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

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://w

ww

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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

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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

mis

pric

ing.

Sup

pose

beh

avio

ral t

radi

ng le

ads

to m

ispr

icin

g.

�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

Tim

ing

Gam

e -

Syn

chro

niz

atio

n

�(W

hen)

will

beh

avio

ral t

rade

rs b

eov

erw

helm

ed b

y ra

tiona

l arb

itrag

eurs

?�

Col

lect

ive

selli

ng p

ress

ure

of a

rbitr

ageu

rsm

ore

than

suf

fices

to b

urst

the

bubb

le.

�R

atio

nal a

rbitr

ageu

rs u

nder

stan

d th

at a

nev

entu

al c

olla

pse

is in

evita

ble.

But

whe

n?�

Del

icat

e, d

iffic

ult,

dang

erou

s T

IMIN

G G

AM

E!

10

Ele

men

ts o

f th

e T

imin

g G

ame

�C

oord

inat

ion

at le

ast �

> 0

arb

s ha

ve to

be

‘out

of t

he m

arke

t’

�C

ompe

titio

n on

ly fi

rst �

< 1

arb

s re

ceiv

e pr

e-cr

ash

pric

e.

�P

rofit

able

rid

erid

e bu

bble

(st

ay in

the

mar

ket)

as

long

as

poss

ible

.

�S

eque

ntia

l Aw

aren

ess

arbs

und

erst

and

that

for

a va

riety

of r

easo

ns (

disp

ersi

on o

f‘v

iew

poin

ts’,

risk

expo

sure

, etc

.) th

ey w

ill in

divi

dual

ly c

ome

up w

ith d

iffer

ent s

olut

ions

whe

n to

exi

t the

mar

ket.

A

Syn

chro

niza

tion

Pro

blem

aris

es!

�A

bsen

t of s

eque

ntia

l aw

aren

ess

com

petit

ive

elem

ent d

omin

ates

� a

nd b

ubbl

e bu

rst i

mm

edia

tely

.

�W

ith s

eque

ntia

l aw

aren

ess

ince

ntiv

e to

TIM

E T

HE

MA

RK

ET

lead

s to

� “

dela

yed

arbi

trag

e” a

nd

per

sist

ence

of b

ubbl

e.

11

mo

del

set

up

intr

oduc

tion

prel

imin

ary

anal

ysis

pers

iste

nce

of b

ub

ble

s

publ

ic e

vent

s

conc

lusi

on

pric

e ca

scad

es a

nd r

ebou

nds

12

Mo

del

set

up

tt 0

t 0+ h

t 0 +

hk

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/h

pt

13

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.

prio

r to

the

cras

h

afte

r th

e cr

ash

for

fir

st r

ando

m o

rder

s up

to �

all

othe

r or

ders

14

Pay

off

str

uct

ure

(ct

d.)

, Tra

din

g�

Rep

utat

iona

l pen

alty

zp t

for

atta

ckin

g if

bubb

le d

oes

not b

urst

�re

lativ

e pe

rfor

man

ce e

valu

atio

n�

draw

dow

ns

�S

mal

l tra

nsac

tions

cos

ts c

ert

�R

isk-

neut

ralit

y bu

t max

/min

sto

ck p

ositi

on�

max

long

pos

ition

�m

ax s

hort

pos

ition

�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:

15

intr

oduc

tion

pers

iste

nce

of b

ub

ble

s

publ

ic e

vent

s

conc

lusi

on

pric

e ca

scad

es a

nd r

ebou

nds

mod

el s

etup

Pre

limin

ary

anal

ysis

pree

mpt

ion

mot

ive

- tr

igge

r st

rate

gies

sell

out c

ondi

tion

16

Tri

gg

er S

trat

egie

s�

Bur

stin

g da

te T

*(t 0

)=m

in{T

(t0

+ ��)

, t0

+

}

�R

ole

of P

reem

ptio

n M

otiv

e�

Rul

es o

ut c

oord

inat

ed s

ell o

ut o

n F

riday

Jul

y 13

th.

�B

ubbl

e ne

ver

burs

ts w

ith s

tric

tly p

ositi

ve p

rob.

at s

ome

t13 .

�S

uppo

se it

wou

ld, t

hen

selli

ng p

ress

ure

wou

ld e

xcee

d �

with

pro

b>0.

�H

ence

, pric

e w

ould

dro

p al

read

y at

t13 �

inc

entiv

e to

sel

l out

ear

lier

�w

ell d

efin

ed d

ensi

ty o

f bur

stin

g da

te �

(t|t i

) fo

r ea

ch a

rb.

�P

ropo

sitio

n 1:

T

rigge

r st

rate

gies

.�

Giv

en c

> 0

, arb

t i n

ever

sel

ls o

ut o

nly

for

an in

stan

t.H

e st

ays

out o

f the

mar

ket a

t lea

st u

ntil

t i +

� s

ells

out

.�

Arb

t i +

� s

tays

out

unt

il t i

+ 2�

exits

and

so

on.

�B

y tr

adin

g eq

uilib

rium

, arb

t i s

tays

out

unt

il t i

+ ��

exits

.

Pro

po

siti

on

1:

17

Sel

l ou

t co

nd

itio

n fo

r ��

perio

ds

�se

ll ou

t at t

if

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)

+ z

] as

t �

18

intr

oduc

tion

prel

imin

ary

anal

ysis

publ

ic e

vent

s

conc

lusi

on

pric

e ca

scad

es a

nd r

ebou

nds

mod

el s

etup

per

sist

ence

of

bu

bb

les

exog

enou

s cr

ashe

s

endo

geno

us c

rash

es

lack

of c

omm

on k

now

ledg

e

19

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

doe

s n

ot

burs

t due

to e

ndog

enou

s se

lling

prio

r to

.

Pro

po

siti

on

2:

20

Seq

uen

tial

aw

aren

ess

tt t

trad

er t i

trad

er t k

trad

er t j

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 j

t k

t j - �

21

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

hk )

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 + ��

22

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

hk )

t i - �

t i - ��

t i + ��

t i

Dis

trib

utio

n of

t0

23

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

hk )

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)

+ z

]/� >

�/(

1-e-

lhk )

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 s

ell o

ut c

ondi

tion:

24 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)

+ z

]/�

> �/

(1-e

-lhk )

bubb

le a

ppre

ciat

ion

bubb

le s

ize

l/(

1-e-l

hk )

25

En

do

gen

ou

s cr

ash

es

�P

rop

osi

tio

n 3

: S

uppo

se

.

�‘u

niq

ue’

trad

ing

equi

libriu

m.

�tr

ader

s be

gin

atta

ckin

g af

ter

a de

lay

of �

* pe

riods

.�

bubb

le b

urs

ts d

ue to

end

ogen

ous

selli

ng p

ress

ure

at a

siz

e of

pt t

imes

Pro

po

siti

on

3:

26

En

do

gen

ou

s cr

ash

es -

der

ivin

g �

*

�

�In

equ

ilibr

ium

trad

er t i

= t 0

+ ��

burs

ts th

e bu

bble

.�

Whe

n sh

e se

lls h

is s

hare

s he

r su

ppor

t of t

0 is

[ti -

��,

t i],

henc

e hi

s ha

zard

rat

e is

h =

�/(

1-ex

p{-���

})(1

)�

The

bub

ble

burs

ts a

t ti =

t 0 +

��

+ �

*,he

nce

it bu

rsts

at a

siz

e of

egt

�*(�*

)bu

bble

app

reci

atio

n/ s

ize

=

(g-r

+z)

/ �*

(�*)

(2

)

equi

libriu

m

h(1

)

bubb

le a

ppre

ciat

ion

bubb

le s

ize

(2)

�*

27

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 si

ze 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

[s

ize

is ��(

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 �

28

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)…

…

29

Rel

ated

th

eore

tica

l lit

erat

ure

�A

sync

hron

ized

clo

cks

�H

alpe

rn &

Mos

es (

1984

) [co

mpu

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.

�no

com

petit

ive

elem

ent (�

= 1

- ca

se o

nly)

�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)

�O

ther

tim

ing

gam

es�

war

of a

ttriti

on -

pre

empt

ion

gam

es (p

rivat

e va

lues

)

�he

rdin

g m

odel

s w

ith e

ndog

enou

s se

quen

cing

(obs

erva

ble

actio

ns)

30

intr

oduc

tion

prel

imin

ary

anal

ysis

pers

iste

nce

of b

ub

ble

s

conc

lusi

on

pric

e ca

scad

es a

nd r

ebou

nds

syn

chro

niz

ing

pu

blic

eve

nts

pre-

sche

dule

d ne

ws

unan

ticip

ated

pub

lic e

vent

s

mod

el s

etup

31

Pre

-sch

edu

led

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

.(m

acro

econ

omic

new

s et

c.)

�p t

= E

t[ps]

for

all

s >

t.��

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)

32

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

arr

ival

rat

e �.

�A

rbitr

ageu

rs w

ho a

re a

war

e of

the

bubb

le b

ecom

ein

crea

sing

ly w

orrie

d ab

out i

t ove

r tim

e.»

only

trad

ers

who

bec

ame

awar

e of

the

mis

pric

ing

mor

e th

an �

e

perio

ds a

go o

bser

ve (

look

out

for)

pub

lic e

vent

s.

33

Pu

blic

eve

nts

& M

arke

t re

bo

un

ds

�P

rop

osi

tio

n 5

:

In ‘r

espo

nsiv

e eq

uilib

rium

’S

ell o

ut

a) a

lway

s at

the

time

of a

pub

lic e

vent

t e,

b)

afte

r t i

+ �

e *

(whe

re �

e *<

�*) ,

ex

cep

t af

ter

a fa

iled

atta

ck a

t tp

, re-

ente

r th

e m

arke

t

for

t �

(t e

, t e

- �

e +

�e *

).

�In

tuiti

on fo

r re

-ent

erin

g th

e m

arke

t:�

for

t e <

t 0 +

��

+ �

e at

tack

fails

, age

nts

lear

n t 0

> t e

- �

e - ��

�w

ithou

t pub

lic e

vent

, the

y w

ould

hav

e le

arnt

this

only

at t

e +

�e

- �e

*.�

the

exis

tenc

e of

bub

ble

at t

reve

als

that

t 0 >

t - �e

* - ��

�th

at is

, no

addi

tiona

l inf

orm

atio

n is

rev

eale

d til

l te

- � e

+ �

e *

�de

nsity

that

bub

ble

burs

ts fo

r en

doge

nous

rea

sons

is z

ero.

Pro

po

siti

on

5:

34

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.

35

intr

oduc

tion

prel

imin

ary

anal

ysis

pers

iste

nce

of b

ub

ble

s

publ

ic e

vent

s

conc

lusi

on

mod

el s

etup

pri

ce c

asca

des

an

d r

ebo

un

ds

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

:

S

ell o

ut

a) a

fter

a pr

ice

drop

if �

i � �

p(H

p)

b)

afte

r t i

+ �

***

(w

here

�**

*< �

*) ,

re-

ente

r th

e m

arke

t afte

r a

rebo

und

at t p

for

t �

(t p

, t p

- �

p +

�**

*).

�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 m

ore

than

�p

perio

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.�

Eve

n se

ll ou

t afte

r an

othe

r pr

ice

drop

is le

ss li

kely

.

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.

39

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

sel

l out

con

ditio

n) s

ell s

hare

s 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!

40

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