next question to address
the determination of
is
submitted by the value buyers at time
the market orders d
The demand of an individual value
1.
buyer is given by:
,„,
(3)
.
d
-
E,(F-P,)
[s-n,d]
V,(F-P2
n,
)
Note that there are two potential sources of uncertainty for value buyers-not only are they uncertain about the terminal value of the asset, they are
also
unsure
particular
about
case,
concerns the time
the
price
equation
2
(2)
P2
which
at
tells
by the value buyers from looking at P 1
that
us
fundamental news
f2
they
.
the
will
only
buy
it.
In
uncertainty
this
in
P2
Everything else can be inferred
.
Equation (3) can be solved to yield the Nash equilibrium market order
made by each value buyer, predicated on the conjecture that all other value
buyers are behaving the same way:
(4)
d
'
^
Knowing how value buyers will behave, market makers can then formulate
their strategies at time
(2)
gives:
1.
Plugging value buyer demand back into equation
7
-
(5)
P2
-
^—
f2
time
At
competition among market makers
1,
for
the
supply shock
s
leads to a price of:
.
Pi . EiP2
(6)
JH1II2L
-
,a
_i_
^]
+
E
In the special case of a non- stochastic n 2
,
the use of market orders
in this framework still leads to a Walrasian outcome by time 2:
of P 2 — f2
as well as the distribution of the supply shock,
s
-
the price
n 1 + n2
n 2 d* = n 2 s and njm 2 =n
with
attained in the
s
,
are all exactly the same as would be
idealized situation where both the market makers and the
buyers
were
auctioneer at
time
value
:
n 1 +n 2
n : +n 2
able
2.
3
submit
to
Intuitively,
entire
their
this
is
demand
nothing new is learned about
an
to
because value buyer demands
are driven by the conditional mean and variance of (F-P 2 )
stochastic,
curves
(F-P 2 )
at
time
When n 2 is non-
.
Thus a value
2.
buyer can predict exactly ahead of time the single point on his Walrasian
demand
curve
market
order.
there
is
a
that
will
be
relevant,
Consequently,
temporary price
can
submit
Grossman-Miller
the
drop
and
at
time
1,
that
result
quantity
is
as
a
reproduced:
when the market makers must
briefly absorb all of the supply shock by themselves, but by time
2,
the
transmission is complete,
c)
Solution when n 2
Stochastic
is
Things change quite dramatically when n 2 becomes stochastic.
the variance of n 2 by o\
.
The price at time
2
will now be given by:
Denote
P7
(7)
-
f
[n, d
-Li-
+
•
-
s]
Now there is more uncertainty for a value buyer trying to guess at
time
1
price
the
information
at
about
realization of n 2 d,
which an order will be
revealed
of
2
or
total number of value buyers.
market
1
-specif ically
is
the
upon
order
1
2
-
Thus
new
,
the
,
it
no
is
the single relevant point on
A trader is likely to regret the size
Walrasian demand curve.
time
his
time
at
(F-P 2 )
longer possible for someone to guess at time
their time
With a„ >0
executed.
learning
price
the
at
which
was
it
executed.
The magnitude of this transactional risk depends on the size of
individual
orders
a
is
happening
in
the
market
and
d
is
On the other hand, when there
transactional risk will be small too.
small,
is
much
not
If
d.
large supply shock that calls for large d's,
transactional risk will
be heightened.
The market order placed by an individual buyer can be calculated as:
,
,
(8)
_,
d
-
E.(F-P2
[s-n2 d]
)
A comparison of equation (8) with equation (3) highlights the effect
of randomness in n 2
identical.
.
However,
When
when
ct£
aj
n 2 is nonstochastic)
=
(i.e.,
is
non-zero,
,
the two are
increased responsiveness by any
given value buyer makes transacting more risky for his peers, and tends to
make
from
the
responsiveness
by
them shy away
increased
a
other words,
In
market.
given
value
buyer
non-zero a 2
for
imposes
a
,
negative
externality on all other potential value buyers.
This
responding
negative
externality
aggressively
to
a
prevents
large
value
voluiie
buyers
shock.
as
a
Equation
group
(8)
from
can
be
9
-
-
rearranged to give an expression for equilibrium value buyer demands:
°" (d
(8')
Figure
}
+(n
1
+ir2
)d -g
,
illustrates
1A
dependence of
the
relationship to the one seen in the Walrasian case.
of d
compares
this
The limiting behavior
for large and small volume shocks can be summarized as follows:
Proposition
As s
(9)
1
When
value of n 2
seen with
large,
the
:
- 0,
As s
(10)
d' -
d
- »,
a
£_-•
-s
volume
the
,
m
—
(9)
3
[
-4
shock
that only
market
3
]
relatively
is
non-stochastic
transmission
n2
is
mechanism
shock,
forced
thus
allocation of risk-bearing.
when
However,
.
increases with the cube
makers
small,
and
breaks
the
thereby determining
plots E(P 2 ) against
without
equals
s,
P 2 as
volume
down- -rather
its
root of
to
swallow
s.
shock
mean
very
a
taking an amount
The much smaller
the
is
absorbing
than
value buyers wind up
remainder- -an
group of
inefficient
The price consequences of this misallocation
can be obtained by plugging the equilibrium value of
obtains
n2
states that the outcome is very close to the Walrasian one
constant proportion of the
(7),
and
on s,
d*
a
d*
back into equation
function of the supply shock
s.
Figure IB
and again compares the relationship to the one that
transactional
risk.
As
can be
seen,
large
volumes
are
associated with increased deviations of prices from "fundamental" Walrasian
levels
-
10
-
Model #2
III.
In the above model,
risk
solely
driven
is
uncertainty as
by
fact
the
value
total
the
to
the relationship between volume and transactional
buyer
affected by volume.
hit
value buyers
volume
large
market
the
shocks,
next model
The
at
once,
exacerbating
the
flow at
order
liquidity- -the extent to which a unit of time
not
volume
greater
that
2
implies
time
more
Market
2.
order flow moves prices- -is
demonstrates
that when not
also be
liquidity may
all
impaired by
The
inefficiencies.
allocational
timing of the model is outlined below:
Time
Time
1
Time
2
Orders of fast
value buyers
arrive, are
executed at P 2
E 2 F=f 2
Supply shock of
s, absorbed by
market makers,
leading to P 2
This activates
n f "fast" value
buyers who
submit market
orders d f and
n s "slow" value
buyers who
submit market
orders d s
.
Time 4
3
Orders of slow
value buyers
arrive, are
executed at P 3
E 3 F=f 2 +f 3
.
Asset pays
F=f 2 +f 3 +f
<,
.
.
.
,
.
EiF-0.
again,
Once
time
there
But now,
1.
random number of value buyers submit market orders at
a
is
further complication, because not all of the
a
uncertainty concerning the number of value buyers
nf
of
are
them
"fast"
and
submit
their
orders
"slow," and don't get their orders in until time
assumed that n f and n s
common variance of
are
fast
knowledge,
or
df
and
slow,
or
a\.
ds
.
are
It
uncorrelated,
is
by
3.
with means
resolved right away-time
while
2,
ns
For simplicity,
of
nf
and n s
are
it is
and a
,
also assumed that buyers know whether they
therefore
This
is
can
assumption
submit
is
demands
conditional
unrealistic -- it
is
more
on
this
likely
-
the
that
will
trades
their
themselves
investors
be
simplifies
uncertainty about the exact time
some
and
executed,
-
that
uncertainty
this
adds
further
However, allowing value buyers to know their execution
transactional risk.
time
face
11
analysis,
the
only
and by ignoring another type of risk,
makes the argument for a crash scenario excessively conservative.
At time 4,
the
asset is liquidated,
the
fundamental value
As
F.
arrives in each period,
market makers.
variance
The
Once again,
a\.
previous
the
some
model,
that holding the asset is always
so
time
in
and everyone holding it receives
time
and
2
innovations,
3
and
f2
about
news
risky to the
f3
,
both have
final piece of news,
the variance of the
F
f4
is
,
normalized to unity.
Solution
b)
The same backward solution technique applied in the previous section
can be used here.
arrived,
At time
3,
will
inventory
market-maker
so
all of the orders of
be
(n f d f + n s d s )
[s
(n f d f
-
will have
+
ns ds )
P2
can
]
.
Consequently, the price will be given by:
(11)
P,-f2
At
[n f d f + n.d. - s]
S-2
f, + -!-£-i
+
time
market-maker
2,
inventory
is
[s
-
nfdf
]
.
Thus
be
determined as:
,
,
(12)
P, -
[s -
,
EAP,)
,
— —
nfdf VAP,)
-
In order to evaluate
variance of P 3 as of time
]
(12),
2.
one needs to find the conditional mean and
To do
so,
One
source of risk to market
they only have partial
information at this time
and variance of n s are given by n s and
makers at time
2
is
that
recall that the conditional mean
about the total value buyer order flow.
a\.
If the number of slow orders,
turns out to be unexpectedly small, P 3 will be unexpectedly low.
ns
,
12
-
Taking these facts into consideration leads to:
[r^d,
_
2
2
'
The
iTs d s -
*
*
s]
[s -
_
n fdf
term
on
2
2
(a D d s /n )]
ni
Ox
last
2
2
[o , +
]
the
hand
right
side
of
represents
(13)
premium built into P 2 by market makers for holding the supply
time
suggested
As
2.
fundamental risk,
order flow,
above,
risk
this
not
-
risk
n £ d£
at
]
only
on
remaining uncertainty about future
but also on the
a\,
depends
premium
[s
the
a*-
Now consider things from the point of view of a value buyer deciding
how large an order to place at time
1.
If he
is
slow trader,
a
he faces
the same type of transactional risk as was seen in Model #l--the execution
price P 3 depends on the magnitude of the uncertain order flow n f d f + n s d s
However,
time
2
also
time
2
is
trader,
things are even worse.
on an uncertain order
sensitive
much more
to
flow,
variations
in
nfdf
the
.
The price at
But the price
order
flow
at
than the
This can be seen explicitly by comparing the derivatives
3.
and dP 2 /d(n f d f )
liquidity at times
(14)
a fast
is
depends
price at time
dP 3 /d(n s d s )
if he
.
dPjd(n.d.)
3
and
which can be thought of as measures of market
respectively:
2
[1 + o f +
dP,
i
/3 1
2
,
'
d(n f d f
The reason that prices at time
2
2
(o n d s
/n
2
)}
flj
)
2
are much more sensitive
to variations
in
order flow is because market makers still face another period of order flow
risk after time
a
2,
and hence are very unwilling to smooth prices.
This is
feature that was absent from Model #1, where market makers were only hit
with one uncertain order flow.
13
-
Thus transactional risk at time
in
Model
Now
#1.
simultaneously:
in addition,
response
(i.e.
(i.e.
pronounced than it was
externality
effects
working
uncertainty about n f means that aggressive
high d f )
imposes risks on other fast traders;
uncertainty about n s means that aggressive slow trader
high
a
a
is even more
adverse
two
are
as before,
1)
fast trader response
and 2)
there
2
ds )
makes
the
market
"illiquid"
at
time
2,
and
thereby exacerbates the effect of n f d f -type risk.
These effects can be seen explicitly when the demand of fast traders
is calculated:
dt
(15)
Now
the
E,(F-P.)
-
V1 {F-P2
d|
fact
and
that
2
^[{s-nfdf (l*o 5
2
?
n tl + f) + a n dj(l
2
)
d^
(o
2
*
n d'
s
o
z
f
/n
2
+
(a n dl/nl))
))
-
n sds
2
]
2
terms both appear in the denominator of (15),
aggressive
responses by either type
negative externalitv effect
that blunts
the
reflecting
of value buyer have
a
demand of fast value buyers.
This results in the following limiting behavior:
Proposition
2
:
_i
(16)
As s
(17)
As
-
°°,
dj - Aj s
s -
°°,
d' -
3
,
where k is
1
a
constant.
i
In
words,
Model #1.
the
However,
k2 s
9
,
where k2 is a constant.
limiting behavior
the
of
slow buyers
is
fast buyers face even more risk,
as
described
in
and their ability
14
-
to assume a
-
portion of the supply shock is even more impaired than before.
Why Don't Value Buyers Use Limit Orders?
IV.
Thus far, the formal analysis has simply assumed that value buyers are
restricted to placing market orders that are uncontingent on the execution
And it is the transactional risk inherent in these market orders
price.
Hence a natural question to ask is
that drives the results of the models.
this:
do
sorts
of
limit orders represent a way for value buyers
described
risk
transactional
them
enabling
thereby
above,
circumvent the
to
to
transmit their demands to the market more forcefully?
Other authors have argued that limit orders will not be appropriate
Grossman and Miller, as well as Rock (1987)
for certain types of traders.
point out that since limit orders carry a risk of non-execution,
be
avoided by traders with
valuable
but
perishable
a
neither
However,
information.
inside
those with
or by
high demand for immediacy,
they will
of
these
suggests that limit orders will not be used by the sorts of value
papers
buyers in our models.
In order to motivate the use of market orders by our value buyers,
focus
on a different drawback of limit orders:
that
fact
the
we
they leave
traders exposed to innovations in fundamentals that occur between the time
Before proceeding to the
an order is placed and the time it is executed.
formal
argument,
violence
to
pension
and
should
we
observed
funds)
absorption capacity,
do not
basis.
4
who
1987
Furthermore,
crash.
5
What
we
attempting
not
are
investors,
institutional
comprise
much
of
economy's
the
to
we
are
a
follows
not
aware
of
any
evidence
do
(e.g.,
risk
appear to make much use of limit orders on
suggests that limit orders played
October
that
Major
reality.
mutual
regular
emphasize
a
that
meaningful stabilizing role during the
is
rationalization of these observations.
meant
simply
to
be
a
theoretical
-
15
-
The tradeoff between market and limit orders is easiest to see in the
Recall equation (7), which gives the execution price
context of Model #1.
received by a trader placing a market order:
\n 7 d - s)
Market orders are risky because n 2 is uncertain- -traders do not know
at the time an order is placed how many other orders will be executed along
impounds
market orders
However,
with theirs.
time
the
innovation
news
2
also have
an advantage,
This
perfectly.
f2
that P 2
in
is
a
direct
consequence of the competition among market makers for these orders.
Limit orders face a different sort of risk.
submits
limit order to buy at a price P L
a
what the realization of n 2
his
a
at time
1,
too high
time
2
a
relative
to
time
However,
fundamentals.
2
A
Walrasian demand curve with limit orders,
because the limit orders are not conditional on time
fundamental news.
2
limit orders suffer from an adverse selection problem:
Consequently,
trader
he can be sure that no matter
he will not pay more than that price.
,
execution price mav be
trader cannot replicate
,
If,
a
buy
order is more likely to be executed at the limit price P L when bad news has
arrived between time
1
and time
2.
a limit buy order
Or said differently,
involves giving away a put option on fundamentals.
orders
Limit
fundamentals
is little
is
o\
are
low.
thus
attractive
when
the
variance
of
Conversely, market orders are preferred when there
uncertainty regarding the number of traders arriving at any given
time--i.e., when a^ is low.
Proposition
For
relatively
3
any
The appendix proves the following proposition:
:
PL
,
and
any
volume
shock
s,
there
exists
sufficiently large so that a limit buy order at price
expected profits.
PL
a
value
of
o\
yields negative
16
-
formalizes
proposition
The
unprofitable for large values of
-
notion
the
a\
so does the range of
As a\ increases,
.
become
orders
limit
that
prices for which rational traders will be unwilling to leave limit orders
on specialists'
books.
This logic may help explain the relative paucity
7
of limit orders in day-to-day trading.
It is more difficult to understand why limit orders should not play an
augmented role in a crash situation.
execution price
while
the
might
expect
However,
this
there
are
a
orders
risk associated with market
balance
the
in
reasons
number of
rises
effectively
also
tip
to
fundamental risk stays constant
If
during
to
like
times
using
of
favor
believe
that
seen
those
one
rises,
orders.
limit
risk
fundamental
October
in
1987.
Enough volume, even if it is known not to contain private information, can
such
about
questions
raise
fundamentals
as
the
adequacy of clearinghouse
Furthermore,
collateral and the stability of other financial institutions.
a
realistic
more
model
than
ours
might
allow
the
for
that
fact
market
participants do not know for sure that all the volume is informationless
Duffee
presents
(1989)
possibility
that
lot
a
such
of
wherein
model,
a
news
arrived.
has
large
In
signals
volume
Duffee'
s
model,
the
large
volume shocks are associated with increased uncertainty about fundamentals.
Finally,
it
should
noted
be
what
that
matters
for
fundamental risk over a given interval of time- -the
order
is
placed
information.
and
If,
as
when
was
can
be
removed,
or
case
in
October
1987,
it
the
limit
orders
is
time between when an
reconditioned
large
volume
on
new
causes
backups and delays throughout the system, this can increase the exposure of
those using limit orders.
Of course,
role
in
none of this
accommodating
large
is
meant to argue that limit orders play no
volume
shocks.
However,
the
arguments
presented above do suggest that limit orders alone may not easily solve all
the
problems
that are evident
in our models with
just market orders.
To
17
-
-
the extent that limit orders are used,
is quite possible
it
that they will
be used timidly, with limit buy orders placed at levels well below current
prices
V
.
Implications of the Models
The Crash of October 1987
A.
Taken together,
two models suggest a couple of reasons why large
the
volume shocks may tend to increase transactional risks and possibly result
in a "crash" of the normal transmission mechanism:
lead to more uncertainty about
Large volume shocks
1)
aggregate value buyer response at any
the
given point in time, so that even if market-maker behavior is unchanged, an
investor faces
order,
and
volume
Large
2)
market makers
risk with respect
more
smooth
to
shocks
can
also
This
prices.
fluctuate more with given variations
"
execution price of a given
the
to
make
more
it
order
for
effect makes prices
illiquidity"
in
dangerous
thereby exacerbating
flow,
the first problem.
models
The
appear
to
Tuesday October 19 and 20,
accord
closely with
1987.
In the
events
the
overall market decline of almost 23% for the day.
have
to
indeed,
indicated
an
attractive
many placed market
orders
at
and
last hour of trading on Monday,
heavy selling volume pushed prices down approximately 12%,
seem
of Monday
These price levels would
opportunity
the
resulting in an
end of
value
for
the
day.
buyers,
and
However,
the
execution price for most of these orders must have come as an unpleasant
surprise- -because
of
the
large
number
of
overnight
orders,
the
market
opened up on Tuesday some 12% above Monday's close.
The
returned
market
to
subsequently
about
the
same
reversals in perspective,
magnitude
to
the
previous
reversed direction,
level
as
Monday's
so
that
close.
by noon
(To
put
it
had
these
note that each 12% leg is roughly comparable in
record
one
day
fall
of
12.8%
on
October
28,
Throughout
1929.)
submitting orders
traders
morning,
Tuesday
virtually
contemporaneously received "fills" at vastly differing prices, both on the
exchanges
and with
magnitude
of
Monday's
drop,
it
is
and
reversals
the
impossible
seem
that
prices
transactions
Even more
over-the-counter stocks.
than
variability
the
with
reconcile
to
overall
the
a
in
Walrasian
model of adjustment to changing fundamentals.
began
investors
As
risks
tremendous
the
inherent
appeared
market
The
evaporated.
support
buying
transacting,
realize
to
in
be
to
in
danger of collapsing completely before many corporations announced buybacks
thereby setting themselves up
afternoon,
on Tuesday
last resort
"value buyers
as
of
.
In addition to the dramatic market-wide reversals,
a variety of other
evidence supports a view of the crash as at least partly non-Walrasian in
Blume
example,
For
nature.
MacKinlay
,
Terker
and
that
find
(1989)
on
Monday October 19, NYSE stocks in the S&P 500 index declined an average of
attribute
difference
this
than NYSE
more
points
percentage
seven
to
greater
stocks
not
the
in
the
index
Information"
Order
imbalances
sell-side
They
index.
for
stocks
B.
Circuit
of
Role
The
Breakers:
Timely vs.
of
implications
"Full
Execution
Our
First,
present
models
the
in
have
two
trading,
all
design
between
the
of
and
and
that
and prices.
everyday
an
costs
trading
benefits
argument is also made by Ho,
Schwartz (1990).
that
illustrate
models
inefficient allocations
the
sorts
of
some
level
this
Thus
for
of
market
risk
leads
is
to
important consideration in
environment
reducing
risk
transactional
transactional
one
architecture.
should
be
transactional
the
tradeoff
risk.
This
Schwartz and Whitcomb (1985) and Bronfman and
As these papers suggest,
there are a number of dimensions
19
-
-
One example
along which the tradeoff might take place.
which
trading
allowed
is
place
take
to
is
8
continuously.
the degree
Another
the
is
extent to which trading takes place in a spatially fragmented setting,
opposed
centralized
the
to
fragmentation/centralization issue
in
is
trading
as
The
here.
turn related
automated
should
degree
what
To
automation:
considered
one
to
questions about
to
systems
used
be
to
aggregate data across spatially separated markets, and to enable traders to
condition their orders on better information? 9
second important feature of our models
The
that
is
the magnitude
of
transactional risk can increase dramatically when the market is confronted
This
with abnormally large volume.
is
implies that a trading mechanism that
"optimal" under everyday circumstances may no longer be well-suited for
handling extremely
volumes.
large
system
A
market and limit orders may represent
a
essence,
something
it may make sense to switch to an
At such times,
purpose
transactional risk,
In
on a day-in,
"circuit breaker" trading mechanism.
basic
The
immediacy)
(e.g.,
but it can nonetheless involve too much transactional risk
when volume is very high.
alternative,
trading with
good balance between transactional
risk and other desirable characteristics
day-out basis,
continuous
of
the
in an effort
trading halt
closer
much
Thus
process occurs.
any
of
to
it
is
circuit
to
be
reduce
to
stimulate value buyer responsiveness.
designed as
should be
the
should
breaker
hypothetical
a
time
during which
full- information
Walrasian
inappropriate to think of circuit breakers as
"sand in the gears" that aims to slow down a fundamental price adjustment;
rather,
their
aim
is
to
patch
up
the
transmission
apparatus
so
that
Walrasian price adjustment can be facilitated.
According to Model #1, one goal of
a
circuit breaker system should be
to help make potential value buyers aware of the
to
large
shocks.
On the exchanges,
this
response of other traders
could be accomplished
>y
having
20
-
-
trading briefly and open their order books
specialists halt
for
general
inspection.
Model
further
#2
suggests
execution
sequential
that
trades
of
at
rapidly oscillating prices may not be the best way for the market to digest
is,
an open period during which orders
have
trades--that
It may instead be preferable to "pool"
a large volume shock.
could be
with a
submitted,
promise that all orders submitted during that period would be executed at
the same price
.
types
These
alternative
of
mechanisms
trading
wholly unknown to stock markets.
On the NYSE,
specialist can delay the
a
During
opening of his stock if he is faced with a large order imbalance.
the
trading halt,
may announce
he
attract additional buy or
sell
clearing prices
trial
In both cases,
periodic "batch" auctions to clear accumulated orders.
net
result
diminish
to
is
importance
the
in an effort
to
European stock markets use
Some
orders.
not
course,
of
are,
of
market
the
makers
the
as
a
transmission device, and to shift the emphasis to direct trade between end
buyers and sellers
contrast between these alternative mechanisms and the continuous
The
typically
trading
tradeoff:
Under
.
seen
between
that
execution
timely
circumstances,
normal
orders
market
uncontingent
equity markets
U.S.
in
the
a
fundamental
information
full
informational
execution.
due
loss
relatively
probably
is
and
illustrates
to
traders
small:
there
may
prices
prices
be
little
that
to
However,
mechanism.
problems
the
with
longer
provide
execution prices.
extreme
continuous
When this
from
gained
be
under
associated
no
prevail when their order
very
is
an
trading
case,
are
much
information
it
submitted.
alternative
circumstances,
accurate
the
using
is
the
can
simply by
anticipate with a good deal of precision their execution prices,
looking at
using
Thus
trading
informational
greater:
about
current
subsequent
may be worthwhile to accept
21
-
some
loss
timeliness
in
order
in
allow each
to
responses on the responses of others.
-
trader
condition his
to
10
A number of criticisms have been raised concerning circuit breakers.
traders enter the market voluntarily, so
One is the "free trade" objection:
how can shutting it down possibly make anybody better off?
Our emphasis on
the negative externalities present in a market crash provides an answer to
Even though rational agents will continue to trade in the
this question.
absence
of
circuit breaker,
a
Intervention that leads to
a
aggregate
the
outcome
inferior one.
an
is
broader distribution of the volume shock can
improve efficiency.
Another objection is that the very existence of circuit breakers might
somehow cause
large
declines
to
feed
According
themselves.
on
to
this
"gravitational", or "magnet" theory, if it is known that the market will be
shut
down after,
say,
selling pressure,
a
10%
investors
as
them in a temporarily
try
to
for
were
in
effects
and
effect,
find
no
futures
significant
lead
further
to
shutdown leaves
the
Empirically,
Kuserk et al
Treasury bond and commodity
can
fall
get out before
illiquid position.
not much support for this theory.
data
initial
an
drop,
however,
there
is
study transactions
(1989)
markets where price
evidence
limits
gravitational
of
n
Finally,
some
observers
have
suggested
that
than
rather
adopting
the exchanges should force market makers to dramatically
circuit breakers,
increase their capital positions. While this would have no direct effect on
it would
the magnitude of transactional risk,
by
reducing
shocks.
and
need
the
However,
Miller
(1988)
capital
to
capital
depends
to
quickly
presumably lessen its impact
value
mobilize
buyers
to
such an approach may be very inefficient.
point
out,
there
market -making activities,
(loosely speaking)
is
and
an
opportunity
the
on average
cost
absorb
As Grossman
to
devoting
appropriate
amount
demands
immediacy.
for
large
of
such
It
22
-
makes
no
sense
for
market
makers
-
aside
set
to
absorb the very largest volume shocks,
enough capital
if such capital
to
easily
unnecessary 99%
is
Circuit breakers have the advantage of only coming into play
of the time.
when there are extremely large shocks, without imposing any cost at other
times
The
Brady
report
advocated
installation
the
In May of 1988,
although it did not go into detail about their design.
Working
Treasury,
Group
the
on
Financial
Markets
Federal Reserve,
(composed
CFTC
the
of
and the
,
breakers,
circuit
of
officials
SEC)
from
the
the
also endorsed the
adoption of circuit breakers in their interim report to the President.
The
It recommends
Working Group report is more specific than the Brady Report.
coordinated, cross-market trading halts after Dow Jones declines of 250 and
Consistent with
400 points.
the
logic
outlined above,
bulk of
the
the
Working Group's discussion centers on procedures for active dissemination
Order imbalances for all major stocks
of information prior to reopening:
are
to
provided.
be
publicized.
Further
orders
Tentative
can
then
quote
be
indications
submitted,
indications will be made available as needed.
and
then
are
to
subsequent
(Appendix A,
page 2)
be
quote
The
Working Group's recommendations were subsequently adopted, and the circuit
breakers described above remain in place
also
recently
endorsed
Confidence Panel
(1990).
by
the
Like
NYSE's
the
today.
Market
12
Circuit breakers were
Volatility
Working Group report,
and
the
Investor
NYSE study
also emphasizes the importance of information dissemination during trading
halts
23
VI
.
Conclusions
continuous
trading
involving
market
and
limit
orders
sacrifices some degree of informational efficiency for timeliness.
Under
A
system
ordinary
of
circumstances,
the
informational
loss
is
small- -prices
evolve
gradually, and traders can thus predict with confidence the levels at which
their orders will be executed.
However, when volume shocks are large,
the
informational problem worsens and the deviation from Walrasian efficiency
When this occurs, it may make sense to temporarily switch to
is magnified.
an
alternative
orders
to
be
transactional
made
switch compromises
participants
contingent
the
mechanism- -a
on
a
larger
"circuit
breaker" - -that
information
set,
ability of the market to provide
even
allows
if
this
immediacy to all
-
2k
Appendix
Proof of Proposition
3:
The proposition is proven in the context of Model #1.
applies for Model /2.
Assuming that all other traders use market orders,
an individual trader faces a time
(A.l)
P
2
-
f
2
+
A similar argument
(n d
pricing function of:
s).
-
£
n
2
l
This is just equation (7) in the text.
Using the results of Proposition
1,
this can be rewritten as:
(A. 2)
P
=
2
f
2
+
on 2
-
0,
where a
a(s) and
shock
The expected return to
s.
fi
0(s) are both increasing functions
-
a
can be expressed as:
(A. 3)
R L = E(f 2
-
P
L
|P
L
> P
2
)
limit order at price
P,
of the volume
,
denoted by Rt,
That is,
P
L
—
?
2
a
limit buyer has his order executed at
^en
This ha PP ens
-
f
<
2
P
L +
-
on 2
.
P,
if and only if
Thu9 R can be written as
L
the following double integral:
»
P
+/9-an
L
R L = /[/(f
(A. U)
2
P
-
2
L
)h(f
2
)df
2
]g(n 2 )dn 2
.
-00*00
where
h(
and
)
respectively.
P
L
density
the
+£-an 2
R L - /[/f 2 h(f
The first term is
increased.
are
)
functions
of
and
£7
The
2
)df
oc
2
]g(n 2 )dn
2
-
P
P
L
+^-on 2
)df ]g(n )dn
L /[/h(f 2
2
2
2
and
decreases
second term is
the
limit price times the probability that
without
bound
as
second,
as
a\
is
Since this probability cannot exceed unity,
the second term must be smaller in absolute magnitude than P,.
2
.
negative
the order will be executed.
fixed P^,
n.
This integral can be broken into two parts:
*
(A. 4')
g(
Thus for a
•
a* is increased,
the first term will eventually dominate the
ensuring that R is negative.
L
This verifies the proposition.
-
26
1.
Limit orders are discussed in Section IV of the paper.
2.
Ho, Whitcomb and Schwartz (1985) and Bronfmen and Schwartz (1990), using
models quite different from the one presented here, also demonstrate that
transactional risk can affect traders' order placement decisions and lead
A key distinction between our work and these
to inefficient outcomes.
others is that we focus on the relationship between large volumes and
transactional risk, rather than simply on the existence of transactional
risk per se in everyday trading.
3.
Note that since all traders (including
efficient risk sharing involves m 2 = d*
4.
One piece of evidence concerning the relative unimportance of limit
A
orders comes from the brokerage commissions of NYSE specialists.
specialist acts as a broker when other traders leave limit orders in the
In 1986, specialists
specialist's book that are subsequently executed.
participated as commission earning brokers in only 12.7 percent of twice
See the Report
total NYSE volume (the sum of all purchases and sales.)
of the Presidential Task Force on Market Mechanisms (1988), (page VI-5).
5.
Given the large price declines that occurred in the last hour of trading
on Monday October 19, and the apparent consensus that much of these lasthour drops were due simply to an exhaustion of market-maker capital (as
opposed to news about fundamentals) one might have expected that a huge
thereby
flow of limit orders would have been submitted overnight,
In actuality, this
stabilizing prices at or above Monday closing levels.
The Task Force report notes that "the
does not appear to have occurred.
vast majority of orders to buy at the market's open were market
This observation is consistent with the price
orders..." (page III - 22
patterns seen on amany stocks. A typical example is provided by the NYSE
That stock fell 9%
stock denoted "number 11" in the report (page VI -38).
It recovered this entire loss at
in the last hour of trading on Monday.
However, there was
the open on Tuesday morning, opening up almost 11%.
not enough buying support at this level to sustain the price, and it fell
almost 24% by 11:30 a.m., to a point roughly 13% below Monday's close.
Evidently, there were not enough limit orders on the specialist's books
to stabilize the price anywher near Monday's close.
)
6.
market
makers)
are
identical,
.
This assumes that when the market price falls, outstanding limit buy
orders are executed at their limit prices, rather then at the more
Although this assumption is generally true,
favorable new market price.
NYSE Rule 127 provides some protection
there is an important exception.
for limit orders that are executed as part of a block transaction crossed
The Task Force Report describes the rule
on the floor of the exchange.
as follows (page VI-10):
The rule requires that unless (i) the trade is to be executed at a
price no more than one eighth below the bid or one eighth above the
offer, and (ii) both sides of the cross consist solely of public
customers, then the member with the block cannot execute part of it
by selling to or buying from the specialist's book at limit prices
For instance, if the stock price is
away from the cross price.
-
27
-
currently bid at 20 and the firm intends to cross a block of stock
at 19 : /2 and limit orders to buy are on the specialist's book at
19 7 /8, 19 3 /4 and 19 5 /8, the firm intending to cross the block cannot
execute part of the order by selling stock to the specialist's book
Thus, the person with a limit
at prices from 20 down to 19 5 /8
order on the book at or near the market cannot suffer an immediate
paper loss, as he would if his order was executed as part of a
series of transactions immediately preceding a cross occurring at a
The person with the order on the book
price away from the market.
will benefit by generally receiving an execution at the cross price.
.
7.
8.
Thus an immediate corollary of the proposition is that in a world where
value buyers use only limit orders, volume shocks can generate large
deviations from Walrasian prices, provided a\ is big enough.
Bronfman and Schwartz contrast the transactional risk properties of call
continuous markets.
vs.
9.
1
Maier,
these questions.
See Cohen,
Schwartz and Whitcomb (1986) for detailed treatment of
Because circuit breakers do involve some cost in terms of timeliness,
their use is justified only to the extent that the extra time really does
enable transactional risk to be reduced in a way that cannot be
Some observers have
accomplished in a continuous trading setting.
reacted to the events of October 1987 and October 1989 by suggesting
improvement that would make the continuous trading system work in a more
Miller's (1990) proposal for "contingent limit
Walrasian fashion.
To the extent that such
orders" can be thought of in this spirit.
proposals can be successful in reducing transactional risk without a halt
in trading, the case for circuit breakers is weakened.
11.
See however, McMillan (1990) who argues that a gravitational effect was
at work on the S&P 500 futures market prior to a trading halt during the
October 13, 1989 "minicrash"
12.
However,
These 250 and 400 point thresholds have not yet been reached.
there are other smaller "circuit breaker" type mechanisms in place that
More modest declines have lead to temporary
have come into play.
shutdowns of futures trading on the Chicago Mercantile Exchange, as well
as to the diversion of program trades in S&P stocks to "sidecar" files.
It is not clear that the latter technique meets any of the criteria for
an effective circuit breaker discussed above.
28
-
-
References
and
Terker,
MacKinlay,
Craig,
Marshall,
Imbalances and Stock Price Movements on October 19
Journal of Finance (September 1989), 827-848.
Bruce,
and 20,
Blume,
"Order
1987,"
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and Schwartz, Robert, "Order Placement and Price
Bronfman, Corinne
Discovery in a Securities Market", mimeo School of Business New York
University, 1990.
,
,
Cohen, Kalman, Maier Steven, Schwartz, Robert and Whitcomb, David, The
Microstructure of Securities Markets 1986 (Englewood Cliffs, New
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Duffee, Greg, "Market Liquidity and the Information Content of Order
Flows," mimeo, Harvard University, 1989.
Greenwald, Bruce and Stein, Jeremy, "The
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the
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Miller, Merton, "Index Arbitrage and Volatility," paper prepared for
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Presidential Task Force on Market Mechanisms: Report Submitted
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Rock,
Kevin,
Explanation
"The Role of the
for Certain Price
Specialist's Order
Anomalies," mimeo,
Book:
A
Harvard
Possible
Business
School, 1987.
Working
1988.
Group
on
Financial
Markets:
Interim
Report
Submitted May
Figure 1A
Value Buyer
Demand
as
a
Function
V» air asian case
Transactional risk case
of
Supply Shock
Figure IB
Prices as
a
Function of Supply Shock
W air a si an case
Transactional risk case
?96&
;70
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SEP
9 1991
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