1

Bu

bb

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and

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ilip

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ton

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vers

ity�

Mar

kus

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runn

erm

eier

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ceto

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ompa

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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

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gh a

s 73

.�

The

com

pany

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er p

aid

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Sto

ry o

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typ

ical

tec

hn

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sto

ck

3

Sto

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CA

-

192

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ompa

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Rad

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orpo

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n of

Am

eric

a (R

CA

)�

Tec

hnol

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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

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98

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ec. 0

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om h

igh

of $

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�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.