1
Bu
bb
les
and
Cra
shes
�D
ilip
Abr
euP
rince
ton
Uni
vers
ity�
Mar
kus
K. B
runn
erm
eier
Prin
ceto
n U
nive
rsity
http
://w
ww
.pri
ncet
on.e
du/~
mar
kus
2
�C
ompa
ny X
intr
oduc
ed a
rev
olut
iona
ry w
irele
ssco
mm
unic
atio
n te
chno
logy
.�
It no
t onl
y pr
ovid
ed s
uppo
rt fo
r su
ch a
tech
nolo
gy b
ut a
lso
prov
ided
the
info
rmat
iona
l con
tent
itse
lf.�
It’s
IPO
pric
e w
as $
1.50
per
sha
re. S
ix y
ears
late
r it
was
trad
ed a
t $ 8
5.50
and
in th
e se
vent
h ye
ar it
hit
$ 11
4.00
.�
The
P/E
rat
io g
ot a
s hi
gh a
s 73
.�
The
com
pany
nev
er p
aid
divi
dend
s.
Sto
ry o
f a
typ
ical
tec
hn
olo
gy
sto
ck
3
Sto
ry o
f R
CA
-
192
0’s
�C
ompa
ny:
Rad
io C
orpo
ratio
n of
Am
eric
a (R
CA
)�
Tec
hnol
goy:
R
adio
�Y
ear:
1920
’s
�It
peak
ed a
t $ 3
97 in
Feb
. 192
9, d
own
to $
2.6
2 in
May
193
2,
050100
150
200
250
300
350
400
450
time
$ Dec
25
Dec
50
4
Inte
rnet
bu
bb
le?
-
19
90’s
NA
SDA
Q C
ombi
ned
Com
posi
te I
ndex
NE
MA
X A
ll S
hare
Ind
ex (
Ger
man
Neu
er M
arkt
)
38 d
ay a
vera
ge
Cha
rt (
Jan.
98
- D
ec. 0
0)
38 d
ay a
vera
ge
Cha
rt (
Jan.
98
- D
ec. 0
0) in
Eur
o
Los
s of
ca.
60
%fr
om h
igh
of $
5,1
32L
oss
of c
a. 8
5 %
85 %
from
hig
h of
Eur
o 8,
583
�A
re b
ub
ble
s re
curr
ent?
�W
hat
hap
pen
ed in
Mar
ch 2
000?
�F
urt
her
evi
den
ce o
f b
ub
ble
�cr
ash
was
not
acc
ompa
nied
by
fund
amen
tal n
ews.
�ex
cess
vol
atili
ty
5
Do
(ra
tio
nal
) p
rofe
ssio
nal
rid
e th
e b
ub
ble
?
�S
outh
Sea
Bub
ble
(171
0 -
1720
)�
Isaa
c N
ewto
n�
04/2
0/17
20 s
old
shar
es a
t £7,
000
prof
iting
£3,
500
�re
-ent
ered
the
mar
ket l
ater
- e
nded
up
losi
ng £
20,0
00�
“I c
an c
alcu
late
the
mot
ions
of t
he h
eave
nly
bodi
es, b
utno
t the
mad
ness
of p
eopl
e”
�In
tern
et B
ubbl
e (1
992
- 20
00)
�D
ruck
enm
iller
of S
oros
’ Qua
ntum
Fun
d di
dn’t
thin
kth
at th
e pa
rty
wou
ld e
nd s
o qu
ickl
y.�
“We
thou
ght i
t was
the
eigh
th in
ning
, and
it w
as th
e ni
nth”
�Ju
lian
Rob
erts
on o
f Tig
er F
und
refu
sed
to in
vest
inin
tern
et s
tock
s
6
�“T
he m
oral
of t
his
stor
y is
that
irra
tiona
l mar
ket
can
kill
you
…�
Julia
n sa
id ‘T
his
is ir
ratio
nal a
nd I
won
’t pl
ay’ a
ndth
ey c
arrie
d hi
m o
ut fe
et fi
rst.
�D
ruck
enm
iller
sai
d ‘T
his
is ir
ratio
nal a
nd I
will
pla
y’an
d th
ey c
arrie
d hi
m o
ut fe
et fi
rst.”
Quo
te o
f a fi
nanc
ial a
naly
st, N
ew Y
ork
Tim
es
A
pril,
29
200
0
Pro
s’ d
ilem
ma
7
Cla
ssic
al Q
ues
tio
n
��S
uppo
se b
ehav
iora
l tra
ding
lead
s to
S
uppo
se b
ehav
iora
l tra
ding
lead
s to
mis
pric
ing
mis
pric
ing
..
�C
an m
isp
rici
ng
s o
r b
ub
ble
s p
ersi
st in
th
ep
rese
nce
of
rati
on
al a
rbit
rag
eurs
?
�W
hat t
ype
of in
form
atio
n ca
n le
ad to
the
burs
ting
of b
ubbl
es?
8
Mai
n L
iter
atu
re
�K
eyne
s (1
936)
��
bu
bble
can
em
erge
bubb
le c
an e
mer
ge�
“It m
ight
hav
e be
en s
uppo
sed
that
com
petit
ion
betw
een
expe
rt p
rofe
ssio
nals
,po
sses
sing
judg
men
t and
kno
wle
dge
beyo
nd th
at o
f the
ave
rage
priv
ate
inve
stor
, wou
ld c
orre
ct th
e va
garie
s of
the
igno
rant
indi
vidu
al le
ft to
him
self.
”
�F
riedm
an (
1953
), F
ama
(196
5)E
ffici
ent M
arke
t Hyp
othe
sis ��
no
bub
bles
em
erge
no b
ubbl
es e
mer
ge�
“If t
here
are
man
y so
phis
ticat
ed tr
ader
s in
the
mar
ket,
they
may
cau
se th
ese
“bub
bles
” to
bur
st b
efor
e th
ey r
eally
get
und
er w
ay.”
�Li
mits
to A
rbitr
age
�ar
bitr
ageu
rs a
re m
yopi
c/sh
ort-
lived
and
ris
k av
erse
(DeL
ong
et a
l. [D
SS
W],
1990
a)�
fund
man
ager
s (a
rbitr
ageu
rs)
face
liqu
idat
ion
risk
due
to p
rinci
pal-a
gent
pro
blem
(S
hlei
fer
& V
ishn
y, 1
997)
�ar
bitr
ageu
rs e
xplo
it de
laye
d re
actio
n of
feed
back
trad
ers
(DeL
ong
et a
l. [D
SS
W],
1990
b)
9
Mar
ket
tim
ing
& S
ynch
ron
izat
ion
�M
arke
t tim
ing
❶rid
e th
e bu
bble
as lo
ng a
s po
ssib
le(c
onfli
ctin
g in
tere
st)
�se
ll rig
ht b
efor
e ot
hers
�S
ynch
roni
zatio
n pr
oble
m�
bubb
le o
nly
burs
ts if
mor
eth
an �
arb
itrag
eurs
atta
ck(c
omm
on a
ctio
n)�
arbi
trag
eurs
bec
ome
sequ
entia
lly a
war
e of
the
mis
pric
ing
Lac
k of
syn
chro
niza
tion
�“d
elay
ed a
rbitr
age”
�
Bub
ble
pers
ists
-ø-ø
CO
NF
LIC
TC
ON
FL
ICT÷-
÷-
10
mo
del
set
up
intr
oduc
tion
pers
iste
nce
of b
ub
ble
s
endo
geno
us c
rash
es
publ
ic e
vent
s
conc
lusi
on
11
Mo
del
set
up
tt 0
t 0+ q
t 0 +
qk
rand
omst
artin
g po
int
t 0+ t
max
imum
life
-spa
n of
the
bubb
le t
k t
rade
rs
are
awar
e of
th
e bu
bble
all t
rade
rs
are
awar
e of
th
e bu
bble
bubb
le b
urst
sfo
r ex
ogen
ous
reas
ons
0
par
adig
m s
hif
t-
inte
rnet
90’
s-
railw
ays
- et
c.
�co
mm
on a
ctio
n of
� a
rbitr
ageu
rs
�se
quen
tial a
war
enes
s(r
ando
m t 0
with
F(t
0) =
1 -
exp
{-�t
0}).
1
1/q
12
Pay
off
str
uct
ure
�C
ash
Pay
offs
(di
ffere
nce)
�S
ell ‘
one
shar
e’ a
t t-�
inst
ead
of a
t t.
p t-�
e r�
- p
t
w
here
pt =
�E
xecu
tion
pric
e at
the
time
of b
urst
ing.
e g
t p
pr
ior
to th
e cr
ash
(1-�
)e g
t p
aft
er th
e cr
ash
for
fir
st r
ando
m o
rder
s up
to �
all
othe
r or
ders
13
Pay
off
str
uct
ure
(ct
d.)
, Tra
din
g
�R
eput
atio
nal p
enal
ty c
p tfo
r at
tack
ing
if bu
bble
doe
s no
t bur
st�
rela
tive
perf
orm
ance
eva
luat
ion
�dr
aw d
owns
�R
isk-
neut
ralit
y bu
t max
/min
sto
ck p
ositi
on�
max
long
pos
ition
� =
0
�m
ax s
hort
pos
ition
� =
1
�du
e to
cap
ital c
onst
rain
ts, m
argi
n re
quire
men
ts e
tc.
�D
efin
itio
n 1
: t
rad
ing
eq
uili
bri
um
�P
erfe
ct B
ayes
ian
Nas
h E
quili
briu
m�
Bel
ief r
estr
ictio
n: tr
ader
who
atta
cks
at ti
me
t bel
ieve
s th
atal
l tra
ders
who
bec
ame
awar
e of
the
bubb
le p
rior
to h
eral
so a
ttack
at t
.
Def
init
ion
1:
14
per
sist
ence
of
bu
bb
les
mod
el s
etup
endo
geno
us c
rash
es
publ
ic e
vent
s
conc
lusi
on
intr
oduc
tion
arbi
trag
eurs
nev
er b
urst
bub
ble
grap
hica
l illu
stra
tion
proo
f for
sym
met
ric s
trat
egie
s
lack
of c
omm
on k
now
ledg
e
15
Per
sist
ence
of
Bu
bb
les
�P
rop
osi
tio
n 1
: S
uppo
se
.
�ex
iste
nce
of a
uni
que
trad
ing
equi
libriu
m
�tr
ader
s be
gin
atta
ckin
g af
ter
a de
lay
of�*
<�
perio
ds.
�bu
bble
nev
er b
urst
s du
e to
end
ogen
ous
selli
ngpr
essu
re. I
t onl
y bu
rsts
at t
0+ �
.
.
Pro
po
siti
on
1:
16
Att
ack
con
dit
ion
for �
perio
ds
�at
tack
at t
�if
prob
that
bub
ble
will
bur
st in
nex
t ins
tant
> 0
�if
prob
that
bub
ble
will
bur
st in
nex
t ins
tant
= 0
appr
ecia
tion
rate
repu
tatio
nal p
enal
tybe
nefit
of a
ttack
ing
cost
of a
ttack
ing
RH
S c
onve
rges
to �
[(g
-r)
+ c
] as
t �
17
Seq
uen
tial
aw
aren
ess
tt t
trad
er t i
trad
er t i
’’
trad
er t i
’
t i - �
sinc
e t i
t 0 +
�Dis
trib
utio
n of
t 0D
istr
ibut
ion
of t 0
+�
(bur
stin
g of
bub
ble
if no
body
atta
cks)
t 0t 0
+�
sinc
e t i �
t 0
t i
t i’
t i’’
t i’ - �
18
Co
nje
ctu
re 1
: Im
med
iate
att
ack
t
� B
ub
ble
bu
rsts
at
t 0 +
��
whe
n �
trad
ers
are
awar
e of
the
bubb
le
t it i
- �
t i - ��
l/(
1-e-l
sk)
If t 0
< t i
- ��
, the
bub
ble
wou
ld h
ave
burs
t alre
ady.
Dis
trib
utio
n of
t0
Dis
trib
utio
n of
t0
+ ��
t i + ��
19
Co
nj.
1 (c
td.)
: Im
med
iate
att
ack
t
� B
ub
ble
bu
rsts
at
t 0 +
��
Dis
trib
utio
n of
t0
+ ��
Bub
ble
burs
ts
for
sure
!
haza
rd r
ate
of th
e bu
bble
h =
�/(
1-ex
p{-�
(ti +
��
- t)
})
l/(
1-e-l
qk)
t i - �
t i - ��
t i + ��
t i
Dis
trib
utio
n of
t0
20
Co
nj.
1 (c
td.)
: Im
med
iate
att
ack
t
� B
ub
ble
bu
rsts
at
t 0 +
��
Bub
ble
burs
ts
for
sure
!
haza
rd r
ate
of th
e bu
bble
h =
�/(
1-ex
p{-�
(ti +
��
- t)
})
l/(
1-e-l
qk)
t i - �
t i - ��
t i + ��
t i
Dis
trib
utio
n of
t0
bubb
le a
ppre
ciat
ion
/ bub
ble
size
low
er b
ound
: (g-
r) +
c >
�/(
1-e-
lqk)
optim
al ti
me
to a
ttack
t i+� i
�� “
del
ayed
att
ack
is o
pti
mal
” “
del
ayed
att
ack
is o
pti
mal
”n
o “
imm
edia
te a
ttac
k” e
qu
ilib
riu
m!
no
“im
med
iate
att
ack”
eq
uili
bri
um
!
Rec
all t
he a
ttack
con
ditio
n:
21 t
haza
rd r
ate
of th
e bu
bble
h =
�/(
1-ex
p{-�
(ti +
��
+ �’
- t)
})
t i - �
t i
Co
nj.
2: D
elay
ed a
ttac
k b
y ar
bit
rary
�’
� B
ub
ble
bu
rsts
at
t 0 +
��
+ �’
< t
0 +
�
t i - �
+ ��
+�’
t i + ��
+�’
t i +�
’
optim
al to
del
ay
atta
ck e
ven
mo
reev
en m
ore
conj
ectu
red
atta
ck
�� a
ttac
k is
nev
er s
ucc
essf
ul
att
ack
is n
ever
su
cces
sfu
l��
bu
bb
le b
urs
ts f
or
exo
gen
ou
s re
aso
ns
at
bu
bb
le b
urs
ts f
or
exo
gen
ou
s re
aso
ns
at t
0 +
�
low
er b
ound
: (g-
r) +
c >
�/(
1-e-
lqk)
bubb
le a
ppre
ciat
ion
bubb
le s
ize
l/(
1-e-l
qk)
22
Fo
rmal
an
alys
is f
or
sym
met
ric
stra
teg
ies
�S
uppo
se e
ndog
enou
s se
lling
pre
ssur
e w
ould
bur
st b
ubbl
eat
, w
here
�fo
r�
for
�(f
rom
atta
ck c
ondi
tion)
sel
l sha
res
at
�m
ass
of a
rbitr
ageu
rs a
war
e of
the
bubb
le is
�m
ass
of a
rbitr
ageu
rs a
ttack
ing
(= s
ellin
g pr
essu
re)
� �fo
r�
cont
radi
ctio
n!
23
Ap
ril 1
3th
- P
re-e
mp
tio
n L
emm
a
�
mig
ht d
epen
d on
t 0 in
asy
mm
etric
equ
ilibr
ia
�E
xam
ple:
all
star
t atta
ckin
g on
Frid
ay, A
pril
13th
.
�bu
bble
wou
ld b
urst
with
str
ictly
pos
itive
pro
babi
lity.
�se
lling
pre
ssur
e s t
=13
> �
, pt=
13 d
rops
alre
ady.
�In
divi
dual
ince
ntiv
e to
atta
ck a
littl
e bi
t ear
lier.
�N
ot a
n eq
uilib
rium
!
24
Lac
k o
f co
mm
on
kn
ow
led
ge
t 0t 0
+ ��
�� s
tan
dar
d b
ackw
ard
s in
du
ctio
n c
an’t
be
app
lied
sta
nd
ard
bac
kwar
ds
ind
uct
ion
can
’t b
e ap
plie
d
t 0 +
�
ever
ybod
y kn
ows
of th
e th
e bu
bble
k t
rade
rs
know
of
the
bubb
le
ever
ybod
y kn
ows
that
ever
ybod
y kn
ows
of th
ebu
bble
t 0 +
2�
t 0 +
3�
ever
ybod
y kn
ows
that
ever
ybod
y kn
ows
that
ever
ybod
y kn
ows
of
the
bubb
le
(sam
e re
ason
ing
appl
ies
for �
trad
ers)…
…
25
Rel
ated
th
eore
tica
l lit
erat
ure
�A
sync
hron
ized
clo
cks
�H
alpe
rn &
Mos
es (
1984
) [c
ompu
ter
scie
nce]
�M
orris
(19
95)
�re
stric
ted
stra
tegy
spa
ce: c
ondi
tion
only
on
own
cloc
kno
con
ditio
ning
on
cale
ndar
tim
e, p
ast p
ayof
fs, e
tc.
�G
loba
l Gam
es(u
niqu
enes
s of
equ
ilibr
ium
in s
tatic
gam
es w
ith s
trat
egic
com
plem
enta
ritie
s)
�C
arls
on &
van
Dam
me
(199
4)�
Mor
ris &
Shi
n (1
998)
26
end
og
eno
us
cras
hes
mod
el s
etup
pers
iste
nce
of b
ub
ble
s
intr
oduc
tion
publ
ic e
vent
s
conc
lusi
on
endo
geno
us li
fe-s
pan
of th
e bu
bble
com
para
tive
stat
ics
27
En
do
gen
ou
s cr
ash
es
�P
rop
osi
tio
n 3
: S
uppo
se
.
�‘m
ost
ag
gre
ssiv
e’ tr
adin
g eq
uilib
rium
.
�tr
ader
s be
gin
atta
ckin
g af
ter
a de
lay
of �
** p
erio
ds.
�bu
bble
bu
rsts
due
to e
ndog
enou
s se
lling
pre
ssur
eat
Pro
po
siti
on
3:
28
En
do
gen
ou
s cr
ash
es
t
haza
rd r
ate
of th
e bu
bble
h =
�/(
1-ex
p{-�
(ti +
��
+ �’
- t)
})
t i - �
t i - ��
t i
low
er b
ound
: (g-
r) +
c >
�/(
1-e-
lqk)
� B
ub
ble
bu
rsts
at
t 0 +
��
+ �*
*
t i - �
+ ��
+�*
*t i
+ ��
+�*
*t i
+�**
optim
al
conj
ectu
red
atta
ck
bubb
le a
ppre
ciat
ion
bubb
le s
ize
29
En
do
gen
ou
s cr
ash
es -
der
ivin
g �
**
�
�In
sym
met
ric e
quili
briu
m tr
ader
t i =
t 0 +
��
burs
ts th
e bu
bble
.�
Whe
n he
sel
ls h
is s
hare
s hi
s su
ppor
t of t
0 is
[ti- ��
, ti],
henc
e hi
s ha
zard
rat
e is
h =
�/(
1-ex
p{-���
})
(
1)�
The
bub
ble
burs
ts a
t ti =
t 0 +
��
+ �
**,
henc
e it
burs
ts a
t a s
ize
of e
gt(1
-exp
{-(g
-r)(��
+ �
**)}
)bu
bble
app
reci
atio
n/ s
ize
= (
g-r+
c) /
(1-e
xp{-
(g-r
)(��
+ �
**)}
) (
2)
equi
libriu
m
h(1
)
bubb
le a
ppre
ciat
ion
bubb
le s
ize
(2)
�**
30
Co
mp
arat
ive
stat
ics
�R
ole
of in
form
atio
n di
sper
sion
�, �
�P
rior
dist
ribut
ion
of t 0
F
(t0)
= 1
- e
xp{-�t
0}
�th
e sm
alle
r �,
the
larg
er th
e lif
e sp
an o
f bub
ble
��
� �
t 0 =
0, n
o in
fo d
ispe
rsio
n �
no
bubb
le��
0 �
dis
trib
utio
ns
uni
form
[life
span
- ln
{1-��(
g-r+
c)}/
(g-r
) ]
�D
ispe
rsio
n of
opi
nion
���
as �
�
� b
ubbl
e’s
life-
span
��
for
�
exo
geno
us c
rash
�R
ole
of m
omen
tum
trad
ers � �
sam
e as
for �
�ex
cess
gro
wth
rat
e (g
- r
) �
[2 e
ffect
s]
�in
stan
tane
ous
appr
ecia
tion
effe
ct �
� li
fe s
pan
of b
ubbl
e �
�si
ze o
f bub
ble
(pas
t app
reci
atio
n) �
� li
fe s
pan
of b
ubbl
e �
31
mod
el s
etup
endo
geno
us c
rash
es
pers
iste
nce
of b
ub
ble
s
conc
lusi
on
intr
oduc
tion
syn
chro
niz
ing
pu
blic
eve
nts
pre-
sche
dule
d ve
rsus
una
ntic
ipat
ed
pric
e ca
scad
es a
nd r
ebou
nds
32
Pre
-sch
edu
led
vs.
un
anti
cip
ated
pu
blic
new
s
�P
re-s
ched
uled
pub
lic e
vent
s�
new
s is
unk
now
n, b
ut ti
min
g is
fixe
d in
adv
ance
.(F
OM
C M
eetin
gs e
tc.)
�“m
artin
gale
new
s”: c
orre
ctly
ref
lect
ed in
the
pric
e��
pre
-sch
edul
ed n
ews
will
onl
y m
ove
pric
e by
its
fund
amen
tal c
onte
nt, b
ut n
ot b
eyon
d.�
Why
? It
cann
ot s
erve
as
a sy
nchr
oniz
atio
n de
vice
.�
If it
wou
ld, t
hen
the
bubb
le w
ould
bur
st w
ith s
tric
tlypo
sitiv
e pr
obab
ility
on
this
dat
e. In
this
cas
e ar
bitr
ageu
rsha
ve in
cent
ive
to a
ttack
slig
htly
ear
lier
(sam
e as
Frid
ay 1
3th
of J
uly)
33
Pre
-sch
edu
led
vs.
un
anti
cip
ated
pu
blic
new
s
�U
nant
icip
ated
pub
lic e
vent
s�
pre-
empt
ion
argu
men
t doe
s no
t app
ly!
�ca
n se
rve
as s
ynch
roni
zatio
n de
vice
.�
ther
e ar
e m
illio
ns o
f pub
lic e
vent
s (w
eath
er, e
tc.)
�vi
ewin
g so
met
hing
as
a pu
blic
eve
nt is
als
o a
coor
dina
tion
prob
lem
in it
self.
�E
xten
ded
setti
ng�
focu
s on
new
s w
ith n
o in
form
atio
nal c
onte
nt (
suns
pots
).�
publ
ic e
vent
occ
urs
with
Poi
sson
den
sity
�p
.�
Arb
itrag
eurs
who
are
aw
are
of th
e bu
bble
bec
ome
incr
easi
ngly
wor
ried
abou
t it o
ver
time.
»on
ly tr
ader
s w
ho b
ecam
e aw
are
of th
e m
ispr
icin
g m
ore
than
�p
perio
ds a
go o
bser
ve (
look
out
for)
pub
lic e
vent
s.
34
Pu
blic
eve
nts
& M
arke
t re
bo
un
ds
�P
rop
osi
tio
n 5
:A
ttac
k a
) al
way
s at
the
time
of a
pub
lic e
vent
t p,
b)
afte
r t i
+ �
***
(w
here
�**
*< �
**) ,
ex
cep
t af
ter
a fa
iled
atta
ck a
t tp
, re-
ente
r th
e m
arke
t
for
t �
(t p
, t p
- �
p +
�**
*) �
(t i
+ �
p,1 )
.
�In
tuiti
on fo
r re
-ent
erin
g th
e m
arke
t:�
for
t p <
t 0 +
��
+ �
p at
tack
fails
, age
nts
lear
n t 0
> t p
- �
p - ��
�w
ithou
t pub
lic e
vent
, the
y w
ould
hav
e le
arnt
this
only
at t
p +
�p
- �*
** .
�th
e ex
iste
nce
of b
ubbl
e at
t re
veal
s th
at t 0
> t
- �*
** -
��
�th
at is
, no
addi
tiona
l inf
orm
atio
n is
rev
eale
d til
l tp
- � p
+ �
***
�de
nsity
that
bub
ble
burs
ts fo
r en
doge
nous
rea
sons
is z
ero.
Pro
po
siti
on
5:
35
Ro
le o
f in
form
atio
n
�O
nly
unan
ticip
ated
pub
lic n
ews
can
burs
t a
bubb
le.
�N
ews
whi
ch is
con
side
red
as im
port
ant c
an b
e
mor
e im
port
ant t
han
real
fund
amen
tal n
ews.
�F
ads
and
fash
ions
in in
form
atio
n.
36
Pri
ce c
asca
des
an
d r
ebo
un
ds
�P
rice
drop
as
a sy
nchr
oniz
atio
n de
vice
(pub
lic e
vent
).�
thro
ugh
psyc
holo
gica
l res
ista
nce
line
�by
mor
e th
an, s
ay 5
%
�E
xog
eno
us
pri
ce d
rop
�af
ter
a pr
ice
drop
�if
bubb
le is
rip
e �
bub
ble
burs
ts a
nd p
rice
drop
s fu
rthe
r.�
if bu
bble
is n
ot r
ipe
yet
� p
rice
boun
ces
back
and
the
bubb
le is
s
tren
gthe
ned
for
som
e tim
e.
37
Pri
ce c
asca
des
an
d r
ebo
un
ds
(ctd
.)
�P
rop
osi
tio
n 6
:A
ttac
k a
) af
ter
a pr
ice
drop
if �
i � �
’ p
b
) af
ter
t i +
�**
**
(whe
re �
****
< �
**) ,
re
-en
ter
the
mar
ket a
fter
a re
boun
d at
t’p
fo
r t
� (
t’ p ,
t’ p -
�’ p
+ �
****
) �
(t i
+ �
’p,1
).
�at
tack
is c
ostly
, sin
ce p
rice
mig
ht ju
mp
back
� o
nly
arbi
trag
eurs
who
bec
ame
awar
e of
the
bubb
le
mor
e th
an �
’ p p
erio
ds a
go a
ttack
the
bubb
le.
�af
ter
a re
boun
d, a
n en
doge
nous
cra
sh c
an b
ete
mpo
raril
y ru
led
out a
ndhe
nce,
arb
itrag
eurs
re-
ente
r th
e m
arke
t.
Pro
po
siti
on
6:
38
Co
ncl
usi
on
�B
ubbl
es�
Dis
pers
ion
of o
pini
on a
mon
g ar
bitr
ageu
rs c
ause
s a
sync
hron
izat
ion
prob
lem
whi
ch m
akes
coo
rdin
ated
pric
e co
rrec
tions
diff
icul
t.�
Arb
itrag
eurs
tim
e th
e m
arke
t and
rid
e th
e bu
bble
.��
Bub
bles
per
sist
�C
rash
es�
can
be tr
igge
red
by u
nant
icip
ated
new
s w
ithou
t any
fund
amen
tal c
onte
nt, s
ince
�it
mig
ht s
erve
as
a sy
nchr
oniz
atio
n de
vice
.
�R
ebou
nd�
can
occu
r af
ter
a fa
iled
atta
ck, w
hich
tem
pora
rily
stre
ngth
ens
the
bubb
le.