Exchange Rate Models Are Not as Bad as You Think

Discussion by

Peter Westaway Bank of England

Presentation given at the 8th Jacques Polak Annual Research Conference Hosted by the International Monetary Fund Washington, DC─November 15-16, 2007 Please do not quote without the permission from the author(s). The views expressed in this presentation are those of the author(s) only, and the

presence of them, or of links to them, on the IMF website does not imply that the IMF, its Executive Board, or its management endorses or shares the views expressed in the presentation.

88TTHH JJAACCQQUUEESS PPOOLLAAKK AANNNNUUAALL RREESSEEAARRCCHH CCOONNFFEERREENNCCEE NNOOVVEEMMBBEERR 1155--1166,, 22000077

Com

men

ts o

n En

gel e

t al (

2007

)‘E

xcha

nge

Rat

e M

odel

s are

N

ot a

s Bad

as Y

ou th

ink’

by

Mar

k A

stle

y an

d Pe

ter W

esta

way

M

onet

ary

Inst

rum

ents

& M

arke

ts D

ivis

ion

Ban

k of

Eng

land

Plan

•D

etai

l mai

n st

rand

s of E

ngel

et a

l (07

) •

Ban

k of

Eng

land

app

roac

h fo

r ac

coun

ting

for e

xcha

nge

rate

m

ovem

ents

‘Pol

icym

aker

’Foc

us

Mai

n St

rand

s of E

ngel

et a

l•

ER

s are

forw

ard-

look

ing!

•En

gel-W

est (

05) t

heor

em: E

Rs s

houl

d be

clo

se to

rand

om w

alks

if d

isco

unt f

acto

r clo

se to

uni

ty

•C

an g

et re

ason

able

var

ianc

e ra

tios

•(P

erce

ived

) mon

etar

y po

licy

reac

tion

cruc

ial i

n de

term

inin

g E

R r

eact

ion

to n

ews

•Pa

nel r

esul

ts: l

ong-

horiz

on p

redi

ctab

ility

!

Mon

etar

y M

odel

→Su

bstit

ute

out i

nter

est r

ates

by

inve

rting

mon

ey d

eman

d eq

ns.

Tayl

or R

ule

Mod

els

→Fo

cus o

n Ta

ylor

rule

coe

ffic

ient

s & e

xpec

ted

futu

re in

flatio

n &

outp

ut g

aps

→A

gain

subs

titut

ing

out (

path

of)

inte

rest

rate

s

But

Why

Sub

stitu

te O

ut In

tere

st R

ates

?Pr

os o

f not

subs

titut

ing

out i

nter

est r

ates

•Li

nk b

etw

een

ER n

ews &

inte

rest

rate

new

s pre

-re

quis

ite fo

r ER

-mac

ro v

aria

ble

link

•Y

ield

cur

ves f

orw

ard-

look

ing

–no

nee

d to

get

into

V

AR

s or s

urve

ys

•Ti

mel

y in

fo fr

om fi

nanc

ial m

arke

tsC

ons o

f not

subs

titut

ing

out i

nter

est r

ates

•A

ccou

ntin

g fr

amew

ork.

.•

Can

’t ge

t at d

eep

issu

e of

whi

ch sh

ocks

are

dr

ivin

g ER

s

Acc

ount

ing

for

ER

mov

es u

sing

UIP

Nom

inal

UIP

(ign

orin

g ris

k pr

emiu

m):

Inte

grat

e fo

rwar

ds:

→Lo

ng-r

un n

omin

al e

xcha

nge

rate

not

wel

l-def

ined

→C

umul

ated

diff

eren

tials

pot

entia

lly u

nbou

nded

() t

tt

ti

ie

Ee

*1

−+

=+

()

1*

11

−+

−+

=+

−+

=∑

kt

kt

n kt

nt

tt

ii

Ee

Ee

Acc

ount

ing

for

ER

mov

es u

sing

UIP

Rea

l UIP

(ign

orin

g ris

k pr

emiu

m):

Inte

grat

e fo

rwar

ds:

→C

umul

ated

real

rate

diff

eren

tials

bou

nded

→U

nexp

lain

ed c

ompo

nent

refle

cts r

evis

ions

to

“equ

ilibr

ium

rate

”or

risk

pre

mia

Brig

den

at a

l (19

97) B

ank

of E

ngla

nd Q

uart

erly

Bul

letin

.

() t

tt

tr

rer

Eer

*1

−+

=+

()

1*

11

−+

−+

=+

−+

=∑

kt

kt

n kt

nt

tt

rr

Eer

Eer

How

to d

eriv

e re

al ra

te e

xpec

tatio

ns?:

•R

equi

res y

ield

cur

ves

prov

ide

good

mea

sure

s of

inte

rest

rate

exp

ecta

tions

•…

and

info

on

expe

cted

real

inte

rest

rate

sO

utpu

ts:

•D

eriv

e es

timat

e of

‘int

eres

t rat

e ne

ws’

, co

mpa

red

to o

bser

ved

ER n

ews

44.2

4.4

4.6

4.8

55.2

05

1015

US F

orw

ard

Yiel

d C

urve

Mat

urity

perc

ent

Perio

d t

Perio

d t+

1

44.2

4.4

4.6

4.8

55.2

05

1015

UK F

orw

ard

Yiel

d C

urve

Mat

urity

perc

ent

Perio

d t

Perio

d t+

1M

inus

=

00.1

0.2

05

1015

UK

-US

'Inte

rest

Rat

e N

ews'

Mat

urity

perc

ent

How

wel

l doe

s it d

o?

2006

•Ev

ent s

tudy

: clo

se li

nk a

roun

d so

me

polic

y ra

te c

hang

es

How

wel

l doe

s it d

o?

2007

•U

nder

stat

es €

/£m

ove

on U

K ra

te ri

se in

Jan-

2007

.

How

wel

l doe

s it d

o?

2006

•C

an’t

acco

unt f

or sh

arp

$ de

prec

iatio

n in

Apr

il 20

06

-10

-50510

05

06

07

Inte

rest

Ra

te

Ne

ws

$/£

Ne

ws

How

wel

l doe

s it d

o?

•But

bro

adly

acc

ount

s for

$/£

new

s sin

ce 2

005Q

1

•Foc

us o

n va

rian

ce ra

tios:

EW

(200

4) fi

nd c

an a

ccou

nt

for 2

0-40

% o

f ER

var

ianc

e•B

ut b

ased

upo

n V

AR

S –

so c

an w

e te

ll st

orie

s?

Lin

ks to

Eng

el e

t al A

ppro

ach?

Var

ianc

e R

atio

= 0

.44;

Cor

rel.

= -0

.07

$/£,

Wit

h B

eta

= 0.

9

19

75

19

78

19

81

19

84

19

87

19

90

19

93

19

96

19

99

20

02

-20

-15

-10-505

10

15

DS

DS

HA

TH

•Im

pres

sive

per

form

ance

for $

/£at

mon

thly

freq

uenc

y:

Var

ianc

e R

atio

= 0

.88;

Cor

rel.

=0.3

2

-6-4-20246

97

98

99

00

01

02

03

04

05

06

07

IRN

$/£

Mon

thly

% C

hang

esH

ow w

ell d

oes U

IP D

ecom

p. d

o?

•Mor

e im

pres

sive

per

form

ance

for q

uarte

rly $

/£m

oves

: V

aria

nce

Rat

io =

1.0

4; C

orre

l. =0

.44

How

wel

l doe

s UIP

Dec

omp.

do?

-8-404897

98

99

00

01

02

03

04

05

06

07

IRN

$/£

Qua

rter

ly %

Cha

nges

•Mos

t of v

aria

nce

of IR

N re

flect

s lon

g-m

atur

ity e

ffec

ts-A

ccor

ds w

ith E

ngel

et a

l (07

) arg

umen

t

Wha

t is D

rivi

ng th

e R

esul

ts?

Var

ian

ce R

atio

s10

Yea

r$/

£$/

€ €/

£Y

/£19

97-2

007

0.88

1999

-200

70.

820.

260.

220.

52

5 Y

ear

$/£

$/€

€/£

Y/£

1997

-200

70.

2219

99-2

007

0.2

0.08

0.1

0.16

2 Y

ear

$/£

$/€

€/£

Y/£

1997

-200

70.

0419

99-2

007

0.04

0.01

0.03

0.03

•Sim

ilar r

esul

t for

oth

er e

xcha

nge

rate

s•A

lthou

gh v

aria

nce

ratio

s are

low

er th

an fo

r $/£

Var

ian

ce R

atio

s10

Yea

r$/

£$/

€ €/

£Y

/£19

97-2

007

0.88

1999

-200

70.

820.

260.

220.

52

5 Y

ear

$/£

$/€

€/£

Y/£

1997

-200

70.

2219

99-2

007

0.2

0.08

0.1

0.16

2 Y

ear

$/£

$/€

€/£

Y/£

1997

-200

70.

0419

99-2

007

0.04

0.01

0.03

0.03

Wha

t is D

rivi

ng th

e R

esul

ts?

(Rob

ustn

ess)

•Cor

rela

tion

betw

een

ER n

ews &

inte

rest

rate

new

s litt

le

affe

cted

by

mat

urity

use

d•C

orre

latio

ns st

rong

est f

or $

/£

Co

rrel

atio

n C

oef

fici

ents

10 Y

ear

$/£

$/€

€/£

Y/£

1997

-200

70.

3219

99-2

007

0.26

0.18

0.1

0.16

5 Y

ear

$/£

$/€

€/£

Y/£

1997

-200

70.

4119

99-2

007

0.35

0.17

0.16

0.12

2 Y

ear

$/£

$/€

€/£

Y/£

1997

-200

70.

380.

1319

99-2

007

0.33

0.14

0.13

0.08

Rob

ustn

ess I

I: E

cono

mic

Con

tent

-6-4-2024699

00

00

01

01

02

03

03

04

04

05

06

06

07

07

IRN

$/€

Mon

thly

% C

hang

es

•Per

form

ance

less

impr

essi

ve fo

r $/€

at m

acro

hor

izon

s:

Var

ianc

e R

atio

= 0

.26;

Cor

rel.

=0.1

8•B

ut sh

ort s

ampl

e!

How

wel

l doe

s it d

o?H

Con

clus

ions

•En

gel e

t al (

07) i

mpo

rtant

focu

s on

role

of f

utur

e ex

pect

ed fu

ndam

enta

ls…

usef

ul c

ount

er to

nih

ilist

ic

rand

om w

alk

appr

oach

. •

Hav

e sh

own

anal

ysis

bas

ed o

n in

term

edia

te

cond

ition

ing

on in

tere

st ra

tes.

•C

ompl

emen

tary

app

roac

h to

Eng

el a

t al –

exam

ines

one

hal

f of j

oint

hyp

othe

sis

–1)

UIP

/RE

–2)

Inte

rest

rate

rule

•M

ore

wor

k re

quire

d -p

aper

forth

com

ing!