1-s2.0-026156069400001h-main

7/27/2019 1-s2.0-026156069400001H-main

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SUTTE RWORTH

E I N E M A N NJournal of International Money and Finance, Vol. 14, No, 1 , pp. 3-26, 1995

C o p y r i g h t ( : 1 9 95 E l s e v i e r S c i e n ce L t dP r i n t e d i n G r e a t B r i t a in . A l l r i g h t s reserved

0261-5606(94)00001-8 0261-5606 /95 $10 .00 + 0 .00

I s t h e c o r r e l a t i o n i n i n t e r n a t i o n a l e q u i t y r e t u r n s c o n s t a n t :

1 9 6 0 - 1 9 9 0 ?

F R ANC OI S L ONGI N

Department of Finance, ESSEC Graduate Business School,95021 Cergy-Pontoise, Cedex, France

A N D

B R UNO S OL NI K

Department of Finance and Economics, HEC-School of Management,78351 Jouy-en-Josas, Cedex, France

We s tudy the c o r re la t ion o f m onth ly excess r e tu rns fo r seven majo r coun t r i e s

ove r the per iod 1960-90. W e find that the in ternat ional co var ianc e and

cor re la t ion ma t r i ces a re uns tab le ove r t ime . A mul t iva r i a te GARCH(1 ,1 )

mode l wi th cons tan t cond i t iona l co r re la t ion he lps to cap tu re some o f

the evo lu t ion in the cond i t iona l covar iance s t ruc tu re . However t e s t s o f

specif ic devia t ion s lead to a re ject ion of the hy pothesis of a con stantcond i t ional corre la t ion. A n expl ic it m odel l ing of the condi t ional c orre la t ion

ind ica tes an inc rease o f the in te rna t iona l co r re la t ion be tween marke t s ove r

the past th i r ty years . We also f ind that the corre la t ion r ises in per iods of

high vola t i l i ty . There is some prel iminary evidence that economic var iables

such as the dividend yie ld and in teres t ra tes conta in informat ion about

future vola t i l i ty and corre la t ion that i s not conta ined in past re turns a lone.

(JE L G 15, F3).

T h e c o r r e l a t i o n m a t r i x o f i n t e r n a t i o n a l a s s e t r e t u r n s p l a y s a s p e c i al ro l e i n t h ef i n a n c e l i t e ra t u r e . S i n c e th e s e m i n a l w o r k o f L e v y a n d S a r n a t ( 19 70 ), G r u b e l a n d

F a d n e r ( 1 9 7 1 ) , L e s s a r d ( 1 9 7 3 ) a n d S o l n i k ( 1 9 7 4 ) , i n t e r n a t i o n a l d i v e r s i f i c a t i o n o f

e q u i t y p o r t f o l io s h a s b e e n a d v o c a t e d o n t h e b a s is o f t h e lo w c o r r e l a t i o n b e t w e e n

n a t i o n a l s t o c k m a r k e t s . T h e c o v a r i a n c e b e t w e e n n a t i o n a l m a r k e t s c o u l d c h a n g e

b e c a u s e t h e v o l a t i l i t y o f n a t i o n a l m a r k e t s e v o l v e s o v e r t i m e , b u t a l so b e c a u s e t h e

i n t e r d e p e n d e n c e a c r o s s m a r k e t s c h a ng e s . L o o k i n g a t t h e m a r k e t c o r r e la t i o n a l l o w s

o n e t o f o cu s o n th e i n t e r d e p e n d e n c e b e t w e e n m a r k e t s . T h e c o v a r i a n c e / c o r r e l a t i o n

m a t r i x i s o n e o f t h e i n p u ts f o r t h e c o m p u t a t i o n o f a t r a d in g p o r t f o l i o . K n o w l e d g e

* W e have benef it ed f rom com m ents by S te fano Cavag l ia , Berna rd Dum as , Cam pbe l l Harvey ,Ev i Kap lan i s , Ken Kro ner , James L o th ian ( the Ed ito r ) Pe te r Pope and p a r t i c ipan t s o f theFrench F inance Assoc ia t ion mee t ings and o f the CEP R wo rkshop on In te rna t iona l F inance .The referee 's com m ents an d sug gest ions helped imp rove the ar tic le substant ia l ly . We areg r at ef u l t o I NQ U I R E , F N E G E a n d F o u n d a t i o n HE C f o r f in a n ci al s u p p o r t.

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Is the correlation in international equity returns constant?." F Lonoin and B Solnik

a b ou t i t s be ha v i o r , s t a b i l i ty a nd p r e d i c t a b i l i t y i s t he n c r uc i a l. I t is a ls o o f pa r t i c u l a r

i m p o r t a n c e f o r t e s t i n g i n t e r n a t i o n a l p r i c i n g t h e o r i e s a s m i s s p e c i f i c a t i o n c o u l d

l e a d t o f a ls e c onc l u s i ons . 1

I t is o f t e n s t a t e d t h a t t h e p r o g r e s s iv e r e m o v a l o f i m p e d i m e n t s t o i n t e r n a t i o n a l

i n v e s t m e n t , a s w e l l as t h e g r o w i n g p o l i ti c al , e c o n o m i c a n d f in a n c i a l in t e g r a t i o n ,

a f fe c t s i n t e r n a t i on a l m a r k e t l i nka ge s . T h i s c o u l d l e a d t o a p r og r e s s i ve i nc r e a s e

i n t h e i n t e r n a t i o n a l c o r r e l a t i o n o f fi n a n c ia l m a r k e t s r e fl e c ti n g t h e ' g l o b a l f i n a n c e '

p h e n o m e n o n . K a p l a n i s (1 98 8) s t u d i e d t h e s t a b il it y o f t h e c o r r e l a t i o n a n d

c o v a r i a n c e m a t r i c e s o f m o n t h l y r e t u r n s o f t e n m a r k e t s o v e r a f i ft ee n y e a r p e r i o d

( 1 9 67 - 8 2 ). S h e c o m p a r e d m a t r i c e s e s t i m a t e d o v e r s u b - p e r i o d s o f 4 6 m o n t h s u s i n g

Box ( 1949 ) a nd J e n r i c h ( 1970 ) t e s t s . T he nu l l hypo t he s i s t ha t t he c o r r e l a t i on

m a t r i x is c o n s t a n t o v e r tw o a d j a c e n t s u b - p e r i o d s c o u l d n o t b e r e j e c t e d a t t h e t 5

p e r c e n t c o n f i d e n c e le ve l. T h e c o v a r i a n c e m a t r i x w a s m u c h l es s s ta b l e ( r e j ec t io n

a t t he 5 pe r c e n t c on f i de nc e l e vel f o r m o s t s ub - pe r i ods ) . T h i s r e s u l t c ou l d be c a u s e db y c h a n g e s i n t h e c o n d i t i o n a l v a r i a n c e s w i t h c o n s t a n t i n t e r n a t i o n a l c o n d i t i o n a l

c o r r e l a t i ons . Ra t ne r ( 1992 ) a l s o c l a i m e d t ha t t he i n t e r na t i ona l c o r r e l a t i ons

r e m a i n e d c o n s t a n t o v e r t h e p e r i o d 1 9 7 3 -8 9 . O n t h e o t h e r h a n d , K o c h a n d K o c h

(1 99 1) l o o k e d a t t h e c o r r e l a t i o n o f e i g h t m a r k e t s u s i n g d a il y d a t a f o r t h r e e s e p a r a t e

ye a r s (1972, 1980 a n d 1987) a n d c o nc l ud e d f r om s i m p l e C ho w t e s t s t ha t

' i n t e r n a t i o n a l m a r k e t s h a v e r e c e n t l y g r o w n m o r e i n t e r d e p e n d e n t ' . V o n

F u r s t e n b e r g a n d J e o n (1 98 9) r e a c h e d a s i m i l ar c o n c l u s i o n u s i n g a V A R a p p r o a c h

f o r f o u r m a r k e t s a n d a v e r y s h o r t t i m e p e r i o d ( 1 9 86 - 8 8) . K i n g , S e n t a n a a n d

W a d h w a n i ( 1 9 9 2 ) c l a i m e d t h a t t h i s i s o n l y a t r a n s i t o r y i n c r e a s e c a u s e d b y t h e

1 98 7 c r as h . I n d e e d , a q u e s t i o n o f t e n r a is e d is w h e t h e r t h e i n t e r n a t i o n a l c o r r e l a t i o ni n c r e a se s in p e r i o d s o f h i g h t u r b u l e n c e . T h e i n t e r n a t i o n a l c o r r e l a t i o n i n c r e a se s

w h e n g l o b a l f a c t o r s d o m i n a t e d o m e s t i c o n e s a n d a f fe c t a ll f in a n c i al m a r k e t s . T h e

d o m i n a n c e o f g l o b a l f a c to r s t e n d s t o b e a s s o c i a t e d w i t h v e r y v o l a ti le m a r k e t s

( t he o i l c r is e s, t he G u l f w a r , e tc .) . U s i ng h i gh - f r e que nc y da t a s u r r ou nd i ng t he

c r a s h o f 1 9 8 7 , K i n g a n d W a d h w a n i ( 1 9 9 0 ) a n d B e r t e r o a n d M a y e r ( 1 9 9 0 ) f o u n d

t h a t i n t e r n a t i o n a l c o r r e l a t i o n t e n d s t o i n c r e a s e d u r i n g t h e s t o c k m a r k e t c r i s i s .

O u r o b j e c ti v e is to t e st t h e h y p o t h e s i s o f a c o n s t a n t i n t e r n a t i o n a l c o n d i t i o n a l

c o r r e l a t io n , i n v e s t ig a t i n g v a r i o u s t y p e s o f d e v i a ti o n s . W e e x p li c it ly m o d e l t h e

c o n d i t i o n a l m u l t i v a r i a t e d i st r i b u t i o n o f i n t e r n a t i o n a l a s s e t r e t u r n s a n d t e st f o r

t h e e x i s t en c e o f p r e d i c t a b l e t i m e - v a r i a t i o n i n c o n d i t i o n a l c o r r e l a t i o n f o r t h e p e r i o d1 9 6 0- 90 . P r e v i o u s w o r k s h a v e c o n s i d e re d u n c o n d i t io n a l c o r r e l a t io n c o m p u t e d

o v e r d i f f e re n t s u b - p e r io d s ; h e r e , w e c o m e u p w i t h a n e x p li ci t m o d e l f o r c o n d i t i o n a l

c o r r e l a ti o n . P r e v i o u s s t u d i e s h a v e a l s o l o o k e d a t a f a i rl y s h o r t h i s t o r y o f m o n t h l y

r e t u r n s o r f o c u s e d o n t h e r e c e n t p e r io d s u r r o u n d i n g t h e c r a s h o f 19 8 7. H e r e , w e

a t t e m p t t o d i s co v e r l o n g e r t e rm p h e n o m e n a b y l o o k i n g a t m o n t h l y d a t a f o r t h e

s e ve n m a j o r s t oc k m a r ke t s ove r t he pe r i od 1960 90 . T h i s i s a f a i r l y o r i g i na l

d a t a b a s e w h i c h i n c lu d e s g o o d - q u a l i t y p r i c e in d i c es a n d d i v i d e n d y i el d s o v e r t h e

t o t a l p e r i o d . T h e d a t a a r e d e s c r i b e d i n A p p e n d i x A . T h e p e r i o d c o v e r s s e v e r a l

bus i ne s s a nd m a r k e t c yc l e s , w i t h t he s t e a dy g r ow t h o f t he s i x ti es , t he o i l c r is e s

a n d t h e 1 9 8 7 m a r k e t c r a s h .A p r e l i m i n a r y l o o k a t t h e d a t a g iv e s a n i n d i c a t i o n o f t h e s t a b il it y o f t h e

c o r r e l a ti o n o f m a r k e t s . N a t i o n a l s t o ck m a r k e t s h a v e n o t b e e n s t r o n g ly c o r r e la t e d

o v e r t h e p a s t t h i r t y y e a r s. T a b l e i r e p o r t s t h e u n c o n d i t i o n a l c o r r e l a t i o n o f n a t i o n a l

4 Journal of International Money and Finance 1995 Volume 14 Number 1

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TABLE 1. Basic statistics.

GE FR UK SW JA CA US

Mean 0.38 0.29 0.47 0.37 0.65 0.30 0.25

S.D. 5.16 5.87 6.19 5.15 4.97 4.81 4.36

GE FR UK SW JA CA US

GE 1.00

FR 0.45 1.00

UK 0.34 0.42 1.00

SW 0.60 0.51 0.45 1.00

JA 0.24 0.26 0.25 0.29 1.00

CA 0.30 0.42 0.48 0.46 0.27 1.00

US 0.38 0.43 0.50 0.55 0.30 0.71 1.00

This table gives the

monthly units) and

1/1960-8/1990.

mean and standard deviation of monthly excess returns (expressed in percentage

the unconditional correlation matrix of national excess returns. The period is

m o n t h l y e x c e s s r e t u rn s e s t i m a t e d f ro m 1 9 6 0 t o 1 99 0. T h e l o w e s t c o e f f i c ie n t i s

0 .2 4 ( G e r m a n y a n d J a p a n ) a n d t h e h i g h e st is 0 .7 1 ( C a n a d a a n d t h e U S A ) . T h e

a v e r a g e c o e f f ic i en t i s a r o u n d 0 .5 . T h e m e a n e x c e ss r e t u r n s p e r m o n t h v a r y f r o m

0 .2 51 p e r c e n t f o r th e U S A t o 0 .6 4 7 p e r c e n t f o r J a p a n . T h e s t a n d a r d d e v i a t i o n s

a r e m o r e s i m i l a r a c r o s s c o u n t r i e s r a n g i n g f r o m 4 . 3 6 p e r c e n t p e r m o n t h f o r t h eU S A t o 6 . 1 9 p e r c e n t p e r m o n t h f o r t h e U K .

T o g e t a v i su a l i m p r e s s i o n o f t h e i n s t a b il i ty o f th e c o r r e l a t i o n a c r o s s m a r k e t s ,

w e p l o t te d t h e m e a n c o r r e l a ti o n o f t h e U S m a r k e t w i th t h e o t h e r s ix m a r k e t s in

F i g u r e 1. T h e c o r r e l a t i o n s a r e e s t i m a t e d o v e r a s l id i n g w i n d o w o f f iv e y e a r s. T h e

c o r r e l a t i o n f l u c t u a t e s o v e r t im e . T h e i n c l u s i o n o f O c t o b e r 1 9 87 i n t h e c a l c u l a ti o n

o f t h e 5 - y e a r c o r r e l a t i o n l e a d s t o a n i n c r e a s e in t h e c o r r e l a t i o n f o r a p e r i o d o f 5

y e a r s .

T h e g l o b a l t es t f o r a c o n s t a n t u n c o n d i t i o n a l c o r r e l a t i o n m a t r i x p e r f o r m e d b y

K a p l a n i s ( 19 8 8) c a n b e r e p l ic a t e d o n t h i s l o n g e r t i m e p e r i o d . W e e s t im a t e t h e

u n c o n d i t i o n a l c o r r e l a t i o n m a t r i x f o r th e se v e n c o u n t r i e s o v e r s ix s u b - p e r i o d s o ff iv e y e a r s a n d t e s t f o r th e e q u a l i t y o f t h e c o r r e l a t i o n m a t r i x o v e r a d j a c e n t

s u b - p e r i o d s a s w e ll a s o v e r n o n - a d j a c e n t s u b - p e r i o d s . T h e J e n r i c h t e st 2 o f e q u a l i t y

o f t w o m a t r i c e s c a l c u l a t e d o v e r d i f fe r e n t ti m e p e r i o d s , h a s a n a s y m p t o t i c

c h i - s q u a r e d i s t r i b u t i o n w i t h 2 1 d e g r e e s o f f r e e d o m f o r a s e v e n b y s e v e n m a t r ix . 3

A s im i l a r t e s t c a n b e a p p l i e d t o t h e c o v a r i a n c e m a t r i x a l t h o u g h t h e n u m b e r o f

d e g r e e s o f f r e e d o m i s n o w 2 8 s in c e t h e d i a g o n a l e l e m e n t s c a n v a r y o v e r t i m e .

T h e r e s u lt s a r e a l s o r e p o r t e d i n T a b l e 2 . T h e n u l l h y p o t h e s i s o f a c o n s t a n t

c o r r e l a t i o n m a t r i x i s r e j e c t e d a t t h e 1 5 p e rc e n t c o n f i d e n c e l e v e l i n 1 0 o u t o f 1 5

c o m p a r i s o n s a n d a t t h e 5 p e r c e n t l e v e l i n 5 o u t o f 1 5 c o m p a r i s o n s . T h e s a m e

t e s t a p p l i e d t o t h e c o v a r i a n c e m a t r i x l e a d s t o a re j e c t io n o f t h e h y p o t h e s i s o f ac o n s t a n t c o v a r i a n c e m a t r i x a t t h e 1 p e r c e n t l ev e l i n a ll c o m p a r i s o n s b u t o n e .

T h e s e r e s u l t s c o n f i r m t h e f in d i n g s b y K a p l a n i s t h a t t h e c o v a r i a n c e m a t r i x is l es s

s t a b l e t h a n t h e c o r r e l a t i o n m a t r i x . H o w e v e r o u r p -v a l u e s f o r t h e c o r r e l a t io n

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Is the correlation in international equity returns constant?." F Longin and B Solnik

0.8

0.7

0.6

0.5

0.4

0.3

0 . 2 h i l l . . . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . i . . . .. . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . . .. . . . . . . i . . . . .. . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . .. . . . . . h . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . i . . . . .. . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . . .. . . . . . J . . . . . . . . .. . . . . . . . . . .. . . . , , , , , , , , , , , , , , , , , . , ,

63 68 73 78 83 88

__ average correlation

FIGURE 1. Correlation of the U S stock market. Th is figure reports the (unweighted) averagecorrelation of the U S stock market with the oth er sev en stock markets. The correlation is

comp uted over sliding windows o f four years, using local currency monthly total returns. Theperiod is December 1959-91.

m a t r i x a r e s o m e w h a t l o w e r t h a n h e rs ; t h is c o u l d b e e x p l a i n e d b y a n i n c r e a s e d

i n s t a b i l i t y i n t h e e i g h t i e s , s i n c e h e r d a t a e n d i n 1 9 8 2 .

W h a t c a n e x p l a i n t h is i n s ta b i l i ty o f t h e u n c o n d i t i o n a l c o r r e l a t i o n m a t r ix ? A

f ir st a l t e r n a t iv e is t h a t t h e c o n d i t i o n a l c o r r e l a t i o n r e m a i n s c o n s t a n t o v e r t im e

b u t t h e m a r k e t e x p e c t e d r e t u r n s a n d v a r i a n c e s v a r y o v e r ti m e . I n d e e d , w e h a v e

e x t e n s iv e i n t e r n a t i o n a l e v i d e n c e o f p r e d i c t a b l e t i m e - v a r i a t i o n s i n t h e e q u i t y r e t u r nd i s t r ib u t i o n . E x p e c t e d r e t u r n s s e e m t o d e p e n d w o r l d w i d e o n a se t o f i n f o r m a t i o n

v a r i a b l e s s u c h a s th e d i v i d e n d y i e l d a n d v a r i o u s i n t e r e s t - r a t e - r e l a t e d v a r i a b l e s . 4

T h e v a r i a n c e o f r e t u r n s h a s b e e n s h o w n t o b e h e t e r o s c e d a st i c . T h e c o n d i t i o n a l

v a r i an c e o f n a t i o n a l e q u i t y m a r k e t s h a s b e e n m o d e l l e d w i t h g o o d s u cc e ss u s in g

a u n i v a r i a t e G A R C H a p p r o a c h ~ f o r s ev e ra l n a t i o n a l m a r k e t s. A s e c o n d

a l t e rn a t i v e o r , r a th e r , a d d i t i o n a l e x p l a n a t i o n is t h a t t h e i n t e r d e p e n d e n c e o f

n a t i o n a l e q u i t y m a r k e t s i s c h a n g i n g t h r o u g h t im e . G r o w i n g i n t e r n a t io n a l

i n t e g r a t i o n c o u l d l e a d t o a p r o g r e s s i v e i n c r e a s e i n m a r k e t c o r r e l a t i o n . M a r k e t s

c o u l d b e m o r e h i g h l y c o r r e l a t e d i n p e r i o d s o f h i g h v o l a t il it y . T h e c o r r e l a t i o n

c o u l d b e h ig h e r w h e n t h e m a r k e t s g o d o w n , r at h e r t h a n u p . T h e c o r r e l a t io n c o u l db e h i g h e r i n s o m e p e r i o d s o f t h e b u s i n e s s c y cl e, f o r e x a m p l e p e r i o d s c h a r a c t e r i z e d

b y h i g h l ev e ls o f i n t e re s t r a t e s a n d d i v i d e n d y ie ld s . T h e s e a r e s o m e o f t h e a r g u m e n t s

of ten hea rd in f inanc ia l c i r c le s .


7/27/2019 1-s2.0-026156069400001H-main


I s t h e c o r r e l a t i o n i n i n t e r n a t i o n a l e q u i t y r e t u r n s c on sta n t? ." F L o n g i n a n d B S o l n i k

T A nL E 2. T e s t o f t h e e q u a l i t y o f t h e c o r r e l a t i o n a n d c o v a r i a n c e m a t r i c e s o v e r t i m e .

C o r r e l a t i o n m a t r i x C o v a r i a n c e m a t r i x

P e r i o d s c o m p a r e d T e s t p - v a lu e T e s t p - va l u e

1960/65 to 1965/70 22.89 0.349 34.95 0.171

1965/70 to 1970/75 31.70 0.062 64.09 0.000

1970/75 t o 1975/80 44.22 0.002 67.07 0.000

1975/80 t o 1980/85 28.69 0.121 49.95 0.006

1980/85 to 1985/90 30.59 0.080 77.23 0.000

1960/65 t o 1970/75 31.72 0.062 76.19 0.000

1960/65 to 1975/80 39.67 0.008 102.18 0.000

1960/65 to 1980/85 24.41 0.273 90.02 0.000

1960/65 t o 1985/90 44.07 0.002 52.47 0.003

1965/70 to 1975/80 7.96 0.995 70.09 0.000

1965/70 to 1980/85 22.93 0.347 72.81 0.000

1965/70 to 1985/90 45.79 0.001 52.74 0.003

1970/75 to 1980/85 20.52 0.488 74.21 0.000

1970/75 to 1985/90 122.06 0.010 71.89 0.000

1975/80 to 1985/90 49.22 0.000 79.96 0.000

C o r r e l a t i o n a n d c o v a r i a n c e m a t r i c e s o f m o n t h l y n a t i o n a l e x c e s s r e t u rn s fo r s e v e n c o u n t r i e s a r e c o m p u t e d

o v e r p e r i o d s o f f i v e y e a r s . W e u s e t h e J e n r i c h t e s t t o t e s t t h e e q u a l i t y o f t h e c o r r e l a t i o n ( a n d c o v a r i a n c e )

m a t r i x o v e r t w o p e r i o d s . T h e r e s t i s a s y m p t o t i c a l l y d i s t r i b u t e d a s a c h i - s q u a r e w i t h 21 d e g r e e s o f f r e e d o m

f o r t h e c o r r e l a t i o n m a t r i x a n d 2 8 d e g r e e s o f f re e d o m f o r t h e c o v a r i a n c e m a t r i x .

T o t e st th e a s s u m p t i o n o f a c o n s t a n t c o n d i t io n a l c o r r e la t io n , w e m o d e l t h e

a s s e t r e tu r n d y n a m i c s e x p l ic i tl y u s i n g a b i v a ri a te G A R C H m o d e l f or e a c h p a i r

o f m a r k e t s . W e a l s o c o n d i t i o n t h e f ir st t w o m o m e n t s o f t h e d i s tr i b u t io n o n a s e t

o f i n f o r m a t i o n v a r i a b l e s o b s e r v a b l e a t t h e s ta r t o f t h e p e r i o d u s e d t o c a l c u l a t e

r e t u r n , n a m e l y t h e d i v i d e n d y i e l d , t h e s h o r t - a n d l o n g - t e r m i n t e r e s t r a t e s a n d a

J a n u a r y s e a s o n a l . T h e p a r s i m o n i o u s G A R C H r e p r e s e n t a t i o n b e s t f i t t e d t o o u r

p u r p o s e i s th e G A R C H c o n s t a n t - co n d i t io n a l - c o r r el a t io n m o d e l p u t fo r w a r d in

B o l l e r s l e v ( 1 9 9 0 ) . T h i s s p e c i f i c a t i o n h a s b e e n e x t e n s i v e l y u s e d t o m o d e l

i n t e r n a t i o n a l a s s e t r e tu r n s ; i t c a n b e f o u n d i n N g ( 1 9 9 1 ), B a i ll ie a n d B o l l e r s le v

( 1 9 9 0 ) a n d G i o v a n n i n i a n d J o r i o n ( 1 9 8 9 ) a m o n g o t h e r s . T h i s w i l l b e o u r m o d e l

o f th e n u l l h y p o t h e s i s o f c o n s t a n t c o r r e l a t i o n a n d w e w i l l t e s t d i ff e re n t d e v i a t i o n s

f r o m t h i s m o d e l . T o i n v e s t ig a t e w h e t h e r t h e c o n d i t io n a l c o r r e l a ti o n o f m a r k e t s

b e c o m e s h i g h e r i n t u r b u l e n t p e r i o d s , w e d e v e l o p a t e s t o n t h e c o n d i t i o n a l

c o r r el a ti o n i n sp ir e d fr o m t h e th r e s h o ld G A R C H m o d e l s o f G o u r i 6 r o u x a n d

M o n f o r t ( 1 9 9 2 ) a n d E n g l e a n d N g ( 1 9 9 3 ) .

L o o k i n g a t c o r r e l a ti o n a l o n e o n e c a n n o t r e a c h c o n c l u s i o n s w i th r e ga r d t o

m a r k e t i n t e g r a t i o n . I n a n a s s e t p r ic i n g s e n s e , m a r k e t s c a n b e fu l ly in t e g r a t e d w i t h

o r w i t h o u t c o r r e l a t i o n a c r o s s a s s e t re t u r n s. T h i s p a p e r f o c u s e s o n t h e

i n t e r d e p e n d e n c e a c r o s s m a r k e t s a n d d o e s n o t p r o v i d e a n a s s e t p r i c i n g t e s t o f

m a r k e t i n t e g r a t i o n .

J o u r n a l ~?( h l t e r n a t i o n a l M o n e y a n d F i n a n c e 1 9 9 5 V o l u m e 1 4 N u m b e r 1 7

7/27/2019 1-s2.0-026156069400001H-main


Is the correlation in international equity returns constant?: F Lonoin and B Solnik

T h e p a p e r p r o c e e d s a s f o l l o w s . I n S e c t i o n I , w e i n t r o d u c e o u r b a s e m o d e l f o r

t h e c o n d i t i o n a l m u l t i v a r i a t e a s s e t p r o c e s s . T h i s i s a b i v a r i a t e G A R C H ( 1 , 1 ) m o d e l

w i t h i n f o r m a t i o n v a r i a b l e s a n d c o n s t a n t c o n d i t i o n a l c o r r e l a t i o n . I n S e c t i o n I I ,

w e te s t v a r i o u s f o r m s o f d e v i a t i o n s f r o m c o n s t a n t c o n d i t i o n a l c o r r e l a t i o n . T h e

f i n d i n g s a r e s u m m a r i z e d i n S e c t i o n I I I .

I . M o d e l l i n g t h e m u l t i v a r i a t e c o n d i t i o n a l r e tu r n p r o c e s s

L A . A m u l t i v a r ia t e c o n d i ti o n a l m o d e l

T h e m u l t i v a r i a t e p r o c e s s f o r a s s e t r e t u r n s c a n b e w r i t t e n a s :

Rt = m,_ 1 + e t,

( 1 ) m , -1 = E (R , IF , - x),

e , lF ,_ 1 ~ N (0 , /~ ) ,

w h e re R t is a v e c t o r o f a s s e t e x c e s s r e t u rn s (d e n o t e d R ~ fo r c o u n t ry i), m r - 1 i s t h e

v e c t o r o f e x p e c t e d r e t u r n s c o n d i t i o n e d o n t h e i n f o r m a t i o n s e t F t - 1, et i s t h e v e c t o r

o f i n n o v a t i o n s o r u n e x p e c t e d r e t u r n s a s s u m e d t o b e c o n d i t io n a l l y n o r m a l w i t h

a c o n d i t i o n a l c o v a r i a n c e m a t r i x ~ . E l e m e n t s o f ~ a r e d e n o t e d h~ j f o r t h e

o f f -d i a g o n a l t e rm s a n d h~ fo r t h e d i a g o n a l t e rm s (v a r i a n ce s ) .

A s m e n t i o n e d i n t h e i n t r o d u c t i o n , t h e r e is e x t e n s iv e e m p i r i c a l e v i d e n c e t h a t

e x p e c t e d r e t u r n s d e p e n d o n a s e t o f i n f o r m a t i o n v a r i a b l e s s u c h a s t h e d i v i d e n dy i e ld a n d v a r i o u s i n t e r e s t- r a t e r e l a t e d v a r i a b le s . T h e e x p e c t e d e x c e s s r e t u r n f o r

m a r k e t i ( it s n a t i o n a l r i sk p r e m i u m ) i s c o n d i t i o n e d o n a s et o f i n f o r m a t i o n v a r i a b l e s

Z I - 1. W e a s s u m e a li n e a r r e l a ti o n b e t w e e n e x p e c t e d e x c e s s r e t u r n s a n d t h e v e c t o r

o f i n f o r m a t i o n v a r ia b l e s:

( 2 ) R I = b " Z i - 1 + e l.

In l in e w i t h s o m e p re v i o u s r e s e a r c h (H a rv e y , 1 9 91 a n d S o l n i k , 1 9 93 ), w e i n c l u d e

i n t h e i n f o r m a t i o n s e t o f c o u n t r y i t h e n a t i o n a l d i v i d e n d y i e ld , s h o r t - t e r m a n d

l o n g - t e r m i n t e r es t r a t e s a s w e l l a s a J a n u a r y s e a s o n a l . 6 T h e s e v a r i a b l e s a r e

c o m m o n l y u s e d in m o d e l s o f t h e U S m a r k e t . W e a d o p t t h e s a m e n a t i o n a l r i skp r e m i u m m o d e l f o r e a c h c o u n t r y b y u s i ng o n l y d o m e s t i c i n f o r m a t i o n v a r ia b le s .

A ' b e t t e r ' r i s k p r e m i u m m o d e l c o u l d c e r t a i n l y b e f o u n d e x p o s t b u t i t w o u l d b e

t h e r e s u l t o f d a t a m i n i n g.

W e u s e a m u l t i v a r i a t e G A R C H s p e c i f i c a t i o n t o m o d e l t h e t i m e - v a r i a t i o n i n

v a r i a n c e s a n d a l s o i n c l u d e t h e i n f o r m a t i o n v a r i a b l e s d i s c u s s e d a b o v e . S e v e r a l

p a r s i m o n i o u s m u l t i v a r ia t e G A R C H s p e ci fi c at io n s h a v e b e e n u s e d i n t h e li te r at u re .

A l l t h e s e s p e c i f i c a t i o n s a r e f i r s t - o r d e r p r o c e s s e s d e n o t e d G A R C H ( 1 , 1 ) . T o t e s t

t h e a s s u m p t i o n o f a c o n s t a n t c o n d i t i o n a l c o r r e l a t i o n a c r o s s m a r k e t s , w e u s e a s

t h e n u l l h y p o t h e s i s t h e c o n s t a n t - c o n d i t i o n a l - c o r r e l a t i o n m o d e l p r o p o s e d b y

B o l l e r s l e v (1 9 9 0 ) . W e u s e e x c e s s e q u i t y r e t u rn s i n l o c a l c u r r e n c y . B e c a u s e o fi n t e r e s t r a t e p a r i t y ( t h e f o r w a r d c u r r e n c y b a s i s i s e q u a l t o t h e i n t e r e s t r a t e

d i f fe r e n ti a l) , t h i s i s e q u a l t o t h e c u r r e n c y -h e d g e d e x c e s s r e t u r n f ro m a n y n a t i o n a l i t y

v i e w p o i n t . T h i s i n v a r i a n c e t o t h e n u m e r a i r e u s e d w o u l d n o t b e p r e s e r v e d i f t h e

8 Journal of lnternational Money and Finance 1995 Volume 14 Number 1

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I s t h e c o r r e l a t io n i n i n t e r n a t i o n a l e q u i t y r e t u r n s c o n s t a n t ? : F L o n g i n a n d B S o l n i k

c o n s t a n t - c o n d i t i o n a l -c o r r e l a ti o n r e p r e s e n ta t i o n w a s w r i t te n o n u n h e d g e d

re turns .7

T h e v a r i a n c e t e r m f o r e a c h m a r k e t i s a s s u m e d t o b e a f u n c t i o n o f t h e p a s t

i n n o v a t i o n a n d c o n d i t i o n a l v a r i a n c e o f t h is m a r k e t , a s w e ll a s s o m e n a t i o n a l

i n f o r m a t i o n v a ri ab l es . H o w e v e r t h e c o n d i ti o n a l c o r r el a t io n b e t w e e n t h e t w o

m a r k e t s i s a s s u m e d t o b e c o n s t a n t o v e r ti m e :

i i i -4- c i h i i , i i ,us i ,us i us( 3 > h I = a i q - b e , _ le ,_ 1 - t - 1 id Z t_ a n d h t = r x / h , x / h , .

T h e c o m b i n a t i o n o f e q u a t i o n s ( 2 > a n d ( 3 > c o n s t i tu t e s o u r b a s e m o d e l w i th

c o n s t a n t c o n d i t i o n a l c o r r e la t i o n . W e e s t i m a t e th i s b a s e m o d e l a n d t h e n a t t e m p t

t o t e s t f o r p o t e n t i a l d e v i a t i o n s f r o m c o n s t a n t c o n d i t i o n a l c o r r e l a t i o n .

L B . E s t i m a t i o n o f t h e b a s e m o d e l w i t h c o n s t a n t c o n d i t io n a l c o r r e la t io n

T h e c o n d i t i o n a l l o g - l i k e l i h o o d f u n c t i o n a t t i m e t , l , (q) , c a n b e e x p r e s s e d a s :

N l n ( 2 r 0 - N l n , ~ , - ~ el/-/te ,4 ) l , ( q) = - - ~

w h e r e q is t h e v e c t o r o f a ll th e p a r a m e t e r s t o b e e s t im a t e d a n d N t h e d i m e n s i o n

o f t h e m o d e l ( t h e n u m b e r o f c o u n t ri e s) . T h u s , t h e l o g - l i k e li h o o d f o r t h e w h o l e

s a m p l e f r o m t i m e l t o T , L ( q ) , i s g iven by :

T

( 5 ) L(q ) = ~ l ,(q ) .t= l

T h i s lo g - l i k e l i h o o d is m a x i m i z e d u s i n g th e B e r n d t , H a l l , H a l l a n d H a u s m a n ( 19 7 4)

a l g o r i t h m 8. A m u l t i v a r i a t e G A R C H e s t i m a t i o n w i t h s e v e n c o u n t r i e s i s n o t f e as ib l e

f o r t e c h n i c a l r e a s o n s a s e x p l a i n e d b e l o w . T h e f u l l m o d e l w o u l d r e q u i r e t h e

e s t i m a t i o n o f 9 8 co e f fi c ie n t s (3 5 f o r t h e m e a n e q u a t i o n s , 3 5 f o r t h e G A R C H t e r m s

a n d t h e in f o r m a t i o n v a r i a b l e s i n t h e c o n d i t i o n a l v a r i a n c e s a n d 2 8 f o r t h e

c o r r e l a t i o n c o e f fi c ie n t s) . T h e l a r g e n u m b e r o f c o e f f ic i e n t s t o b e e s t i m a t e d m a k e s

t h e i t e r a ti o n p r o c e s s v e r y l o n g . M o r e o v e r t h e r e l a ti v e ly s m a l l s iz e o f t h e d a t a b a s e

( 36 8 o b s e r v a t i o n s ) a n d t h e lo w f r e q u e n c y o f t h e d a t a ( m o n t h l y o b s e r v a t i o n s ) m a k e

t h e c o n v e r g e n c e o f th e i t e ra t i v e m e t h o d v e r y d i ff ic u lt e sp e c i a ll y i f s o m e o f th ec o e ff ic i en t s a re n o t s t r o n g l y s ig n i fi c an t . 9 H e n c e w e o n l y c o n d u c t t h e e s t i m a t i o n s

f o r c o u n t r y p a i rs . T o s i m p l if y th e e x p o s i t i o n w e fo c u s o n t h e c o r r e l a t io n o f t h e

U S m a r k e t w i t h f o r e i g n m a r k e t s a n d h e n c e e s t i m a t e s i x b i v a r i a t e G A R C H

p r o c e s s e s . W e h a d t o e s t i m a t e t h e G A R C H m o d e l s w i t h a l a r g e n u m b e r o f

p a r a m e t e r s f o r e a c h c o u n t r y p a i r: t e n i n t h e m e a n e q u a t i o n s (f iv e f o r e a c h c o u n t r y ) ,

s e v en to m o d e l t h e G A R C H p r o c e s s p l u s o n e te r m f o r e a c h i n f o rm a t i o n v a r ia b l e

i n t h e c o n d i t i o n a l v a r i a n c e e q u a t i o n . T h i s is v e r y c o m p u t e r - t i m e - c o n s u m i n g a n d

l e a d s t o a c o n v e r g e n c e p r o b l e m u n l e s s g o o d s t a r t i n g v a l u e s a r e f o u n d f o r t h e

p a r a m e t e r s . T h i s is p a r t i c u l a r l y t r u e f o r t h e p a r a m e t e r s i n th e v a r i a n c e e q u a t i o n s .

W e u s e o n l y t h e n a t i o n a l d i v i d e n d y i e ld a n d s h o r t - t e rm i n t e re s t r a te a s in f o r m a t i o nv a r i a b l e s f o r e a c h v a r i a n c e e q u a t i o n . T h i s g i v es a t o t a l o f 2 1 p a r a m e t e r s t o b e

e s t i m a t e d . A s u f f i c i e n t , b u t n o t n e c e s s a r y , c o n d i t i o n f o r p o s i t i v e d e f i n i t i v e n e s s o f

t h e c o v a r i a n c e m a t r i x i s to c o n s t r a i n t h e c o e ff ic i en t s o f t h e i n f o r m a t i o n v a r i a b l e s

J o u r n a l ¢71 I n t e r n a t i o n a l M o n e y a n d F i n a n c e 1 9 9 5 V o l u m e 1 4 N u m b e r 1 9

7/27/2019 1-s2.0-026156069400001H-main


I s t h e c o r r e l a ti o n i n i n t e r n a t i o n a l e q u i t y r e t u r n s c o n st a nt ? ." F L o n # i n a n d B S o l n i k

T AB LE 3 . E s t i m a t i o n o f t h e n a t i o n a l r i sk p r e m i u m m o d e l s .

A . R e t u r n e q u a t i o n s

bo b l b2 ba b 4 L i k

G E 0 . 01 5 2 .2 1 - 0 . 8 9 - 2 . 7 4 0 .0 1 4 1 26 1.3

( 0.8 4) ( 0.6 0 ) ( - 0 . 4 3 ) ( - 0 . 7 6 ) ( 1.5 3)

F R 0 .001 5 .46 1 .22 - 3 . 62 0 .035 1209 .9

(0.00) (1.84) (0.74) ( - 1.23) (3.49)

U K - 0 . 0 5 0 1 3.9 2 - 2 . 5 8 2 .1 4 0 .0 1 7 1 24 6.7

( - 4 .3 0 ) (5 .14 ) ( - 1 .43 ) (0.90 ) (1 .92)

S W 0 .0 1 3 6 . 94 - 2 . 2 7 - 4 . 5 5 0 . 02 3 1 29 8.1

(1 .38) (1 .17) ( - 1 .41) ( - 1 .17) (3 .00)

JA 0 .012 1 .22 - 2 . 64 0 .47 0 .020 1255 .4

(0 .90 ) (0 .51 ) ( - 0 .9 2 ) (0 .13 ) (1 .85 )

C A - 0 . 0 1 2 8 .7 5 - 1 .2 4 - 0 . 6 5 0 .0 2 1 1 4 06 .6

( - 0 .94) (2 .23) ( - 0 .68) ( - 0 .27) (3 .46)

U S - 0 .021 15 .16 - 3 . 28 - 0 . 87 0 .009

( - 2.20) (3.69) ( - 2.15 ) ( - 0.42 ) (1.49)

B. V a r i a n c e e q u a t i o n s a n d c o r r e l a t i o n

a. 103 b c dx d2 r

G E 0 . 70 5 0 . 1 30 0 . 7 4 0 - 0 . 1 8 4 0 . 05 3 0 . 35 3(1.91) (2.57) (8.75) ( - 1.92) (1.66) (8.39)

F R 0 . 5 5 8 0 . 0 8 6 0 . 6 5 7 0 . 0 0 9 0 . 0 3 7 0 . 4 0 7

(1 .00) (1 .38) (2 .35) (0 .11) (0 .68) (8 .54)

U K 0 . 1 9 9 0 . 1 1 8 0 . 6 3 0 - 0 . 0 1 8 0 . 0 7 9 0 . 4 6 9

(0 .57 ) (1 .70 ) (3 .61 ) ( - 0 .2 2 ) (1 .76 ) (11 .4 )

S W 0 .1 9 3 0 . 0 1 0 0 .9 7 5 - 0 . 0 9 1 0 . 01 5 0 .5 0 8

(2.95) (0.12) (86.6) ( - 4.46 ) (4.28) (15.3)

JA - 0 .007 0 .070 0 .901 - 0 . 002 0 .016 0 .297

( - 0 . 0 1 ) ( 2 .6 2) ( 2 2 .9 ) ( - 0 . 1 7 ) ( 1.0 7) ( 5.4 3)

C A - 0 . 5 5 0 . 12 5 0 . 43 5 0 . 22 5 0 . 1 26 0 . 7 2 3

( - 1.18) (2.28) (1.80) (1.20) (1.98) (28.5)

U S 0 .2 7 1 0 . 05 5 0 . 74 7 - 0 . 0 4 4 0 .0 3 5

(1 .09 ) (1 .58 ) (4 .34 ) ( -0 .64 ) (1 .16 )

Est im at ion of b iva r ia te projec tions :

R I = b~o + b] D I ~ _ I i i i , i ib 2 S T , - 1 + b a L T , - a + b a J A N , + e , ( 2 )

h[ = a i + b ' e i _ l e ~ - a + c l h i - i - t- d ° Z[ _ l a n d h i ' ' = ri'U'x/h~rx/hrs ( 3 )

where RI is the excess re turn for m arke t i in pe r iod t , hi i s the co ndi t ion a l va r iance of marke t i , h i " i s the

c ond i t i ona l c ova r i a nc e be t we e n ma rke t i a nd t he US D I V e _ 1, S T y _ l , L T [ _ a a n d J A N t are respectively the

dividen d y ie ld , the sh or t - te rm in te res t ra te , the long- te rm in te res t ra te of count ry i obse rved in t - 1 anda Jan uary du m m y tha t t akes the va lue one i f t i s the m on th of Janua ry an d ze ro o the rwise . The t -s ta ti st ic s

adjus ted for heteroscedast ic i ty are rep orted in parentheses. Lik is the value of the log-likelihood of the

biva r ia te mode ls . Th e pe r iod of e s t ima t ion is 1 /1960-8/1990. Es t im a t ion result s for the U SA are those

ob t a i ne d for t he U K / U S pa i r.

10 J o u r n a l o f I n t er n a t io n a l M o n e y a n d F i n a n ce 1 9 9 5 V o l u m e 1 4 N u m b e r 1

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I s t h e c o r r e l a t i o n i n i n t e r n a t i o n a l e q u i t y r e t u r n s c o n s t a n t ? : F L o n g h t a n d B S o l n i k

t o b e a l l p o s i t i v e a s t h e v a r i a b l e s a r e a l w a y s p o s i t i v e . T h i s i s n o t s a t i s f a c t o ry

f r o m a n e c o n o m i c v i e w p o i n t a s it w o u l d r u l e o u t t h e p o s s i b i l i ty o f a n e g a t i v e

i n f lu e n c e o f o n e o f t h e v a r i a b l e s o n t h e v a r i a n c e o r c o v a r i a n c e . N e g a t i v e

c o e f f i c i e n ts c o u l d s t il l l e a d t o p o s i t i v e d e f i n it i v e n e s s o f t h e c o v a r i a n c e m a t r i x o v e r

t h e s a m p l e s p a c e . I n p r a c t ic e , w e n e v e r e n c o u n t e r e d t h e p r o b l e m o f a n e g a t iv e

c o n d i t i o n a l v a r i a n c e i n o u r s a m p l e o r f o r a n y p l a u s i b l e v a l u e o f t h e i n f o r m a t i o n

v a r i a b l e s .

R e s u l t s o f t h e e s t i m a t i o n a r e g i v e n in T a b l e 3 . T h e t o p p a n e l g i v e s th e

p a r a m e t e r s o f t h e m e a n e q u a t i o n s . T h e b o t t o m p a n e l g iv e s t h e p a r a m e t e r s o f t h e

c o v a r i a n c e e q u a t i o n s . A s m e n t i o n e d a b o v e , t h e s e a r e t h e r es u l ts o f a b i v a r i a t e

e s t i m a t i o n o f t h e U S A a n d a fo r e ig n c o u n t ry . T h e l a s t l in e g iv e s t h e r e s u l ts o f

t h e e s t im a t i o n o f t h e U S A d e r iv e d f r o m t h e U K / U S e s ti m a t io n . T h e v a l u e s f o r

t h e U S A d e r i v e d f r o m t h e o t h e r b i v a r i a t e m o d e l s a r e v e r y si m il ar .

T h e r e s u lt s fo r t h e c o n d i t i o n a l e x p e c t e d r e t u r n s ( P a n e l A ) c o n f i r m p r e v i o u sf i n d in g s . T h e c o e f f i c ie n t s o f t h e d i v i d e n d y i e l d t e n d t o b e p o s i t i v e a n d t h e

c o e f f i c ie n t s o f t h e s h o r t - t e rm i n t e r e s t r a t e t e n d t o b e n e g a t i v e ; t h e r e is a p o s i t i v e

J a n u a r y s e a s o n a l i n a l l c o u n t r i e s .

T h e c o e f fi c ie n t s f o r th e v a r i a n c e e q u a t i o n s ( P a n e l B ) s h o w s ig n i fi c an t G A R C H

e f fec t s f o r m a n y c o u n t r i e s . T h e d i v i d e n d y i e l d te n d s t o h a v e m i x e d s i g n s 1 ° i n t h e

v a r i a n c e e q u a t i o n s . T h e re i s o n e n e g a t i v e c o e f f i c ie n t f o r S w i t z e r l a n d , s t a t i s t ic a l l y

s ign i f i can t a t th e 1 pe rce n t l eve l . Th e in te r es t ra t e ha s a pos i t iv e coe f f ic ien t in a ll

v a r i a n c e e q u a t i o n s . T h e c o e ff i ci e n ts h a v e t h e s a m e s ig n f o r e a c h c o u n t r y , b u t

t h e i r s i g n i f ic a n c e le v e l i s s o m e w h a t m a rg i n a l . T h e f a c t t h a t t h e c o n d i t i o n a l

v a r i a n c e i s p r e d i c t a b l y l o w e r i n p e r i o d s o f h i g h d i v i d e n d y i e ld s c o u l d h a v e ap l a u s i b l e e x p l a n a t i o n : w i t h h i g h d i v i d e n d y ie ld s , m o r e o f t h e c u r r e n t v a l u e o f a

f i r m i s d e r i v e d f r o m n e a r - t e r m d i v i d e n d s , w h i c h c a n b e r e g a r d e d a s m o r e

p r e d i c t a b l e t h a n r e m o t e f u t u r e d i v id e n d s . T h e p o s i t i v e re l a t io n b e t w e e n v o l a t il i ty

a n d i n t e r e s t r a t e l e v el s i s n o t s u rp r i s i n g e i th e r . I n f l a t i o n a ry p e r i o d s l e a d t o h i g h e r

vo la t i l i ty in f inanc ia l p r ices .

W e t e s t t h e s i g n if i ca n c e o f t h e v a r i o u s f a c t o r s b y e s t i m a t i n g t h r e e n e s t e d m o d e l s .

T h e s i m p l e s t m o d e l i s t h e b i v a r i a t e h o m o s c e d a s t i c m o d e l w i t h n o i n f o r m a t i o n

v a r i a b le s ; i t r e q u i r e s t h e e s t im a t i o n o f o n l y t w o u n c o n d i t i o n a l m e a n t e r m s a n d

t h r e e c o v a r i a n c e t e r m s . I t s c o m p u t e d l i k e l i h o o d f u n c t i o n i s r e f e r r e d t o a s L i k l .

T h e s e c o n d m o d e l i s a b i v a r ia t e h o m o s c e d a s t i c m o d e l w i t h i n f o r m a t io n v a r i ab l e si n t h e m e a n e q u a t i o n . I t s c o m p u t e d l i k e l i h o o d f u n c t i o n i s r e f e r r e d t o a s L i k 2 .

T h e b a s e m o d e l i s t h e b i v a r i a t e G A R C H ( 1 , 1 ) w i t h i n f o r m a t i o n v a r i a b l e s i n t h e

m e a n a n d v a r i a n c e e q u a t i o n s a n d c o n s t a n t c o n d i t i o n a l c o r r e l a t i o n . T h e

e s t i m a t i o n o f t h is b a s e m o d e l is r e p o r t e d i n T a b l e 3 a n d t h e c o m p u t e d l i k e l ih o o d

fu n c t i o n i s r e f e r r e d t o a s L i k 3 . T h e t h r e e s p e c i f i c a t i o n s a r e n e s t e d , s o w e c a n

p e r fo rm l i k e l i h o o d - r a t i o t e s t s (L R t e s t h e r e a f t e r ) .

T h e r e s u l t s r e p o r t e d i n T a b l e 4 in d i c a t e t h a t b o t h t h e m o d e l l i n g o f t h e

c o n d i t i o n a l e x p e c t e d r e t u r n a n d v a r i a n c e a r e s ig n if ic a n t. T h e f ir st s e c ti o n o f T a b l e

4 g iv e s t h e v a l u e o f t h e l i k e l i h o o d f u n c t i o n o f t h e s i m p l e b i v a r i a t e h o m o s c e d a s t i c

m o d e l . T h e s e c o n d s e c t i o n g i ve s t h e v a l u e o f t h e l i k e l i h o o d f u n c t i o n o f t h e b i v a r i a t eh o m o s c e d a s t i c m o d e l w i t h i n f o r m a t i o n v a r i a b l e s i n t h e m e a n , a s w e l l a s t h e

p - v a l u e o f t h e L R t e st a g a i n s t t h e n u l l o f th e s i m p l e m o d e l . T h e h y p o t h e s i s o f a

c o n s t a n t e x p e c t e d r e t u rn is r e j e c t e d a t t h e 1 p e r c e n t l e v e l i n a ll ca s e s. T h e t h i rd

J o u l v la l o /" h l t e r n a t i o n a l M o n e y a n d F i n a n c e 1 9 9 5 V o l u m e 1 4 N u m b e r 1 11

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Is the correlation in international equity returns constant?: F Longin and B Solnik

TABLE 4. L ikel ihoo d ra t io tes ts of b ivar ia te G A R C H specificat ions .

1 . Log- l ike l ihood o f b iva r ia te homoscedas t i c

M a r k e t G E / U S F R / U S U K / U S S W / U S J A /U S C A / U S

L ik l 1225.5 1186.9 1184.5 1264.4 1228.1 1355.6

2 . B iva r ia te cond i t iona l mean /ho mo scedas t i c


Li k2 1237.5 1200.2 1204.2 1282.2 1246.0 1368.9

p-v alu e/m od el 1 0.002 0.001 0.000 0.000 0.000 0.001

3. Base model


Lik 3 1261.3 1209.9 1246.7 1298.1 1255.4 1406.6

p-v alu e/m od el 1 0.000 0.000 0.000 0.000 0.000 0.000

p-v alu e/m od el 2 0.000 0.013 0.000 0.001 0.016 0.000

s e c t i o n g i v es t h e v a l u e o f t h e l i k e l i h o o d f u n c t i o n o f t h e b a s e m o d e l a s w e l l a s

L R t e s t a g a i n s t t h e a l t e rn a t i v e o f t h e t w o h o m o s c e d a s t i c m o d e l s . B o t h s i m p l e r

m o d e l s a r e r e je c te d . W e s e e t h a t t h e h y p o t h e s i s o f c o n s t a n t v a r i a n c e s i s r e j e c te d

a t t h e 5 p e r c e n t l e v e l i n a l l c a s e s . I t s h o u l d b e s t r e s s e d t h a t w e e s t i m a t e b i v a r i a t e

m o d e l s o f t h e U S a n d f o r e ig n e q u i t y m a r k e t s ; t h e p r e d i c t a b i l i t y in t h e c o n d i t i o n a l

U S e x p e c t e d r e t u r n a n d v a r i a n c e a f fe c ts t h e s i g n if ic a n c e le v e ls r e p o r t e d f o r e a c h

b i v a r i a t e e s t i m a t i o n .W e c a n te s t w h e t h e r t h e e s t im a t e d G A R C H p a r a m e t r i z a t i o n p r o v i d e s a n

a d e q u a t e d e s c r i p t i o n o f t h e h e t e ro s c e d a s ti c i ty b y p e r f o r m i n g L j u n g - B o x

p o r t m a n t e a u m i s s p e c i f i c a t i o n t e s t s o n t h e s q u a r e d r e s i d u a l s a s s u g g e s t e d b y L i

a n d M c L e o d (1 98 3). T h i s t e s t is p e r f o r m e d o n t h e s ta n d a r d i z e d s q u a r e d r e s i d u a l s

o f c o u n t r y i , e l e l / h I ' o b t a i n e d f o r t h e c o n s t a n t c o r r e l a t i o n s p e c i f i c a t i o n . T h e

L j u n g - B o x s t a t i s t i c s w i t h 2 0 l a g s r a n g e s f r o m 7 t o 1 5 f o r t h e s i x c o u n t r y - p a i r s ,

w h i l e t h e 5 p e r c e n t c r i t i c a l l e v e l i s 3 1 . 4 4 . W e c a n n o t r e j e c t t h e s p e c i f i c a t i o n o f

v a r i a n c e s a t t h i s c o n f i d e n c e l e v e l f o r a n y c o u n t r y . A m o r e d i r e c t t e s t h a s b e e n

s u g g e s t e d b y B o l l e r sl e v (1 99 0). T h e G A R C H p a r a m e t r i z a t i o n a s s u m e s t h a t a l l

r e l e v a n t p a s t i n f o r m a t i o n F t - 1 i s r e f le c t ed in t h e G A R C H e s t i m a t e o f t h e v a r i a n c e

( 6 ) E ( e I • e ~ [ F t _ 1 ) = h l " j .

T h i s c a n b e t e s t e d b y i n c l u d i n g i n t h e i n f o r m a t i o n s e t F,_ 1 p a s t r e s id u a l s a n d

re g re s s i n g e l e l / h l - 1 o n 1 / h ~ , e i _ l e ~ _ l / h l , . . . , e i _ k e i _ k . 2 / h ~ . S t o p p i n g a t k = 5 , w e

t e s t w h e t h e r t h e e s t i m a t e d r e g r e s s i o n c o e f f i c i e n t s a r e d i f f e r e n t f r o m z e r o w i t h a

F - t e s t . T h e 5 p e r c e n t c r i t i c a l v a l u e fo r a F (6 , 3 6 1 ) i s 2 . 1 3 . T h e F - t e s t s r e p o r t e d i n

T a b l e 5 r a n g e f r o m 0 .2 8 fo r C a n a d a t o 1 . 61 f o r F r a n c e a n d d o n o t l e a d t o a

r e j e c t i o n o f t h e c o n s t a n t c o r r e l a t i o n s p e c i f i c a ti o n . A s i m i l a r t e s t i s p e r f o rm e d

f o r t h e c r o s s - p r o d u c t o f r e s id u a l s. W e r e g r e s s e ~ . e ~ / h i ' J - 1 o n 1 / h ~ J ,i • e ~ l / h i ' J , , i j i o ' / l , ~ i , J a n d ~ _ l e 1 / h ~ " j . T h e 5e t - 1 . . . . e t - 5 " e t - s / h ~ " j as we l l a s e t_ 1~t- 1/,,t

p e r c e n t c r i t i c a l v a l u e fo r a F (8 , 3 5 9 ) i s 1 . 9 7 a n d a l l F - t e s t s f a l l b e l o w t h a t v a l u e

a s s e en i n T a b l e 5. A l t o g e t h e r , n o e v i d e n c e is f o u n d t o r e j e c t o u r b a s e m o d e l , u s i n g


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T AB L E 5 . H e t e r o s c e d a s t i c i t y s p e c i f i c a t i o n t e s t s.

S q u a r ed r e si d ua l s G E F R U K S W J A C A

F -t es t 0.571 1.611 1.374 0.469 0.896 0.283

p- va lu e (0.754) (0.143) (0.224) (0.831) (0.498) (0.945)

C r o s s- p ro d u c t G E / U S F R / U S U K / U S S W / U S J A / U S C A / U S

F- te st 0.592 0.658 0.825 1.195 1.296 0.451

p- va lu e (0.785) (0.728) (0.581) (0.301) (0.244) (0.890)

u s

0.518(0.794)

This table gives the results of heteroscedasticity specification tests as suggested in Bollersleu (1990),

Stan dard ized squared residuals an d cro ss-prod uct of residuals are regressed on lagged variables. The

residuals are from th e base mo del (a bivariate GA RC H (1, 1) with consta nt co ndition al correlation). F-tests

are reported with their p-values in parentheses.

s t a n d a r d h e t e r o s c e d a s t i c i t y t es ts . H o w e v e r , m o r e p o w e r f u l te s ts c a n b e d e s i g n e d ,

b y a n e x p l ic i t m o d e l l i n g o f t h e d e v i a t i o n s f r o m o u r c o n s t a n t c o r r e l a t i o n b a s e

m o d e l .

I I . I s the c ond i t i ona l c or r e la t i on c ons tant?

T h e r e a r e m a n y r e a s o n s w h y th e in t e r n a ti o n a l m a r k e t c o r r e la t io n s h o u l d n o t

r e m a i n c o n s t a n t o v e r ti m e . W e e x a m i n e t h r e e p o t e n t i a l s o u r c e s o f d e v i a t i o n f r o m

o u r b a s e m o d e l o f c o n s t a n t c o n d i t i o n a l c o r r e la t i o n : a t i m e t re n d , t h e p r e s e n c eo f t h r e s h o l d a n d a s y m m e t r y , a n d t h e i n fl u e n c e o f e c o n o m i c v a ri a b le s . D u e t o t h e

l a rg e n u m b e r o f p a r a m e t e r s t o b e e s t im a t e d w e h a v e t o s t u d y s e p a r a te l y e a c h

c a u s e o f d e v i a t i o n f r o m t h e b a s e m o d e l .

II.A. A time trend

I t is o f t e n s t a te d t h a t t h e p r o g r e s s iv e r e m o v a l o f i m p e d i m e n t s t o i n t e r n a t i o n a l

i n v e s t m e n t a s w e l l a s t h e g r o w i n g p o l i t i c a l , e c o n o m i c a n d f i n a n c i a l i n t e g r a t i o n

a f fe c ts i n t e r n a t i o n a l m a r k e t l i n k a g es . M o r e i n t e g r a t e d e c o n o m i e s c o u l d m e a n

t h a t n a t i o n a l f ir m s a re m o r e a n d m o r e i n f l u e n c e d b y g l o b a l f a c to r s . T h e e x t e n to f i n t e r n a t i o n a l a c t iv i t ie s b y c o m p a n i e s t h e m s e l v e s i s g r o w i n g . M o s t c o m p a n i e s

c a n n o w b e r e g a r d e d a s a d iv e r si fi e d p o r t fo l i o o f i n t e r n a t i o n a l a c t iv i ti e s t h r o u g h

t h e i r e x p o r t s a n d t h r o u g h f o r e ig n im p l a n t a t i o n . T h e i r s t o c k p r i c e s h o u l d b e h a v e

l ik e t h a t o f a n i n t e r n a t i o n a l l y d i v e rs i fi e d p o r t fo l i o a n d , h e n c e , b e m o r e c o r r e l a t e d

w i t h t h a t o f o t h e r f ir m s w o r l d w i d e . T h i s c o u l d l e a d t o a p r o g r e s s i v e i n c re a s e i n

t h e i n t e r n a t i o n a l c o r r e l a t i o n o f e q u i t y m a r k e t s .

W e u s e o u r l o n g p e r i o d o f t im e t o t e s t t h is i n c r e a s e in c o r r e la t i o n . T h e r e a r e

n o s p ec i fi c e v e n t s ( o r t o o m a n y o f t h e m ) t h a t s h o u l d b e u s e d a s c u t o f f p o i n t s o r

s t r u c t u r a l b r e a k s ( th e m o n t h l y f r e q u e n c y o f o u r d a t a w o u l d a l s o li m i t t h e p o w e r

o f s t u d i e s o v e r s h o r t s u b - p e r io d s ) . W e u s e a s i m p l e t e s t to d e t e c t a p r o g r e s s i v ei n c r e a s e i n c o r r e l a t i o n o v e r t h e p a s t 3 0 y e a r s . W e a u g m e n t o u r b a s e m o d e l t o

i n c l u d e a l i n e a r t i m e - t r e n d i n t h e c o r r e l a t i o n s p e c i f i c a t i o n a n d t e s t t h e n u l l

h y p o t h e s i s t h a t t h i s c o e f fi c i e n t i s z e r o . I n o t h e r wo r d s , t h e c o v a r i a n c e t e r m o f

Journal of International Mon ey and Finance 1995 Volume 14 Number 1 13

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Is" t h e c o r r e l a t io n i n i n t e r n a t i o n a l e q u i t y r e t u r n s c o n s t a n t ? . F L o n g i n a n d B S o l n i k

e q u a t i o n ( 3 ) is n o w w r i tt e n as:

i , u s i u s( 7 ) h l " s = ( r ~ u s + r I t ) x / h t x / h t .

T o r e m o v e p o t e n t i a l b i a s e s c r e a t e d b y a st r u c t u r a l i n c r e a s e in c o n d i t i o n a l v a r i a n c e ,

w e a l s o a d d a t r e n d t e r m i n e a c h v a r i a n c e e q u a t i o n . N e e d l e s s t o s a y , t h i s

s p e c i f i c a t i o n is a s i m p l i s t ic m o d e l l i n g o f t h e i n c r e a s e i n c o r r e l a t i o n o v e r t im e ,

a n d o t h e r s p e c i f ic a t io n s o f t h e t r e n d c o u l d h a v e b e e n u s e d . I n t h e a b s e n c e o f a

f o r m a l m o d e l , o u r s o le p u r p o s e i s t o t e s t t h e e x is t e n c e o f a t r en d . E s t i m a t i o n o f

t h e a u g m e n t e d m o d e l a r e r e p o r t e d i n T a b l e 6 , w h e r e w e o n l y r e p o r t t h e c o e ff ic i en t s

o f t h e t i m e t r e n d s . T h e c o e f f ic i e n t s f o r th e v a r i a n c e s a r e s m a l l a n d s t a t i st i c a l ly

i n s i g n i f i c a n t . T h e r e i s n o s e c u l a r i n c r e a s e i n e x p e c t e d m a r k e t v o l a t i l i t y . T h e

G A R C H ( 1 , 1 ) s p e c if ic a ti o n s e em s t o a d e q u a t e l y c a p t u r e t h e t im e e v o l u t i o n o f t h e

m a r k e t v a r i a n c e s a n d n o a d d i t i o n a l t i m e - t r e n d n e e d s t o b e a d d e d i n t h e v a r i a n c e

e q u a t i o n . T h e c o n c l u s i o n i s q u i t e d i f f e r e n t f o r t h e c o r r e l a t i o n , a n d h e n c e t h ec o v a r i a n c e , a c r o s s m a r k e t s . T h e r e i s a p o s i t iv e t i m e - t r e n d i n c o n d i t i o n a l

c o r r e l a t i o n f o r a l l c o u n t r i e s . T h e t r e n d i s s t a t i s t i c a l l y s i g n i f i c a n t a t t h e 5 p e r c e n t

l e v e l f o r f o u r c o u n t r i e s o u t o f s ix . A s im i l a r c o n c l u s i o n i s o b t a i n e d i f we e s t i m a t e

a G A R C H m o d e l w i t h a t r e n d s o l e l y i n t h e c o r re l a t i o n b u t n o t i n t h e v a ri a n c e s.

I n o t h e r w o r d s , t h e i n t e r n a t i o n a l c o r r e l a t i o n s e e m s t o b e i n c r e a s i n g o v e r t i m e ,

e v e n af te r t h e v a ri a n c e t e r m s h a v e b e e n m o d e l l e d w i t h a G A R C H p a r a m e t r iz a t io n .

T h e a v e r a g e i n c r e a s e i n c o r r e l a t i o n o v e r 3 0 y e a r s i s 0 . 3 6 , o r s l i g h t l y m o r e t h a n

0 .0 1 p e r y e a r . O b v i o u s l y s u c h a c o n s t a n t l in e a r t r e n d i s n o t c o n s i s t e n t w i t h t h e

d e f i n it i o n o f a c o r r e l a t i o n c o e ff ic i en t . O t h e r f o r m s o f t r e n d c o u l d b e m o d e l l e d ,

b u t n o t h e o r y e x i st s o f t h e e x a c t f o r m o f t h is t r e n d . W e t r i ed a n e x p o n e n t i a l t r e n dq

TABLE 6. T im e- tren d in c o r r e l a t i o n .


d i 0.01 0.21. 0.35 - 0.0 0 0.01 0.0 7

(0 .44) (0 .98) (1 .75) ( - 0 .0 3 ) (0 .43) (1 .70)

d "s 0 .17 0 .15 0 .20 0 .17 0 .23 0 .10

(1.03) (0.96) (1.06) (0.96) (1.05) (1.52)

ro 0 .27 0 .13 0 .09 0 .41 0 .10 0 .65

(3.16) (1.22) (0.95 ) (5.39) (0.99) (11.61 )

r~ 0 .20 0 .49 0 .76 0 .25 0 .38 0 .16

(1.55) (3.1 5) (6.13) (2.40) (2.33) (1.82)

L R tes t 10 .0 17 .4 30 .4 11 .2 17 .8 11 .2

p- va lu e (0 .019) (0 .001) (0 .000) (0 .011) (0 .001) (0 .011)

This table g ives the es t ima tes of the aug me nted m ode l wi th t ime-t rend. This mode l i s s imi la r to the b ase

mode l w i th a n a dd i t i ona l t ime - t r e nd i n t he va r i a nc e e qua t ions (d+ or cou ntry i and d u+ for th e U S) a nd

in the corre la t ion . The co rre la t ion i s now es t im a ted as :

h~ "~ = (r~ u~ + ril""~t)~/h~x/ h'~+ ( 7 )

T-stat ist ics appea r be low the est im ated coeffic ients. Th e l ikel ihoo d rat io (p-va lue in parentheses) is a test

of the augmented mode l aga ins t the base mode l .

14 J o u r n a l o f I n te r n a ti o n a l M o n e y a n d F i n a n c e 1 99 5 V o l u m e 1 4 N u m b e r 1

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I s t h e c o r r e l a t io n i n i n t e r n a t i o n a l e q u i t y r e t u r n s c o n st a nt ?. " F L o n g i n a n d B S o l n i k

o f t h e f o r m b y m o d e l l i n g t h e c o r r e l a t i o n a s f o ll o w s :

- a t i u s( 8 ) h l ""~ = ( r T M + r ''"~ (1 -- e ) ) ~ / h , x / h , .

I f a is p o s i t i v e , c o r r e l a t i o n v a r i e s f ro m r a t t h e b e g i n n i n g o f t h e p e r i o d t o

r0 + r l ( 1 - e - ° r ) a t t h e e n d o f th e p e r i o d T ; i f t h e t w o b o u n d s ro a n d r o + r l a r e

b e t w e e n - 1 a n d + 1, t h e n t h e c o r r e l a t i o n i s a l w a y s d e fi n e d . T o a s s u r e t h e

c o n v e r g e n c e o f t h e a l g o r i th m , a c o n s t r a i n t c a n b e i m p o s e d o n r o a n d r o + r l s u c h

t h a t t h e c o r r e l a t i o n is a l w a y s d e f i n ed . E m p i r i c a l ly f o r t h e p a i r J A / U S , w e f o u n d

a c o r r e l a t i o n i n c r e a si n g f r o m - 0 . 3 9 7 t o 0 .3 5 6 a t a n e x p o n e n t i a l r a t e 1 1.8 18 . t l

F o r t h e o t h e r p a i r s o f c o u n t r ie s , t h e c o n s t r a i n t s w e r e b i n d i n g o u t o f s a m p l e

( G E / U S a n d F R / U S ) o r i n s a m p le ( U K / U S , S W / U S a n d C A / U S ) w i th a n e g at iv e

v a l u e fo r t h e r a t e o f c o n v e rg e n c e ( a < 0) . S u c h a r e s u l t c o u l d b e e x p l a i n e d b y a

s h a r p i n c r e a s e in c o r r e l a t i o n a t t h e e n d o f t h e p e r i o d ( th e e ig h ti es ). T h e p r o p o s e d

s i m p l e e c o n o m e t r i c m e t h o d o l o g y ( a l i n e a r t i m e - t r e n d ) h o w e v e r s a t i s f i e s o u ro b j e c t i v e t o t es t, a n d r e je c t, th e n u l l h y p o t h e s i s o f a c o n s t a n t c o n d i t i o n a l

c o r r e l a t i o n .

l l . B . T h r e s h o l d a n d a s y m m e t r y in t he c o n d i t io n a l c o rr e la t io n

I n t e r n a t i o n a l m a r k e t l i n k a g e s a re d u e to c o m m o n f a c t o r s t h a t a f f ec t a ll e c o n o m i e s

a t t h e s a m e t im e . I t is o f te n c l ai m e d t h a t t h e r e a r e p e r i o d s w h e n i n t e r n a t i o n a l

f a c t o r s d o m i n a t e p u r e l y d o m e s t i c f a c t o r s a n d v i c e v e r s a .

T h e c o n s t a n t c o r r e l a t i o n G A R C H m o d e l a s s u m e s t h a t t h e c o n d i t i o n a l

c o v a r i a n c e , h i "~, e s t i m a t e d f ro m i n fo rm a t i o n a v a i l a b l e a t t i m e t - 1 , is e q u a l t o

a c o n s t a n t c o r r e l a t i o n t im e s t h e p r o d u c t o f t h e tw o c o n d i t i o n a l s t a n d a r di u sd e v i a t i o n s ~ / h t x / h ~ f o l l o w i n g a f i r s t o r d e r G A R C H p r o c e s s . I t i s o f t e n c l a i m e d

t h a t t h e i n t e r n a t i o n a l c o r r e l a t i o n i n c r e as e s in p e r i o d s o f h i g h m a r k e t t u r b u l e n c e ,

w h e n i n t e r n a t i o n a l f a c t o r s d o m i n a t e . F o r e x a m p l e , a l l m a r k e t s w e n t d o w n

t o g e t h e r d u r i n g t h e s e c o n d o i l s h o c k o f 1 9 7 4 a n d i n O c t o b e r 1 98 7, a n d w e n t u p

a t t h e e n d o f th e G u l f W a r . T h i s h y p o t h e s is c a n b e t e st e d b y i n t ro d u c i n g a

t h re s h ol d in th e c o n s t a n t co r r el a ti o n G A R C H m o d e l. T h r es h o l d G A R C H m o d e l s

h a v e b e e n e x t e n s i v e l y u s e d i n t h e u n i v a r i a t e c a s e b u t n o t i n th e m u l t i v a r i a t e c a s e

( se e A p p e n d i x B fo r a d is c u s s i o n a n d r e s u lt s o f t h e u n i v a r i a t e a s y m m e t r i c t h r e s h o l d

G A R C H m o d e l f o r t h e s e v e n c o u n t r i e s u n d e r s t u d y ) . T o t e s t t h e h y p o t h e s i s o f

h i g h e r in t e r n a t i o n a l c o r r e l a t i o n d u r i n g t u r b u l e n t p e r i o d s , w e i n t r o d u c e at h r e s h o l d e f f e ct i n o u r b i v a r i a t e c o n s t a n t c o r r e l a t i o n G A R C H s p e c if i ca t io n . W i t h

t h is t h r e s h o l d o n c o r r e l a ti o n , t h e c o v a r i a n c e t e r m o f t h e G A R C H s p e c i fi c a ti o n

c a n b e w r i t t e n a s :

h , - ( r o + r 1 S t _ l ) x / h , x / h , ,9 > i . . . . i , u s i , u s i u s

w h e r e S ,_ 1 i s a d u m m y v a r i a b l e t h a t t a k e s t h e v a l u e 1 i f t h e e s t i m a t e d c o n d i t i o n a l

v a r i a n c e o f t h e U S m a r k e t is g r e a t e r t h a n i ts u n c o n d i t i o n a l v a l u e a n d 0 o t h e rw i s e .

T h e u n c o n d i t i o n a l v a r i a n c e o f i n n o v a t i o n s f r o m t h e b a s e m o d e l i s t a k e n a s t h e

e x o g e n o u s t h r e s h o l d . I n o t h e r w o r d s , t h e t i m e - t i n t e r n a t i o n a l c o r r e l a t i o n i s

c o n d i t i o n a l o n t h e t i m e - t v o l a t il i ty o f t h e U S m a r k e t ; n o t e t h a t b o t h t h e c o r r e l a t i o na n d t h e U S v o l a t i l i t y a r e e s t i m a t e d u s i n g o n l y i n f o r m a t i o n o b s e r v a b l e a t t i m e

t - 1 . T h e c o e f f i c i e n t q w i ll b e p o s i t i v e i f t h e c o r r e l a t i o n i n c r e a s e s w h e n t h e

c o n d i t i o n a l U S v a r i a n c e i s h i g h ; it w il l b e z e ro i f t h e r e i s n o t h r e s h o l d e f fe c t.

J o u r n a l o f I n t er n a t io n a l M o n e y a n d F in a n c e 1 99 5 V o l u m e 1 4 N u m b e r 1 15

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I s the cor r e la t ion in in te r na t iona l equ i t y r e tur ns cons tan t? : F Long in a nd B So ln ik

TABLE 7. Th reshold in correlation.

LR test

ro rl r (p- value)

GE /U S 0.327 0.134 0.353 2.4

(5.52) (1.75) (0.121)

FR /U S 0.331 0.194 0.407 4.8(5.44) (2.43) (0.028)

U K /U S 0.468 0.057 0.469 0.6(9.34) (0.74) (0.438)

SW /US 0.458 0.192 0.508 8.0(8.70) (3.12) (0.010)

JA/US 0.265 0.101 0.297 2.2(3.82) (0.99) (0.138)

CA /US 0.729 0.024 0.723 1.0

(26.02) (0.65) (0.317)

The table gives the estimation of the bivariate GARCH(1,1) models with threshold

correlation. The correlation is conditioned on the size of the US expected variance:

i . u s - - i . u s i , u s i u s

h t - ( r o + r I S , _ O x /h t x /h t (9)

The coefficient r is the estimate from the base model with constant correlation, as

given in Table 3. The likelihood ratio test from the base model with constant

correlation is indicated in the last column, with p-value in parentheses.

T h e r e s u lt s o f t h e e s t i m a t i o n o f t h e t h r e s h o l d c o r r e l a t i o n s p e c i fi c a ti o n a r e

r e p o r t e d i n T a b l e 7 . T h e e s t i m a t e d c o e ff ic i en t r1 i s p o s i t i v e f o r a l l c o u n t r i e s a n d

i n d i v i d u a l l y s i g n i f i c a n t a t t h e 5 p e r c e n t c o n f i d e n c e l e v e l i n t wo c a s e s . T h e

m a g n i t u d e o f t h e c o e f f i c ie n t i s q u i t e l a r g e i n m o s t c a s e s . W e c a n i l l u s t r a t e t h e

r e su l t s i n th e c a s e o f F r a n c e . T h e c o n s t a n t c o r r e l a t i o n e s t i m a t e d w a s e q u a l t o

0 . 40 7 ; t h i s c o m p a r e s w i t h a c o n s t a n t t e r m ro o f 0 .3 3 1 a n d a t u r b u l e n c e e f fe c t rl

o f 0 .1 9 4. I n o t h e r w o r d s t h e c o r r e l a t i o n i s e s t i m a t e d t o b e e q u a l t o 0 .3 31 i n

p e r i o d s o f l o w v o l a t i li t y a n d 0 .5 2 5 i n p e r i o d s o f h ig h v o l a ti l it y . T h e a v e r a g e

c o r r e l a t i o n i n t h e s i x c o u n t r y - p a i r s w a s e q u a l t o 0 . 4 6 0 w h e n u s i n g t h e c o n s t a n t

c o r r e l a t i o n m o d e l . T h e a v e r a g e o v e r a ll c o u n t r i e s o f t h e c o r r e l a t i o n ro i s equa lt o 0 . 4 3 0 wh i l e t h e a v e r a g e t u r b u l e n c e e f fe c t rx i s e q u a l t o 0 . 1 17 . T h e c o r r e l a t i o n

c o e f fi c ie n t se e m s t o i n c r e a s e b y a b o u t 2 7 p e r c e n t i n p e r i o d s o f h i g h t u r b u l e n c e .

W e o n l y i n t ro d u c e d o n e e x o g e n o u s t h r e s h o l d a r b i t ra r i ly s et at t h e

u n c o n d i t i o n a l v a r i a n c e . W e w o u l d h a v e l i k e d t o u s e s e v e r a l t h r e s h o l d s b u t w e r e

l i m i t e d b y t h e s iz e o f o u r d a t a b a s e t o g e t r e l i a b le s t a t i s ti c a l r e s u l ts . W e a l s o

r e p l ic a t e d t h e s e te s t s b y c o n d i t i o n i n g t h e c o r r e l a t io n o n t h e c o n d i t i o n a l v a r i a n c e

o f t h e fo r e i g n m a r k e t r a t h e r t h a n t h a t o f t h e U S m a r k e t . T h e c o n c l u s i o n s w e r e

q u i t e s i m i l a r a n d t h e r e s u l t s a r e n o t r e p o r t e d h e r e .

W e c a n s a y m o r e a b o u t c o r r e l at i o n b y l o o k i n g a t a s y m m e t r y . I n th e p r e v i o u s

t h r e s h o l d G A R C H m o d e l , a p o s i ti v e o r n e g at iv e s h o c k ( e t - 1 ) o b s e r v e d a t t i m et - 1 h a s t h e s a m e i m p a c t o n c o r r e l a t i o n . I t i s i n t e r e s t i n g t o t e s t w h e t h e r n e g a t i v e

a n d p o s i t i v e s h o c k s h a v e a d i ff e re n t i m p a c t o n t h e c o n d i t i o n a l c o r r e l a t i o n . R a t h e r

t h a n c o n d i t i o n i n g t h e c o r r e l a t i o n o n t h e U S m a r k e t v o l a t i l it y ( a n d h e n c e i n d i r e c tl y

16 J o u r n a l o f I n t e r n a t i o n a l M o n e y a n d F i n an c e 1 99 5 V o l u m e 1 4 N u m b e r 1

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I s t he co r r el a ti on i n i n t e r na t i on a l equ i t y r et u r ns const an t ? ." F L ong i n and B So l n i k

o n t h e a b s o lu t e m a g n i t u d e o f e~ L ) , w e c o n d i t i o n t h e c o r r e l a t i o n o n b o t h t h e

s i g n a n d m a g n i t u d e o f p a s t 12 s h o c k s e~ ~_ r T h i s t h r e s h o l d , a s y m m e t r i c c o r r e l a t i o n

G A R C H s p e c i f i c a t i o n c a n b e w r i t t e n a s:

i , u s i , u s i , u s i , u s i u s( 1 0 ) h ~ 'U S ( r l S l , t _ l + r 2 S2 ,t _l + r 3 S3 ,t _t + r 4 S 4 , t _ t ) x / h , x / h t ,

w h e r e S k , t - 1 a r e d u m m y v a r i a b l e s t h a t t a k e t h e v a l u es :

S t , t - 1 = 1 i f e l ~_ x i s l e s s t h a n - a u s,

S 2 , t - 1 = 1 i f e u ~t_ l i s l e s s th a n O ,

S 3 , t - t = 1 i f e US t-t i s g r e a t e r t h a n O ,

S 4 , t - t = 1 i f e ust_~ i s g r e a t e r t h a n + ~ s ,

a n d z e r o o t h e r w i s e .

cr"~ ( th e u n c o n d i t i o n a l s t a n d a r d d e v i a t i o n o f th e i n n o v a t i o n s e "s f r o m t h e b a s e

m o d e l ) , - a " s a n d z e r o ar e t h e e x o g e n o u s t h r e s h o l d s u s e d f o r t h e a u g m e n t e d

m o d e l . N o t e t h a t t w o d u m m y v a r i a b l es w i ll b e e q u a l t o o n e f o r l ar g e n e g a t iv es h o c k s ( S L t _ ~ a n d S 2 , t- x ) a n d f o r l a rg e p o s i t iv e s h o c k s ( $ 3 , t _ 1 a n d S 4 a - 0 . T h i s

m o d e l a l l o w s o n e t o c a p t u r e a s y m m e t r y i n th e i m p a c t o f s h o c k s (r2 :/: r3) a n d

d i ff e r en t i m p a c t s f o r l a r g e a n d s m a l l s h o c k s ( r1 # 0 a n d r4 ¢ 0 ) . I f t h e i m p a c t o f

s m a l l a n d l a r ge s h o c k s a r e s im i l a r , w e s h o u l d f i n d t h a t t h e t w o c o e f f i c ie n t s q

a n d r a r e e q u a l t o z e r o .

T h e r e s u l t s a r e r e p o r t e d i n T a b l e 8 . T h e r e s u l t s c o n f i r m t h e p r e v i o u s f in d i n g s .

S e v e r a l c o e f f i c ie n t s q a n d r 4 a r e s i g n i f i c a n t l y p o s i t i v e , i n d i c a t i n g t h a t l a r g e s h o c k s

TABLE 8. A s y m m e t r y i n c o r r e l a t io n .

L R t e s t

r 1 r2 r3 r ( p - v a l u e )

G E / U S 0 . 3 0 7 0 . 3 1 3 0 . 3 2 7 0 . 3 0 4 1 0.2

(2.95) (5.10) (3.76) (2.33) (0.016 )

F R / U S 0 . 1 6 5 0 . 3 6 5 0 . 3 0 9 0 . 3 4 5 6. 2

(1.59) (5.92) (3.73) (2.92) (0.102 )

U K / U S 0 . 0 0 5 0 . 48 9 0 .4 5 2 0 . 11 7 0 . 6

(0.05) (8.34) (6.64) (0.91) (0.896)S W / U S 0 . 2 8 2 0 . 4 6 8 0 . 5 4 4 - 0 . 0 0 3 1 0.2

(3.54) (8.60) (8.95) ( - 0.36) (0.016)

J A / U S - 0 . 2 0 1 0 . 32 9 0 .3 3 2 0 .0 8 4 2 .8

( - 1.20) (3.82) (4.67) (0.46) (0.423 )

C A / U S - 0 . 1 1 5 0 .7 8 0 0.7 49 - 0 . 0 9 9 4 .8

( - 1.64) (27.06 ) (25.40 ) ( - 1.29) (0.187 )

T h i s t a b l e g iv e s t h e e s t i m a t i o n o f a b i v a r ia t e a s y m m e t r i c c o r r e l a ti o n G A R C H ( 1 , 1 ) w h e r e t h e c o r r e l a t io n

i s m o d e l l e d a s:

h~ . U s = i . u s i . u s r i . U s i . u s i u s( r l S l a - i +r2 S 2 , t - I + 3 S 3 . t - i +r4 S ,*a - l ) x / h t x / h t (10)

T h e c o r r e l a t i o n i s c o n d i t i o n e d o n t h e si g n a n d s i ze o f p a st U S s h o c k s . N o a s y m m e t r y c o r r e s p o n d s to t h e

case : r1 = r4 a n d r2 = r . N o t h r e s h o l d e f fe c t c o r r e s p o n d s t o t h e c a s e: r1 = r4 = 0. T h e l i k e l i h o o d r a t i o t e s t

c o m p a r i n g t h e a s y m m e t r i c m o d e l t o t h e b a s e m o d e l w i t h c o n s t a n t c o r r e l a t io n is i n d i ca t e d i n t h e la s t

c o l u m n , w i t h p - v a l u e i n p a r e n t h e s e s .

Journal of lnternational Money and Finance 1995 Volume 14 Number 1 17

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I s t h e c o r r e l a t i o n i n in t e r n a t i o n a l e q u i t y r e t u r n s c o n s t a n t ? : F L o n g i n a n d B S o l n i k

t e n d t o i n c r e a s e t h e c o n d i t i o n a l c o r r e l a ti o n . H o w e v e r w e h a v e l i tt le e v i d e n c e o f

a s y m m e t r y a s t h e c o e f f ic i en t s rE a nd r 3 a r e qu i t e s i m i l a r ; f u r t he r m or e w e f i nd no

e v i de nc e t ha t t he c oe f f i c ie n t q is s y s t e m a t i c a l l y g r e a t e r t ha n r4. T h e c o r r e l a t i o n

s e e m s t o i nc r e a s e i n pe r i ods o f h i gh t u r bu l e nc e ( f o ll ow i ng l a r ge pos i t ive o r ne ga t i ves hoc ks ) bu t i s no m or e s e ns it ive t o n e ga t i ve t h a n t o p os i t ive s hoc ks . 13

I I . C . I n f lu e n c e o f i n f o r m a t i o n v a r ia b l e s o n c o r r e la t io n

W e h a v e s e en t h a t t h e i n f o r m a t i o n v a r i a b l e s a ff e ct t h e c o n d i t i o n a l c o v a r i a n c e

m a t r i x . E v e n w i t h a c o n s t a n t c o r r e l a t i o n , t h e c o n d i t i o n a l c o v a r i a n c e b e t w e e nt w o n a t i o n a l m a r k e t s is a f u n c t i o n o f t h e i n f o r m a t i o n v a r i ab l e s, a s e a c h n a t i o n a l

c o n d i t i o n a l s t a n d a r d d e v i a t i o n i s. F o r e x a m p l e , i f a ll n a t i o n a l v a r i a n c e s in c r e a s e

i n pe r i od s o f h i gh i n t e r e s t r a t e s, t he c o va r i a n c e s w i ll i nc r e a s e i n pa r a l le l . T h er e m a i n i n g q u e s t i o n is w h e t h e r t h e c o v a r i a n c e s w i ll i n c r ea s e m o r e ( o r le ss) t h a n

t h e v a r ia n c e s . T h i s c a n b e i n v e s t ig a t e d b y t e s t in g a n a u g m e n t e d m o d e l , id e n t i c a l

t o t h e b a s e m o d e l b u t w i t h t h e h y p o t h e s i s t h a t t h e c o n d i t i o n a l c o r r e l a t i o n i t s e l f

is p r e d i c t a b l e b a s e d o n p a s t v a l u e s o f t h e i n f o r m a t i o n v a r i ab l e s. H e n c e t h e

c o v a r i a n c e e q u a t i o n i n m o d e l ( 3 ) is r e p la c e d by :

i us s( 1 1 1 h i'" ' ( r ' + g i' D I V ~ t _ l - u - i ' " s " l ~ . s ~ / , .i / h "= " Y 2 o t - l l ~ / n t ~ / t •

T h e i n f o r m a t i o n s e t i s s u p p o s e d t o b e e q u a l t o t h e U S d i v i d e n d y i e l d a n d

i n t e re s t r a te . E s t i m a t e s o f t h e c o r r e l a t i o n p a r a m e t e r s a r e g i v e n in T a b l e 9 . T h i s

t a b l e a ls o g i v es a l ik e l i h o o d - r a t i o t e s t o f t h e a u g m e n t e d m o d e l a g a i n s t t h e b a s em o de l . S e ve r a l o f t he c oe f f ic i e n ts g ' s a r e s i gn i f i c a n t a t t he 5 pe r c e n t l eve l bu t no t

a t t he 1 pe r c e n t l eve l. T h e p - va l ue s o f t he l i ke l i hoo d r a t i o t e st s s how a r e j e c t i on

o f t h e b a s e m o d e l f o r h a l f o f t h e c o u n t r y - p a i r s a t t h e 5 p e r c e n t le v el . W i t h o n e

T AB LE 9 . I n f o r m a t i o n v a r i a b l e s i n c o r r e l a t i o n .


r' 0.467 0.248 0.684 0.355 0.375 0.936

(2.24) (1.41) (4.35) (2.68) (1.78) (9.27)

g t - 1 1 4 . 4 - 8 . 4 7 - 1 5 7 . 6 1 . 3 7 - 1 4 7 . 7 - 9 6 . 2

( - 1 . 3 2 ) ( - 0 . 1 1 ) ( - 2 . 1 6 1 (0 .0 2) ( - 1 . 8 5 ) ( - 2 . 1 7 )

92 43.5 25.3 47.8 27.8 63.3 15.9

(2.23) (1.49) (2.91) (2.21) (3.33) (1.36)

L R tes t 0 .0 0 .2 7 .6 9 .6 8 .6 5 .6

p- va lu e (0.999) (0.999) (0.022) (0.008) (0.013) (0.060)

This tab le gives the estimates of the augmented m odel with information variables (US dividend yield and

US sh ort-term interest rate) in the conditio nal correlation. T he cond itiona l corre lation is now estimated as:h; . . . (r' + g~'"sOlV ~t ~_ 1 + ff~ ST '~t ~- t)~/h,~/h,i ,, ( 11 )

T-statis tics ap pea r below the estimated coefficients. The likeliho od ratio (p-value in parentheses) is a test

of the augmented model agains t the base m odel.

1 8 J o u r n a l o f I n t er n a t io n a l M o n e y a n d F i n a n ce 1 9 95 V o l u m e 1 4 N u m b e r 1

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I s t h e c o r r e l a t i o n i n i n t e r n a t i o n a l e q u i t y r e t u r n s c o n s t a n t ? . F L o n g i n a n d B S o l n i k

e xc e p t i on , t he s i gn pa t t e r n i s c ons i s t e n t . T he c ond i t i ona l c o r r e l a t i on i s p r e d i c t e d

t o i n c r e a s e i n p e r i o d s o f l o w d i v i d e n d y i e ld a n d h i g h i n t e r e s t r at e s.

T h i s r e s u l t is c o n s i st e n t w i t h t h e r e l a t i o n b e t w e e n c o n d i t i o n a l c o r r e l a t i o n a n d

v a r i a n c e f o u n d i n t h e p r e v i o u s s e c ti o n . F o r e x a m p l e , w e f o u n d t h a t t h e c o n d i t i o n a lva r i a n c e i nc r e a s e s w i t h t h e le ve l o f i n t e r e s t r a t e s a nd t ha t t he c o r r e l a t i o n i nc r e a s e s

i n p e r i o d s o f h ig h v o l a t il it y . W e c o n f i r m h e r e t h a t t h e c o n d i t i o n a l c o r r e l a t i o n is

h i gh e r i n pe r i ods o f h i gh i n t e r e s t r a t e s.

III. Sum m ary and conc lus ions

W e s t u d i e d t h e c o r r e l a t i o n o f m o n t h l y e x c e ss r e t u r n s f o r se v e n m a j o r c o u n t r i e s

o v e r t h e p e r i o d 1 9 6 0 -9 0 . W e f in d th a t t h e i n t e r n a t i o n a l c o v a r i a n c e a n d c o r r e l a t i o n

m a t r i c e s a r e u n s t a b l e o v e r t i m e . A m u l t i v a r i a t e G A R C H ( 1 , 1 ) m o d e l w i t h

c o n s t a n t c o n d i t i o n a l c o r r e l a t i o n h e lp s c a p t u r e s o m e o f t h e e v o l u t io n i n t h e

c o n d i t i o n a l c o v a r i a n c e s t r u c t u r e . W e i n c l u d e i n f o r m a t i o n v a r i a b l e s i n t h e m e a n

a n d v a r i a n c e eq u a t io n s . T h e v o l a t il it y o f m a r k e t s c h a n g e d s o m e w h a t o v e r t h e

p e r i o d 1 9 6 0 - 9 0 a n d t h e p r o p o s e d G A R C H m o d e l a l l o w s o n e t o c a p t u r e t h i s

e vo l u t i on i n va r i a nc e s . H o w e v e r t e st s o f s pe c if ic de v i a t i ons l e a d t o a r e j e c t i on o f

t h e h y p o t h e s i s o f a c o n s t a n t c o n d i t i o n a l c o r r e l a t io n . A n e x p li ci t m o d e l o f t h e

c o n d i t i o n a l c o r r e l a t i o n i n d i c a t e s a n i n c r e a s e i n t h e i n t e r n a t i o n a l c o r r e l a t i o n

b e t w e e n m a r k e t s o v e r t h e p a s t 3 0 y e a r s . W e a l s o f i n d t h a t t h e c o r r e l a t i o n r i s e s

i n p e r i o d s w h e n t h e c o n d i t i o n a l v o l a t il i ty o f m a r k e t s is la r g e. T h e r e i s s o m e

p r e l i m i n a r y e v i d e n c e th a t e c o n o m i c v a r i a b le s s u c h a s t h e d i v i d e n d y i el d a n d

i n t e r e s t r a t e s c o n t a i n i n f o r m a t i o n a b o u t f u t u r e v o l a t i l i t y a n d c o r r e l a t i o n t h a t i s

n o t c o n t a i n e d i n p a s t r e t u r n s a l o n e . H o w e v e r , f u r t h e r t h e o r e t ic a l w o r k is r e q u i r e d

t o p r o v i d e a s a t is f a c t o ry m o d e l . T h e e f fe c ts a r e n o t o f g r e a t m a g n i t u d e b u t a r e

of t en s t a t i s t i ca l ly s ign i f i can t .

O u r r e s u l t s c o n f i r m a n d c o m p l e t e s o m e p r e v i o u s f i n d i n g s m e n t i o n e d i n t h e

i n t r o d u c t i o n . T h e s e st u d ie s (e .g . K o c h a n d K o c h 1 9 91 , a n d V o n F u r s t e n b e r g a n d

J e on , 1989) typ i c a l l y c o m pu t e d c o r r e l a t i on c oe f f i c ie n t s ove r s h o r t s u b - pe r i ods ,

u s i n g h i g h - f r e q u e n c y d a t a , a n d t h e n l o o k e d a t t h e i r e v o l u t i o n o v e r ti m e . H e r e

w e e x p li c it ly m o d e l t h e m u l t i v a r i a t e a s se t r e t u r n p r o c e s s a n d u s e a m u c h l o n g e rt i m e p e r io d . I n t h e i r A P T t e st o f g l o b a l m a r k e t i n t e g r a t io n , K i n g e t a l . (1992)

b r ie f ly l o o k e d a t c h a n g e s i n c o n d i t i o n a l c o r r e l a t io n . T h e y a l so e x p l ic i tl y m o d e l

t h e c o n d i t i o n a l c o r r e l a ti o n , u s i n g m o n t h l y d a t a o v e r t h e p e r i o d 1 9 7 0 -8 8 . I n b o t h

c a s e s , a v e r y p a r s i m o n i o u s p a r a m e t r i z a t i o n i s u s e d , b u t t h e m o d e l s f o r t h e

c o v a r i a n c e a n d c o r r e l a t i o n a r e d if f er e n t. T h e y a s s u m e t h a t t h e n a t i o n a l m a r k e t s

a r e c o r r e l a t e d t h r o u g h c o m m o n f a c t o r s w i t h c o n s t a n t f a c t o r l o a d i n g s . I n t h e i r

f a c t o r m o d e l , t h e c o r r e l a t i o n c a n o n l y i n c r e a s e o v e r t i m e i f t h e v a r i a n c e s o f t h e

c o m m o n f a c t o r i n c r e a s e r e l a t i v e t o t h e n a t i o n a l r e s i d u a l v a r i a n c e s . K i n g e t a l .

( 1 9 9 2 ) c a l c u l a t e d t h e m o n t h l y c o n d i t i o n a l c o r r e l a t i o n a n d f o u n d o n l y a m o d e s t

( ne g li g ib l e) i nc r e a s e ov e r t im e , w i t ho u t e xp l i c it s i gn i f ic a nc e te s t. A s e c u l a r t r e n dd u e t o i n c r e a s e d i n t e r n a t i o n a l m a r k e t i n t e g r a t i o n , o r t r a n s i t o r y c h a n g e s d u e t o

b u s in e s s c y c le s , c a n n o t b e m o d e l l e d 14 a n d t e st e d . O n t h e o t h e r h a n d , o u r

p a r s i m o n i o u s p a r a m e t r i z a t i o n a l lo w s a d i r e c t t e st o f th e e x i s te n c e o f a t i m e t r e n d

J o u r n a l o]" I n t e r n a t i o n a l M o n e y a n d F i n a n c e 1 9 9 5 V o l u m e 1 4 N u m b e r 1 19

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a n d v a r i o u s i n f l u e n c e s i n t h e c o n d i t i o n a l c o r r e l a t i o n . W e d o f i n d e v i d e n c e o f

p r e d i c t a b l e c o m p o n e n t s i n t h e t im e - v a r i a t i o n o f i n t e r n a t i o n a l c o r r e l a t io n .

S o m e w o r d s o f c a u t i o n a r e in o r d e r . W e a r e a b l e t o r e je c t t h e h y p o t h e s i s o f

c o n s t a n t i n t e r n a t i o n a l c o r r e l a t i o n b u t f al l s h o r t o f a fu ll m o d e l . W e t e s t s e p a r a t e l ys e v e r a l d e v i a t i o n s f r o m a c o n s t a n t c o r r e l a t i o n m o d e l b e c a u s e t h e e c o n o m e t r i c

m e t h o d o l o g y u s e d d o e s n o t a l l o w u s t o i n c l u d e a ll o f t h e m i n a si n g le m o d e l . I n

o u r G A R C H e q u a t i o n , w e a l l o w e d t h e c o e ff i ci e n ts o f t h e ( p o si ti v e ) i n f o r m a t i o n

v a r i a b l e s t o b e n e g a t i v e . T h i s m e a n s t h a t t h e c o v a r i a n c e m a t r i x c o u l d l o s e i t s

p o s i t iv e - d e f in i t iv e n e s s f o r s o m e l a r g e v a l u e s o f t h e d i v i d e n d y i el d. N e g a t i v e

c o e f f i ci e n t s c o u l d s t il l l e a d t o p o s i t i v e -d e f i n i t i v e n e s s o f t h e c o v a r i a n c e m a t r i x o v e r

t h e s a m p l e s p a c e. In p r a c t ic e , w e n e v e r e n c o u n t e r e d t h e p r o b l e m o f a n e g a t i v e

c o n d i t i o n a l v a r i a n c e i n o u r s a m p l e o r f o r a n y p l a u s i b l e v a l u e o f t h e i n f o r m a t i o n

v a r i a b l e s a n d w e f el t t h a t t h e r e w a s n o e c o n o m i c r a t io n a l e t o r u le o u t n e g a t i v e

c o e ff ic ie n ts . T h e n e x t s t e p w o u l d b e t o d e s c r i b e t h e e v o l u t i o n i n c o r r e l a t i o n o v e rt i m e b y a r i ch e r m o d e l t h a n t h e l in e a r ( o r e x p o n e n t i a l ) t i m e - t r e n d u s e d i n th e

h y p o t h e s i s t e st in g . S o m e f o r m o f e v e n t m o d e l l i n g w o u l d b e m o r e s a t is f a c to r y i f

s t r u c t u r a l b r e a k i n g p o i n t s c o u l d b e i d e n t i f i e d . I n d i c a t o r s s u c h a s t h e n u m b e r o f

r e s t ri c t io n s t o f re e c a p i t a l m o v e m e n t s c o u l d a l s o b e u s e d .

T h e m e t h o d o l o g y d e v e l o p e d i n t h is p a p e r c o u l d b e a u s e fu l ba s is f o r a m o r e

d e t a i l e d s t u d y o f t h e i n t e r n a t i o n a l i n t e g r a t i o n o f f i n an c i a l m a r k e t s . H o w e v e r s u c h

c o n c l u s io n s c a n n o t b e re a c h e d b y l o o k i n g a t t h e c o r r e l at i o n a l o n e a n d a n

i n t e r n a t i o n a l a s s e t p r i c in g m o d e l m u s t b e e x p l ic i tl y u s e d . T h e m e t h o d o l o g y c o u l d

a l s o b e a p p l i e d t o o t h e r a r e a s o f f i n a n c e in w h i c h c o r r e l a t i o n is i n v o l v e d , s u c h

a s t h e p r i c in g o f f i n an c i a l i n s t r u m e n t s l ik e d i ff e r en t i al s w a p s o r o p t i o n s o n m u l t ip l eas se t s .

F u t u r e r e s ea r c h s h o u l d a l s o f o c u s o n t h e fu n d a m e n t a l d e t e r m i n a n t s o f

i n t e r n a t i o n a l c o r r e l a t i o n a c r o s s e q u i t y m a r k e t s . T h i s c o r r e l a t i o n is l ik e l y t o b e

a f f ec t ed b y t h e in d u s t r y m i x o f e a c h n a t i o n a l m a r k e t a s w e ll a s t h e c o r r e l a t i o n

o f t h e c o u n t r i e s ' b u s i n e s s c y c l es .

Appendix A: Da ta description

T h e d a t a o n i n t e r n a t i o n a l f in a n c i a l m a r k e t s v a r y g r e a t l y in t e r m s o f a v a i l a b i l i t y , q u a l i t y a n dc o m p a r a b i l i t y . W e h a v e c h o s e n t o r e s t ri c t th e t i m e p e r i o d a n d t h e n u m b e r o f c o u n t r ie s s e l ec t e d

t o i n s u r e g o o d q u a l i t y o f t h e d a t a . W e g e t g o o d m o n t h - e n d d a t a f o r s t o c k p r ic e s , a s w e ll a s

d i v i d e n d y i e ld , l o n g - a n d s h o r t - t e r m m a r k e t i n t e r e s t r a t e s u s e d a s i n s t r u m e n t s , f o r th e s e v e n

m a j o r f i n a n c i a l m a r k e t s o v e r t h e p e r i o d J a n u a r y 1 96 0 t o A u g u s t 1 9 9 0 . T h e c o u n t r i e s a re :

F r a n c e ( F R ) , G e r m a n y ( G E ), S w i t z e r l a n d ( SW ) , U K ( U K ) , J a p a n ( JA ) , C a n a d a ( C A ) a n d t h e

U S A ( U S ) . T h e s e a r e t h e s e v e n l a r g e s t m a r k e t s i n t e r m s o f s iz e a n d t h e i r c o m b i n e d s t o c k

m a r k e t c a p i t a l i z a t i o n is m o r e t h a n 9 0 p e r c e n t o f t h a t o f t h e w o r l d . I n m a n y t a b l e s , t h e s e

c o u n t r i e s w i l l b e c a l l e d b y t h e l e t t e r s i n d i c a t e d i n p a r e n t h e s e s .

Common stock returns: M o n t h - e n d s t o c k m a r k e t i n d i c e s c a l c u l a te d i n l o ca l c u rr e n c y c o m e

f ro m M o r g a n S t a n le y C a p i t a l I n t e r n a t i o n a l (M S C I ) . T h e M S C I s a m p l e c o v e rs a r o u n d 6 5 pe r -

c e n t o f e a c h m a r k e t c a p i t a l i z a t i o n , w i t h a n a t t e m p t t o s t r a ti f y t h e i r s a m p l i n g b y i n d u s t r yb r e a k d o w n s o t h a t e a c h i n d u s t r y i s r e p r e s e n t e d i n t h e n a t i o n a l i n d e x i n p r o p o r t i o n t o i t s

n a t i o n a l w e i g h t ; h e n c e t h e s e l e c ti o n o f i n d i v i d u a l c o m p a n i e s i s n o t s o l e l y b a s e d o n t h e i r m a r k e tc a p i t a l i z a t i o n . T h e d a t a s i n ce 1 97 0 i s p u b l i c l y a v a i l a b l e a n d w i d e l y u s ed ; t h e p r i c e i n d i c e s fr o m

1 96 0 t o 1 96 9 w e r e b a c k - c a l c u l a t e d b y M S C I . 15 F o r e a c h m a r k e t w e c a l c u l a t e d a t i m e - s e ri e s


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I s the cor re la t ion in in te r na t iona l equ i t y r e tur ns constan t?: F Long in an d B So ln ik

s i g n a n d m a g n i t u d e , is :

(B2>h , = a ' + b , S t . , _ , ( e2 _ , - tr 2) + b2 Sz , , _ ~ e2- ~ + b3S 3. , - xe2-1 + b4 S , , . , - x (e2 - ~ - a 2) + c ' h , - t

w h e r e S k . t - 1 a r e d u m m y v a r i a b le s t h a t t a k e t h e v a lu e s:S 1 a - 1 = 1 i f e , - l i s l e s s t h a n - t r,

$ 2 . , -1 = 1 i f e t - 1 i s l e ss t h a n 0 ,

$ 3 . , - ~ = 1 i f e , _ ~ i s g r e a t e r t h a n 0 ,

S 4 a - 1 = 1 i f e t _ x i s g r e a t e r t h a n tr ,

a n d z e r o o t h e r w i s e .tr ( th e u n c o n d i t i o n a l s t a n d a r d d e v i a t i o n o f t h e i n n o v a t i o n s e f r o m t h e G A R C H m o d e l ), - t r

a n d z e r o a r e t h e e x o g e n o u s t h r e s h o l d s u s e d i n th i s th r e s h o ld , a s y m m e t r i c m o d e l . N o t e t h a t

t w o d u m m y v a r i ab l e s w il l b e e q u a l t o o n e f o r l a rg e p o s i t iv e o r n e g a t i v e i n n o v a t i o n s . T h i s

m o d e l a l l o w s u s t o c a p t u r e a s y m m e t r y i n t h e i m p a c t o f i n n o v a t i o n (b 2 ¢ b3 ) a n d d i ff e re n t

i m p a c t s f o r l a r g e a n d s m a l l n e w s ( b 1 ¢ 0 a n d b 4 ¢ 0 ). I f t h e i m p a c t o f s m a l l a n d l a r g e i n n o v a t i o n s

a r e s i m i l a r , w e s h o u l d f i n d t h a t t h e t w o c o e f fi c ie n t s b ~ a n d b 4 a r e e q u a l t o z e r o ; o n t h e o t h e r

s i d e , i t i s o f t e n c l a i m e d t h a t l a r g e s h o c k s s h o u l d h a v e a s h o r t e r p e r s i s t e n c e t h a n s m a l l s h o c k s( ba a n d b 2 n e g a t i v e ) . S i m i l a r l y , i t i s o f t e n s t a t e d ( s ee B l a c k , 1 9 7 6 , N e l s o n , 1 9 9 0 a n d C a m p b e l l

a n d H e n t s c h e l , 1 9 92 ) th a t n e g a t i v e n e w s s h o u l d i n c r e a s e v o l a t i l i ty m o r e t h a n p o s i t iv e n e w s

(b 2 > b3 ). A s u f f ic i e n t c o n d i t i o n f o r t h e p o s i t i v e n e s s i s o f t h e c o n d i t i o n a l v a r i a n c e i s t h a t

bx + b 2 > 0 a n d b 3 + b 4 > 0 .T h e r e s u lt s o f t h e e s t i m a t i o n o f t h e u n i v a r i a t e t h r e s h o l d G A R C H s p e c if i ca t io n a r e g i v e n

i n T a b l e 1 0. T h e m e a n e q u a t i o n i n c l u d e s th e i n f o r m a t i o n v a r ia b l e s as b e fo r e, a n d o n l y t h e

T AB LE 1 0. T h r e s h o l d a n d a s y m m e t r y i n t h e c o n d i t i o n a l v a r ia n c e .

L R t e s t

b l b 2 b 3 b 4 b ' L i k L i k ' ( p - v a l u e )

G E - 0 . 0 5 5 0 .1 4 1 0 .2 8 1 - 0 . 2 6 0 0 . 10 5 5 8 8. 3 5 8 4. 5 7 .6

( - 0 .4 3 ) (1 .47 ) (2.44 ) ( - 1 .95 ) (3.19 ) (0 .055)

F R - 0 . 3 4 8 0 . 4 24 0 .1 4 5 - 0 . 1 2 9 0 . 13 9 5 3 5 .6 5 30 .1 1 1.0

( - 1 .97) (2 .71) (0 .81) (0 .54) (2 .00) (0 .011)

U K 0 . 4 8 0 - 0 . 0 5 1 0 .3 9 8 - 0 . 3 7 8 0 . 23 2 5 5 5. 6 5 4 9 .0 1 3.0

( 1.7 5) ( - 0 . 3 7 ) ( 2 .8 2 ) ( - 2 . 3 8 ) ( 2 .3 9 ) ( 0 .0 0 5 )

S W - 0 . 0 8 5 0 . 06 6 0 .2 0 9 - 0 . 2 5 8 0 .0 5 8 5 8 8. 3 5 8 1. 7 13 .2

( - 1 .34) (1 .21) (3 .94) ( - 3 .59) (2 .46) (0 .004)J A 0 . 20 5 - 0 . 1 2 8 0 . 1 87 - 0 . 2 3 3 0 .0 6 7 6 0 2 .4 5 9 1 .4 2 2 .0

(1 .93) ( - 1 .34 ) (2.29 ) ( - 2 .5 7 ) (2.41 ) (0 .000)

C A - 0 . 1 3 1 0 . 1 46 0 . 16 5 - 0 . 1 1 7 0 . 08 0 6 1 1 .7 6 1 0 .5 2 .4

( - 1 .05 ) (1 .45 ) (1 .52) ( - 0 .8 9 ) (2 .89) (0 .493)

U S - 0 .241 0 .250 - 0 .032 0 .135 0 .058 649 .3 643 .4 11 .8

( - 2 . 1 1 ) ( 2.5 5) ( - 0 . 4 5 ) ( 2.1 1) ( 2 .1 2 ) ( 0 .0 0 8 )

The table g ives the es t im at ion of the un ivar ia te GARCH(1,1) m ode l wi th threshold , a symm etr ic cond i t iona l

variance . Th e var iance i s con di t ioned on the s ign and the s ize of the pas t in nov a t ion and on the pas t

con dit io nal variance. Th e coeffic ients bk (k = 1, 2, 3, 4) capture the as ym m etry in the co nd it ion al variance.

b 1 a nd b4 captu re the size effect and b 2 and b 3 the sign effect . Th e t-sta t ist ics are repor ted in parentheses.No asymmetry corresponds to the case : b l = b4 = 0 and b 2 = b 3 = b ' . L ik an d Lik ' a re the va lues of the

log-l ike lihood func t ion of the unco ns t ra in ed and c ons t ra ined GARCH (1,1) mode ls . The l ike l ihood ra t iotest (LR test) is indicated in the last column with the p-value in parentheses. The stat ist ics of the test

fol lows asymptotical ly a chi-square with 3 degrees of freedom.

22 J o u r n a l o f I n t e r n a t io n a l M o n e y a n d F i n a n c e 19 9 5 V o l u m e 1 4 N u m b e r 1

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I s the cor r e la t ion in in te r na t iona l equ i t y r e tur ns cons tan t? . " F Lono in and B So ln ik

e s t i m a t e d b c o ef f ic i e n ts a r e r e p o r t e d i n t h e f i r st f o u r c o l u m n s o f t h e t a b l e . T h e n e x t c o l u m n

r e c a l ls t h e s i n g le co e f fi c ie n t b ' o f t h e u n i v a r i a t e G A R C H w i t h o u t t h r e s h o l d s . T h e l o g - l i k e l i h o o d

a r e r e p o r t e d f o r t h e t h r e s h o l d G A R C H ( L i k ) a n d s i m p l e G A R C H ( L i k ') s p e c i fi c a t io n s , a s w e ll a s

a l i k e l i h o o d r a t i o t e s t b e t w e e n t h e t w o s p e c i f i c a t i o n s ( 3 d e g r e e s o f fr e e d o m ) . S i g n i f i c a n t t h r e s h o l d

e ff ec ts a re f o u n d f o r a m a j o r i t y o f t h e c o u n t r i e s. M o s t a u t h o r s f o u n d t h a t n e g a t i v e n ew s h a da s t r o n g e r i m p a c t o n t h e v o l a t i l i t y i n t h e c a se o f t h e U S s t o c k m a r k e t . O u r d a t a f o r t h e U S A

c o n f i r m t h a t f i n d i n g (b 2 > b3) , b u t w e c a n n o t r e a c h t h e s a m e c o n c l u s i o n f o r o t h e r c o u n t r i e s

e x c e p t F r a n c e . O n t h e o t h e r s i d e , t h e c o e f f ic i e n t s f o r l a r g e s h o c k s a r e n e g a t i v e i n 1 1 o u t o f 1 4

c a se s , p r o v i d i n g e v i d e n c e t h a t l a r g e s h o c k s h a v e a s m a l l e r p e r s is t e n c e t h a n s m a l l s h o c k s.

N o t e s

1. T h e u s e o f a t i m e - v a r y i n g c o n d i t i o n a l c o v a r i a n c e / c o r r e l a t i o n m a t r i x c a n b e f o u n d i n

s t u d i e s b a s e d o n i n t e r n a t i o n a l a s s e t p r ic i n g m o d e l s ( se e E n g e l a n d R o d r i g u e s , 1 98 9 a n dC h a n e t a l . , 1 99 2 f o r e x a m p l e ) .

2 . K a p l a n i s ( 19 88 ) a l s o u s e d a s t a b i l i t y t e s t d e s i g n e d b y B o x (1 9 49 ) f o r t h e c o v a r i a n c e m a t r i x .

T h e r e s u lt s a r e q u i t e s i m i l a r . B o t h t e s ts a r e a s y m p t o t i c a l l y e q u i v a l e n t b u t t h e i r

s m a l l - s a m p l e p r o p e r t i e s a r e n o t k n o w n . W e c o n d u c t e d b o t h t y p e s o f t e st s o n o u r d a t a

w i t h s i m i l a r c o n c l u s i o n s a n d o n l y r e p o r t e d t h e J e n r i c h t e s t in T a b l e 2 .

3 . S i m u l a t i o n s c o n d u c t e d b y K a p l a n i s s h o w e d t h a t t h e le n g t h o f t h e t im e p e r i o d o f 5 0

m o n t h s i s a d e q u a t e f o r t h e a s y m p t o t i c r e s u l ts . T e s t s o f c o v a r i a n c e s t a b i li t y , s u c h a s

J e n r i c h ' s t e st , m a y l e a d t o a n i n c o r r e c t r e j e c t i o n o f t h e n u l l i f a s s e t r e t u r n s f o l l o w s t a b l e

P a r e t i a n d i s t r i b u t i o n s ( se e L o r e t a n a n d P h i l l ip s , 19 94 ).

4 . S o m e r ec e n t s t u d i e s f o r t h e U S m a r k e t a r e B r e e n e t a l . (1989) , Campbe l l (1987) , F ama

a n d F r e n c h ( 19 88 ), F e r s o n ( 19 8 9) , F e r s o n a n d H a r v e y (1 99 1) . B e k a e r t a n d H o d r i c k ( 19 92 )

l o o k a t t h e s to c k m a r k e t s a n d e x c h a n g e r a t es o f J a p a n , U K a n d G e r m a n y f o r t h e p e r io d

1 / 1 98 1 - 12 / 1 98 9 ; C a m p b e l l a n d H a m a o (1 99 2) l o o k a t J a p a n f o r t h e p e r i o d 1 / 1 9 7 0- 3 /1 9 9 0 ;

C u m b y (1 99 0) l o o k s a t G e r m a n y , U K a n d J a p a n f o r t h e p e r i o d 1 / 1 9 7 5 - 12 / 1 9 8 7 u s i n g

m o n t h l y o b s e r v a t i o n s o f q u a r t e r l y r e t u r n s h e n c e r e q u i ri n g a n a d j u s t m e n t f o r o v e r la p p i n g ;

C u t l e r e t a l . (1 99 1) l o o k a t 1 2 f o r e i g n s t o c k a n d b o n d m a r k e t s a s w e l l a s t h e i r a s s o c i a t e d

e x c h a n g e r a t e s w i t h o b s e r v a t i o n s s t a r t i n g b e t w e e n 1 /1 9 60 a n d 7 /1 9 69 , d e p e n d i n g o n t h e

c o u n t r y , a n d e n d i n g i n 1 9 88 ; H a r v e y (1 99 1) l o o k s a t 1 6 f o r e i g n s t o c k m a r k e t s f o r t h e

p e r i o d 1 / 1 9 7 0 - 5 /1 9 8 9 . S o l n i k (1 99 3) l o o k s a t 7 f o r e i g n s t o c k m a r k e t s f o r t h e p e r i o d

1 / 1 9 7 1 - 8 / 1 9 9 0 .

5 . A r e v i e w o f t h e l i t e r a t u r e c a n b e f o u n d i n B o l l e r s l e v e t a l . (1992).

6 . C o n d i t i o n a l v o l a t i l i t y i s n o t i n c l u d e d i n t h e r i sk p r e m i u m e q u a t i o n s i n ce m o s t s t u d i e s

h a v e f a i l e d t o d i s c o v e r a s i g n if i c a n t i n f lu e n c e u s i n g m o n t h l y d a t a ( se e fo r e x a m p l e B a i l li ea n d D e G e n n a r o , 1 99 0 a n d S e n t a n a a n d W a d h w a n i , 1 9 91 ). W e g o t s i m i la r i n d i c a ti o n s

o n o u r d a t a .

7. F o r e x a m p l e , a c o n s t a n t -c o r r e l a t i o n G A R C H m o d e l w r it t e n o n U S d o l l a r re t u rn s , i.e .

u s i n g t h e U S d o l l a r a s a b a s e c u r re n c y , w o u l d g e n e r a l l y n o t g i v e a c o n s t a n t - c o r r e l a t i o n

G A R C H m o d e l tr a n s l a t e d i n a n o t h e r b a s e cu r re n c y .

8 . W e a r e g ra t e fu l t o K e n K r o n e r fo r p r o v i d i n g us w it h a c o p y o f h is F o r t r a n G A R C H

p r o g r a m .

9 . G A R C H e ff ec ts f o r e x a m p l e t e n d t o d e c r e a s e b y t e m p o r a l a g g r e g a t i o n a s t h e d i s t r ib u t i o n

o f r e t u r n s t e n d s t o w a r d n o r m a l i t y ( se e D i e b o l d , 1 98 8).

1 0. T h i s f i n d i n g i s c o n s i s t e n t w i t h p r e v i o u s re s e a r c h . F o r e x a m p l e , A t t a n a s i o (1 99 1) , S e n t a n a

a n d W a d h w a n i ( 1 9 9 1 ) , G l o s t e n e t a l . ( 19 89 ) i n c l u d e d t h e d i v i d e n d y i e l d in u n i v a r i a t e

G A R C H s p e c i f ic a t i o n s w i t h m i x e d r e su l ts .! 1. P a r a m e t e r s e s t i m a t e s a re : r = - 0 . 3 9 7 ( - 0 . 7 3 ) , r ' = 0 .7 5 3 (1 .4 1) a n d a = 1 1. 81 8 (1 .0 1) w i t h

Li k = 1251.6 , L R tes t -- - 8 .0 (p-v alu e = 0 .018) .

12 . I t is n o t p o s s i b l e t o c o n d i t i o n o n t h e fu t u r e s h o c k e , a n d w e c a n n o t t e s t w h e t h e r t h e

c o r r e l a t i o n is h i g h e r w h e n t h e m a r k e t s g o u p o r g o d o w n .

J o u r n a l o f I n t e r n a t io n a l M o n e y a n d F i n a n c e 1 9 95 V o l u m e 1 4 N u m b e r 1 23

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13. The statistical significance of this phenomenon is rather low, so the conclusions are onlytentative.

13. Economic variables do enter 'observable' factors, but again the assumption of constantb's imply that only changes in relative variance of these 'observable' factors can affect

the correlation across markets.15. We thank Morgan Stanley for making these data available to us for research purposes.16. By interest rate parity the forward basis is equal to the short-term interest rate differential

between the country of the asset and that of the investor. Hence the excess returns inlocal currency are (approximately) equal to the excess returns hedged against currencyrisk obtained by an investor of any nationality.

17. Remember that the volume of Eurodollar transactions is enormous and the LIBOR(London Interbank Offer Rate) has become the reference short-term dollar interest ratefor borrowing in the USA. This is demonstrated by the fact that the Eurodollar futurescontract has the largest transaction volume of all financial contracts in terms of underlyingcapital. A similar comment applies to other currencies.

18. We did not impose this constraint in our estimation and the sum turned out to be slightly

negative in a couple of cases.

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