PACIFIC-BASIN
FINANCE
JOURNAL
ELSEVIER
Pacific-Basin Finance Journal 3 (1995) 1-29
Market segmentation and time variation in the
price of risk: Evidence on the Korean stock
market
Kee-Hong Bae
*
Department of Economics and Finance, City University of Hong Kong, 83 Tat Chee Auenae, Kowloon,
Hong Kong
Abstract
This study e x a m i n e s the t i m e - v a r y i n g b e h a v i o r of the risk p r e m i u m s in the K o r e a n
equity m a r k e t and investigates the impact o f capital controls o n the pricing of K o r e a n
equities. U s i n g a bivariate G A R C H - M m o d e l that allows for the t i m e - v a r i a t i o n in the price
of risk, the conditional expected excess returns are estimated for the Korean C o m p o s i t e
Stock Price I n d e x and the M o r g a n Stanley Capital International world index b e t w e e n 1980
and 1990. W h i l e the K o r e a n m a r k e t c o m m a n d s higher risk p r e m i u m s than the w o r l d
market, there is s o m e e v i d e n c e in the later sample period that these p r e m i u m s decline after
a n n o u n c e m e n t s of capital control relaxation, as one w o u l d expect if the K o r e a n market is
b e c o m i n g m o r e integrated to the w o r l d capital market. It is also s h o w n that the structure of
the Korean equity market is consistent with the predictions of the " m i l d s e g m e n t a t i o n "
hypothesis w h e r e b o t h d o m e s t i c and international factors are important in explaining the
excess returns o f K o r e a n equities.
Keywords: Time-varying price of risk; Kalman filter; GARCH-M
JEL classification: G12, G15
This paper is from part of my dissertation at the Ohio State University. I would like to thank K.C.
Chart, Ira Ho[owitz, Andrew Karolyi, Sridhar Ramamoorti, Paul Schultz, James Tompkins and two
anonymous referees for valuable comments. I am especially grateful to my advisor, Ren~ Stulz, for his
guidance and suggestions. All errors are my own.
* Corresponding author. Phone: + 852 788-7975, Fax: + 852 788-8806, E-mail:
EFKHBAE@CITYU.EDU.HK
0927-538X/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved
SSDI 0 9 2 7 - 5 3 8 X ( 9 4 ) 0 0 0 2 4 - 7
2
K.-H. B a e / P a c i f i c - B a s i n F i n a n c e J o u r n a l 3 (1995) 1 - 2 9
1. I n t r o d u c t i o n
It is g e n e r a l l y a g r e e d that n a t i o n a l asset m a r k e t s h a v e b e c o m e m o r e i n t e g r a t e d
in r e c e n t y e a r s , in large part as a c o n s e q u e n c e o f the t r e n d t o w a r d f i n a n c i a l
d e r e g u l a t i o n in the m a j o r e c o n o m i e s c o u p l e d w i t h t e c h n o l o g i c a l d e v e l o p m e n t s that
h a v e g r e a t l y r e d u c e d t r a n s a c t i o n and i n f o r m a t i o n costs. W h e a t l e y ( 1 9 8 8 ) , H a r v e y
( 1 9 9 1 ) and C h a n et al. ( 1 9 9 2 ) p r o v i d e e v i d e n c e o f i n t e g r a t i o n u s i n g the capital
asset p r i c i n g m o d e l ( C A P M ) , w h i l e C h o et al. (1986), G u l t e k i n et al. ( 1 9 8 9 ) , and
K o r a j c z y k a n d V i a l l e t ( 1 9 8 9 ) use the a r b i t r a g e p r i c i n g f r a m e w o r k . Capi t al m a r k e t s
are said to b e i n t e g r a t e d i n t e r n a t i o n a l l y if assets w i t h i d e n t i c a l risk c h a r a c t e r i s t i c s
h a v e the s a m e p r i c e r e g a r d l e s s o f the l o c a t i o n in w h i c h t h e y are traded. M a r k e t s
are said to b e s e g m e n t e d if this c o n d i t i o n d o e s not hold. S e g m e n t a t i o n m a y arise
e i t h e r b e c a u s e o f i m p e d i m e n t s to i n t e r n a t i o n a l i n v e s t m e n t ( g o v e r n m e n t r e s t r i c t i o n s
o n c ap ital f l o w , l i m i t a t i o n s on f o r e i g n s hare o w n e r s h i p , and t r a n s a c t i o n s t a x e s ) or
b e c a u s e o f i n v e s t o r s ' a v e r s i o n to i n v e s t i n g a b r o a d .
S e v e r a l p a p e r s i n v e s t i g a t e the i m p a c t o f b a r r i e r s to i n t e r n a t i o n a l i n v e s t m e n t o n
the e q u i l i b r i u m p r i c e s o f the a f f e c t e d s e c ur i t i es. E r r u n z a and L o s q ( 1 9 8 5 ) p o s t u l a t e
a m a r k e t s t r u c t u r e cal l ed " m i l d l y s e g m e n t e d " w h e r e local i n v e s t o r s can trade in
all s e c u r i t i e s a v a i l a b l e w h e r e a s f o r e i g n i n v e s t o r s c a n trade o n l y in a s u b s e t o f the
securities. In this f r a m e w o r k , t h e y s h o w that the r e t u r n r e q u i r e d b y local i n v e s t o r s
o n t h e local s e c u r i t i e s will be h i g h e r c o m p a r e d to the r e t u r n w i t h o u t such
restrictions. E u n and J a n a k i r a m a n a n ( 1 9 8 5 ) a n a l y z e the e f f e c t s o f e q u i t y o w n e r ship r e s t r i c t i o n s on the p r i c i n g o f s e c u r i t i e s and s h o w that local i n v e s t o r s d e m a n d
a h i g h e r p r i c e d i s c o u n t on s e c u r i t i e s as e q u i t y o w n e r s h i p c o n s t r a i n t s b e c o m e m o r e
r e s t ri ctiv e. A l e x a n d e r et al. ( 1 9 8 8 ) e x a m i n e the b e h a v i o r o f s t o c k r e t u r n s s u r r o u n d ing i n t e r n a t i o n a l listings and f i nd that the i n t e r n a t i o n a l listing o f a s e c u r i t y l eads to
a r e d u c t i o n in its e x p e c t e d return. H i e t a l a ( 1 9 8 9 ) d e r i v e s e q u i l i b r i u m c o n d i t i o n s in
a m a r k e t s ettin g w h e r e local i n v e s t o r s are a l l o w e d to hol d o n l y their s e c u r i t i e s
w h e r e a s the rest o f t he i n v e s t o r s are e s s e n t i a l l y a l l o w e d to h o l d all securities. In
s u c h a m a r k e t setting, he a r g u e s that l ocal i n v e s t o r s w o u l d b e w i l l i n g to p a y less
f o r their s e c u r i t i e s than f o r e i g n i n v e s t o r s and fi nds s u p p o r t i n g e v i d e n c e in the
F i n n i s h s t o c k m a r k e t . B o n s e r - N e a l et al. ( 1 9 9 0 ) test w h e t h e r a r e l a t i o n s h i p exists
b e t w e e n a n n o u n c e m e n t s o f c h a n g e s in i n t e r n a t i o n a l i n v e s t m e n t r e s t r i c t i o n s a n d
c h a n g e s in c o u n t r y f u n d p r i c e - n e t asset v a l u e ratios. T h e y fi nd that an a n n o u n c e m e n t o f a l i b e r a l i z a t i o n is a s s o c i a t e d w i t h a s i g n i f i c a n t d e c r e a s e in the p r i c e - n e t
asset v a l u e ratio. M i t t o o ( 1 9 9 2 ) f i nds that the C a n a d i a n risk p r e m i a on the
i n t e g r a t e d m a r k e t i n d e x o f the C a n a d i a n n o n - i n t e r l i s t e d and U.S. s t o c k s are
c o n s i s t e n t l y h i g h e r in the 1 9 7 7 - 8 1 p e r i o d , b u t b e c o m e si m i l ar in the 1 9 8 2 - 8 6
p e r i o d , s u g g e s t i n g a m o v e f r o m s e g m e n t a t i o n to i n t e g r a t i o n o v e r time.
In s u m m a r y , the m a i n c o n c l u s i o n o f t h e s e st udi es is that i n t e r n a t i o n a l i nvest m e n t r e s t r i c t i o n s l ead to h i g h e r risk p r e m i u m s o f the a f f e c t e d securities. C o n v e r s e l y , r e l a x a t i o n o f r e s t r i c t i o n s w o u l d i m p l y a d e c l i n e in the m e a n e q u i t y
p r e m i u m . A l t h o u g h p r e v i o u s r e s e a r c h s u g g e s t s that r e l a x a t i o n o f i n t e r n a t i o n a l
K.-H. Bae // P a c i f i c - B a s i n F i n a n c e J o u r n a l 3 (1995) 1--29
3
i n v e s t m e n t r e s t r i c t i o n s will l ead to a r e d u c t i o n in the e x p e c t e d e x c e s s returns, t here
are f e w e m p i r i c a l f i n d i n g s to s u p p o r t this v i e w . T h i s p a p e r s e e k s to p r o v i d e
a d d i t i o n a l e m p i r i c a l e v i d e n c e on this issue, f o c u s i n g on the e x p e r i e n c e o f the
Korean equity market.
S p e c i f i c a l l y , this s t u d y e x a m i n e s the i m p a c t o f capital c o n t r o l s on the p r i c i n g o f
K o r e a n e q u i t i e s and the t i m e - v a r y i n g b e h a v i o r o f the risk p r e m i u m s in the K o r e a n
m a r k e t and its r e l a t i o n s to the w o r l d e q u i t y m a r k e t . I n v e s t i g a t i o n o f the r e l a t i o n s
b e t w e e n the K o r e a n and w o r l d capital m a r k e t s has s e v e r a l p o t e n t i a l i m p l i c a t i o n s .
F o r in s tan ce, it w o u l d be u s e f u l in a s s e s s i n g w h e t h e r the l i b e r a l i z a t i o n p r o c e s s
r e d u c e s the co s t o f capital f or local f i r m s and al so in u n d e r s t a n d i n g h o w the
l i b e r a l i z a t i o n its el f a f f e c t s the risk p r e m i u m s o f f i n a n c i a l assets and the p e r f o r m a n c e o f capital m a r k e t s .
T h i s s tu d y u tili z e s the c o n d i t i o n a l asset p r i c i n g a p p r o a c h . A b i v a r i a t e G A R C H M m o d e l that a l l o w s f or the p r i c e o f risk to c h a n g e o v e r t i m e is e m p l o y e d to
e s t i m a t e the time series o f the risk p r e m i u m s f o r the K o r e a n and w o r l d s t o c k
m a r k e t s b e t w e e n 1980 and 1990. T h e e v i d e n c e c o n f i r m s the i m p o r t a n c e o f
a l l o w i n g f o r the t i m e v a r i a t i o n in the p r i c e o f risk in that the t i m e - v a r y i n g p r i c e o f
r i s k m o d e l p r o v i d e s m o r e a c c u r a t e e s t i m a t e s o f risk p r e m i u m s than the c o n s t a n t
p r i c e o f risk m o d e l . W h i l e the K o r e a n s t o c k m a r k e t c o m m a n d s h i g h e r risk
p r e m i u m s than the w o r l d m a r k e t , t her e is s o m e e v i d e n c e that risk p r e m i u m s
d e c l i n e to a rate cl os e to t h o s e o f the w o r l d e q u i t y m a r k e t , as o n e w o u l d e x p e c t to
result f r o m i n t e g r a t i o n o f capital m a r k e t s . T h e test results also s u g g e s t that b o t h
d o m e s t i c an d i n t e r n a t i o n a l f a c t o r s are i m p o r t a n t in e x p l a i n i n g the e x c e s s ret urns o f
K o r e a n equities.
T h e rest o f the p a p e r p r o c e e d s as f o l l o w s . S e c t i o n 2 b r i e f l y d e s c r i b e s the
K o r e a n s t o c k m a r k e t and its e x p e r i e n c e w i t h capital c o n t r o l s . S e c t i o n 3 e x p l a i n s
the test m e t h o d w i t h i n a C A P M f r a m e w o r k . S e c t i o n 4 d e s c r i b e s the data and
s u m m a r y statistics. S e c t i o n 5 p r e s e n t s the m a i n e m p i r i c a l results. S e c t i o n 6
e x a m i n e s the r o b u s t n e s s o f results to an a l t e r n a t i v e s p e c i f i c a t i o n and e s t i m a t i o n
m e t h o d , and S e c t i o n 7 c o n c l u d e s .
2. T h e K o r e a n
Stock Market:
A brief account
T h e K o r e a n s t o c k m a r k e t has e m e r g e d as o n e o f the f a s t e s t - g r o w i n g capital
m a r k e t s in the w o r l d . Fig. 1 s h o w s that a p e r i o d o f r e l a t i v e l y l ow s t o c k p r i c e l e v e l s
is f o l l o w e d b y a p e r i o d o f r a p i d l y rising e q u i t y v a l u e s in the s e c o n d h a l f o f the
1980s. T h e K o r e a n s t o c k m a r k e t has t u r n e d i n c r e a s i n g l y bullish si nce 1985. T h e
K o r e a n C o m p o s i t e S t o c k Pr i c e I n d e x ( K O S P I ) w e n t f r o m 160 at the e n d o f 1985
to 2 7 2 at th e e n d o f 1986. T h e b o o m w a s s u s t a i n e d and p e a k e d on M a r c h 31,
1989, w i t h the i n d e x r e a c h i n g 1003. T h e n u m b e r o f f i r m s listed on the e x c h a n g e ,
m a r k e t c a p i t a l i z a t i o n s and t r a d i n g v o l u m e s h a v e also i n c r e a s e d d r a m a t i c a l l y
4
K . - H . B a e ~ P a c i f i c - B a s i n F i n a n c e J o u r n a l 3 (1995) 1 - 2 9
1000.00
900.00
800.00
700.00
600.00
500.00
400.00
300.00
200.00
100.00
0.00
I
811209
I
831~
J
I
I
851106 ~ ' 8 7 1 0 1 4
890927
Fig. 1. Cumulative equity values for the KOSPI and MSCI.
d u r i n g t h e s e c o n d h a l f o f t h e 1 9 8 0 s ( s e e T a b l e 1). B y t h e e n d o f 1 9 9 0 , m a r k e t
c a p i t a l i z a t i o n s t o o d at $ 1 1 0 b i l l i o n , m o r e t h a n 15 t i m e s the 1 9 8 5 v a l u e a n d 1 9 9 0
e n d e d w i t h 6 6 9 c o m p a n i e s l i s t e d o n the s t o c k e x c h a n g e , u p f r o m 3 3 7 at the e n d o f
1985. The major driving forces behind this growth appear to be the excellent
performance of the Korean economy and the expected internationalization of the
Korean capital markets.
Table 1
Growth of the Korean stock market
The database used to obtain Table 1 contains daily closing prices adjusted for dividends and capital
structure changes, trading volumes, and number of shares outstanding for all common stocks that were
traded on the Korean Stock Exchange between January 1980 and December 1990. The data were
obtained from the PACAP Database compiled by the Pacific-Basin Capital Markets (PACAP) Research
Center at the University of Rhode Island
Year
(December)
No, of firms
Market value
(Billion $)
Trading volume
(Thousands)
80
81
82
83
84
85
86
87
88
89
90
309
311
311
312
326
337
355
389
496
626
669
2.79
3.92
4.13
4.10
5.74
7.10
13.52
32.15
93.56
140.98
110.55
514
1019
1040
960
1446
1937
3400
5856
10367
11755
10865
K. -1-1. B a e / P a c i f i c - B a s i n F i n a n c e J o u r n a l 3 (1995) 1 - 2 9
Table 2
Capital control changes in Korea
Date
Events
01/15/81
08/22/84
11/13/85
South Korea will allow foreigners limited access to its securities market
The listing of the Korea Fund on the NYSE
Qualifying Korean firms will be permitted to offer foreign investors
convertible bonds
South Korean government will allow foreigners to exchange convertible
bonds for stocks
The government is likely to allow securities, insurance and investment
trust firms to buy foreign stocks
South Korean government announced the plans to open Seoul's securities
markets to direct foreign investment
Seoul eliminated the $100,000 ceiling on the amount of foreign currency
that non-residents may take into the country
South Korea will let foreign financial firms operate in the country and
trade shares under the same rules that apply to Korean financial firms
12/03/87
03/29/88
12/06/88
12/19/91
03/30/92
The Korean government has maintained fairly strict controls both on foreign
exchange and on foreign share ownership as a policy tool to manage international
capital flows. These investment barriers were "intended
to p r o t e c t d o m e s t i c
business interests from being controlled by foreign investors". Until 1984, no
foreign investors were allowed to directly buy Korean stocks, bonds or other
K o r e a n s e c u r i t i e s . F o r e i g n e r s w e r e a l l o w e d to b u y o n l y b e n e f i c i a l c e r t i f i c a t e s
issued by domestic trust and investment companies.
A s s h o w n in T a b l e 2, 1 a s t e a d y l i b e r a l i z a t i o n p r o c e s s o f o p e n i n g d o m e s t i c
capital markets to foreign investment began in 1984. One notable event among
these changes is the listing of the Korea Fund on the NYSE in August 1984.
Although many Korea funds were created for indirect foreign investment, none
were listed on any exchange before the Korea Fund, which is the largest of the
seven closed-end traded Korea funds. The second largest, the Korea Europe Fund,
was established in March 1987 on the London exchange. The introduction of a
c o u n t r y f u n d w a s n o t at a l l s u f f i c i e n t t o e n s u r e m a r k e t i n t e g r a t i o n . S u c h a c h a n g e
w a s n e v e r t h e l e s s i m p o r t a n t s i n c e it ~ p r o v i d e d a w a y f o r f o r e i g n i n v e s t o r s to
participate in the strictly regulated market for the first time.
The major capital control change came in late 1988 when the Korean Finance
Ministry announced a step-by-step liberalization plan including: expansion of
e x i s t i n g o v e r s e a s f u n d s f o r i n d i r e c t e q u i t y i n v e s t m e n t s t a r t i n g in 1 9 8 9 ; o p e r a t i o n
of foreign financial firms starting in 1991; and direct foreign equity investment
1 Indications of changes in investment restrictions in Table 2 are collected from the Wall Street
Journal Index.
6
K. -H. B a e / Pacific-Basin F i n a n c e J o u r n a l 3 (1995) 1 - 2 9
starting in 1992. W h i l e the K o r e a n m a r k e t is still not f u l l y open to the outside
w o r l d , the K o r e a n g o v e r n m e n t has i m p l e m e n t e d these liberalization plans and its
capital m a r k e t has b e c o m e m o r e accessible in recent years. The K o r e a n g o v e r n m e n t r e c e n t l y a l l o w e d direct portfolio i n v e s t m e n t o f f o r e i g n investors starting
J a n u a r y 1, 1992.
T h e liberalization process p u r s u e d by the K o r e a n g o v e r n m e n t over the last
d e c a d e a f f o r d s a v a l u a b l e o p p o r t u n i t y to e x a m i n e the i m p a c t of capital controls
and to assess w h e t h e r liberalization r e d u c e s the cost o f capital for local firms.
3. T h e e c o n o m e t r i c
approach
3. I. The constant p r i c e o f risk m o d e l
Stulz (1981a) s h o w s that the capital asset pricing m o d e l h o l d s i n t e r n a t i o n a l l y
u n d e r the a s s u m p t i o n that the w o r l d m a r k e t portfolio is p e r f e c t l y correlated w i t h
w o r l d c o n s u m p t i o n . The c o n d i t i o n a l v e r s i o n o f the international C A P M restricts
the c o n d i t i o n a l l y e x p e c t e d return on a p o r t f o l i o to be p r o p o r t i o n a l to its c o v a r i a n c e
w i t h the w o r l d m a r k e t portfolio,
E ( r kt l
D'-1)
=
E ( r ~ , I -(2t 1)
V~
( r.~, i -~t-_~ )
COY(
r kt "
r~, I aQt
-'
)
"
(1)
w h e r e rk~ is the return on the K o r e a n stock m a r k e t portfolio f r o m t i m e t - 1 to t
in excess o f a risk-free return, rwt is the excess return on the w o r l d m a r k e t
portfolio, and £2t_ ~ is the i n v e s t o r s ' i n f o r m a t i o n set.
S u p p o s e the risk p r e m i u m c h a n g e s o n l y w h e n the volatility o f the w o r l d m a r k e t
portfolio c h a n g e s . 2 T h e n ,
E ( r w t [ g-2,_,) = A o V A R ( r w , I S2,_ 1),
(2)
and Eq. (1) m a y be rewritten as,
E ( r k , ] aQ,_l) = h o C O V ( r k , , r w t l g 2 ,
t)"
(3)
Here A o has the interpretation o f the a g g r e g a t e w e a l t h - w e i g h t e d relative risk
a v e r s i o n c o e f f i c i e n t , w h i c h is a s s u m e d to be constant. A l t e r n a t i v e l y , H a r v e y
(1991) interprets the p r o p o r t i o n a l i t y factor as the w o r l d price o f c o v a r i a n c e risk.
2 M e r t o n (1980) s h o w s that Eq. (2) a p p r o x i m a t e s the e q u i l i b r i u m r e l a t i o n s h i p if either the first
partial derivative o f the i n v e s t o r ' s o p t i m a l c o n s u m p t i o n f u n c t i o n with r e s p e c t to w e a l t h is m u c h larger
than the first partial derivative o f the i n v e s t o r ' s o p t i m a l c o n s u m p t i o n f u n c t i o n with r e s p e c t to state
variables, or the v a r i a n c e o f the c h a n g e in w e a l t h is m u c h larger than the v a r i a n c e o f the c h a n g e in state
variables.
K.-H. Bae / Pacific-Basin Finance Journal 3 (1995) 1--29
7
A test o f the 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 h y p o t h e s i s can be c o n d u c t e d b y
restricting the w o r l d price o f risk to be the s a m e across markets. It is u n l i k e l y ,
h o w e v e r , that the K o r e a n m a r k e t p o r t f o l i o w o u l d be s o l e l y e x p l a i n e d b y the
c o v a r i a n c e o f its returns w i t h the w o r l d m a r k e t portfolio, g i v e n the capital c o n t r o l s
i m p l e m e n t e d b y the K o r e a n g o v e r n m e n t and to the e x t e n t that these capital
c o n t r o l s h a v e b e e n e f f e c t i v e in s e g m e n t i n g the K o r e a n stock market. It is therefore
u s e f u l to be able to test a m o r e g e n e r a l m o d e l that can deal w i t h the case o f a
partially s e g m e n t e d or i n t e g r a t e d capital m a r k e t in the p r e s e n c e o f barriers to
international investment.
T h e m o d e l o f E r r u n z a a n d L o s q (1985), d e v e l o p e d in a t w o - c o u n t r y f r a m e w o r k
w i t h the u n e q u a l access a s s u m p t i o n , s e e m s the right c h o i c e in this regard. T h e
p r i m a r y d i s t i n g u i s h i n g f e a t u r e o f their m o d e l f r o m the s t a n d a r d C A P M is that the
e q u i l i b r i u m price o f a local s e c u r i t y in a m i l d l y s e g m e n t e d m a r k e t is d e t e r m i n e d
j o i n t l y b y its i n t e r n a t i o n a l and n a t i o n a l risk p r e m i u m s :
E ( r k , I ~'~t-- 1) ~--- A ~ V A R ( r k , I g2t 1) + A k w C O V ( r k t , r w t I &f~t--1)"
(4)
E ( r w , j g-2, 1 ) = ~kwVAR(.rwt I ~¢~t- 1 ) ,
(5)
w h e r e Ak is the price o f the risk f r o m o w n - m a r k e t v a r i a n c e (hereafter called the
price o f v a r i a n c e risk), Akw is the price o f risk f r o m the c o v a r i a n c e w i t h the w o r l d
m a r k e t p o r t f o l i o ( h e r e a f t e r called the price o f c o v a r i a n c e risk), 3 a n d Aw d e n o t e s
the w o r l d price o f risk. A l t e r n a t i v e l y , Eq. (4) can be interpreted as the t w o - f a c t o r
v e r s i o n o f the arbitrage p r i c i n g t h e o r y o f R o s s (1976) w h e r e b o t h d o m e s t i c a n d
i n t e r n a t i o n a l factors a f f e c t the e q u i l i b r i u m returns.
T h i s s t u d y f o c u s e s on Eqs. (4) and (5). T h e m o d e l i n c o r p o r a t e s the i m p a c t o f
i n v e s t m e n t barriers on the pricing o f securities and o f f e r s a w e l l - d e f i n e d null
h y p o t h e s i s against w h i c h the h y p o t h e s i s o f no barriers to i n t e r n a t i o n a l i n v e s t m e n t
can be tested. T h e full i n t e g r a t i o n h y p o t h e s i s i m p l i e s that Ak = 0, Akw = A~, w h i l e
the c o m p l e t e s e g m e n t a t i o n h y p o t h e s i s s u g g e s t s that A , > 0 ,
Akw=0. "Mild
s e g m e n t a t i o n " i m p l i e s that Ak and Akw > 0.
For an e m p i r i c a l i m p l e m e n t a t i o n o f the m o d e l , the f o l l o w i n g s y s t e m o f
e q u a t i o n s is p r o p o s e d :
rk, = cek + Akhk, + Akwhkw,t + O'kZk,t--1 + ~:kt"
(6)
rwt = °~w + Awhwt + OwZw.t-i + •wt,
(7)
3 In Eq. (4), the w o r l d m a r k e t p o r t f o l i o i n c l u d e s the capitalization o f the K o r e a n s t o c k m a r k e t
portfolio. Ideally, b y d e c o m p o s i n g the w o r l d m a r k e t portfolio into the K o r e a n and n o n - K o r e a n parts,
m o r e p r e c i s e c o v a r i a n c e ( f o r e i g n ) e f f e c t s can b e m e a s u r e d . T h i s p r o c e d u r e is not e m p l o y e d s i n c e the
data o n the capitalization o f K o r e a n s t o c k s relative to w o r l d m a r k e t c a p i t a l i z a t i o n are not available and
the c a p i t a l i z a t i o n o f K o r e a n s t o c k s is o n l y a small part o f the capitalization o f the w o r l d m a r k e t
portfolio.
8
K.-H. Bae ~Pacific-Basin Finance Journal 3 (1995) 1 - 2 9
~t ~ N ( O , H , ) ,
H t = P'P
and H,
+ F'H t
thwk.,
1 F + G'Et_ , E;
hw ' ],
(8)
(9)
1G ,
w h e r e hkt d e n o t e s t he c o n d i t i o n a l v a r i a n c e o f rkt, hkw,, d e n o t e s the 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 n rkt and rwt, and h w t d e n o t e s the c o n d i t i o n a l v a r i a n c e o f rw,.
~t = [Ekt, Ew,]' is the n o r m a l e r r o r v e c t o r w h i c h is a s s u m e d to f o l l o w a b i v a r i a t e
n o r m a l d is tr ib u tio n. T h e i n f o r m a t i o n set o f i n v e s t o r s , /'2, 1, is p r o x i e d b y a set o f
i n s t r u m e n t s , Z t a, w h i c h i n c l u d e s o n l y past returns. T h e s p e c i f i c a t i o n for the
K o r e a n m a r k e t p o r t f o l i o i n c l u d e s t h r e e l a g g e d r e t u r n s to i n c o r p o r a t e the e f f e c t s o f
i n f r e q u e n t t r a d i n g on the d y n a m i c s o f i n d e x returns. T h e c h o i c e o f A R ( 3 ) t e r m s is
m o t i v a t e d b y th e l ar ge a u t o c o r r e l a t i o n s p r e s e n t at lag 2 and 3 in the K o r e a n m a r k e t
i n d e x r etu r n s . T h e A R ( 1 ) t e r m is also i n c l u d e d f o r the w o r l d m a r k e t p o r t f o l i o in
o r d e r to c a p t u r e a n y serial d e p e n d e n c e d ue to n o n s y n c h r o n o u s t r a d i n g o f the
c o m p o n e n t s o f the w o r l d m a r k e t index. T h e d y n a m i c s o f the v a r i a n c e - c o v a r i a n c e
m a t r i x , H t , f o l l o w the s p e c i f i c a t i o n o f B a b a et al. ( 1 9 8 9 ) ( B E K K ) w h e r e P is an
u p p e r t r i a n g u l a r m a t r i x o f c o e f f i c i e n t s , and F a n d G are free m a t r i c e s o f
c o e f f i c i e n t s . T h i s f o r m o f the g e n e r a l i z e d A R C H s t r u c t u r e e n s u r e s that the
c o n d i t i o n a l v a r i a n c e - c o v a r i a n c e m a t r i x is p o s i t i v e d e f i n i t e and is also r e l a t i v e l y
p a r s i m o n i o u s w i t h r e s p e c t to the n u m b e r o f p a r a m e t e r s to b e e s t i m a t e d (11 f o r the
b i v a r i a t e s y s t e m u s e d here). T h i s e m p i r i c a l s p e c i f i c a t i o n a l l o w s the risk p r e m i u m s
to c h a n g e as a result o f t i m e v a r i a t i o n in the c o n d i t i o n a l s e c o n d m o m e n t s o f e x c e s s
r e t u r n s alone.
G i v e n a s a m p l e o f T o b s e r v a t i o n s o f the r e t u r n s v e c t o r , rt, the p a r a m e t e r s o f
the b i v a r i a t e s y s t e m in Eqs. ( 6 ) - ( 9 ) are e s t i m a t e d b y c o m p u t i n g the 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 f o r e a c h t i m e p e r i o d as
1
1
L , ( ~ b ) = -- l o g 2 r r - - -2 l ° g I H t ( q ~ ) I - - "~ e ; ( t l b ) H t - I ( q b ) e t ( t l b ) ,
(10)
T
L(¢/)) = ~L,(qb),
(11)
t=l
w h e r e qb is th e v e c t o r o f all p a r a m e t e r s . N u m e r i c a l m a x i m i z a t i o n o f ( 1 1 )
f o l l o w i n g the B e r n d t et al. ( 1 9 7 4 ) a l g o r i t h m y i e l d s t he m a x i m u m l i k e l i h o o d
e s t i m a t e s and a s s o c i a t e d a s y m p t o t i c s t a n d a r d errors. S i n c e the a s s u m p t i o n o f
c o n d i t i o n a l n o r m a l i t y m a y not hol d, s t a n d a r d e r r o r s that are r o b u s t to n o n - n o r m a l ity are also c o m p u t e d f o l l o w i n g the p r o c e d u r e s u g g e s t e d in B o U e r s l e v and
W o o l d r i d g e (1990).
O n e f l a w w i t h the a b o v e m o d e l is that it c a n n o t c a p t u r e a p o s s i b l e t i m e
v a r i a t i o n o f the c o e f f i c i e n t s o n c o n d i t i o n a l v a r i a n c e s and c o v a r i a n c e . F o r a r a p i d l y
d e v e l o p i n g m a r k e t s u c h as K o r e a , o n e w o u l d e x p e c t the t i m e v a r i a t i o n in the p r i c e
o f risk c o n s i d e r i n g the s t r u c t u r a l c h a n g e s o b s e r v e d in the K o r e a n s t o c k m a r k e t
o v e r the last d e c a d e and g i v e n that t he p r i c e o f risk is an i n d i c a t o r o f t h e s e
K.-H. Bae / Pacific-Basin Finance Journal 3 (1995) 1--29
9
c h a n g e s . T h u s , the t i m e v a r i a t i o n o f the p r i c e o f risk n e e d s to b e e x p l i c i t l y
m o d e l l e d . N o t i c e also that the e s t i m a t e d risk p r e m i u m a s s u m i n g a c o n s t a n t p r i c e
o f risk m a y o v e r - or u n d e r s t a t e the true risk p r e m i u m s w h e n in f a c t t here is a
s i g n i f i c a n t v a r i a t i o n in the p r i c e o f risk.
3.2. The time-varying
price
of risk model
F o l l o w i n g C h o u et al. ( 1 9 9 2 ) , the f o l l o w i n g s y s t e m o f e q u a t i o n s is p r o p o s e d to
a l l o w f o r p a r a m e t e r v a r i a t i o n in Eqs. (6) and (7):
rkt = Otk + A k t h k t + A k w , t h k w , t + O ' k Z k , l - 1 + • k t '
(12)
rwt = cew + A w t h w t + O f v Z w , t _ 1 -i- E w t ,
(13)
At = At-1 + u,,
(14)
E,- N(0,H,),
(15)
I-1t = P ' P
(16)
where
+ F ' H t _ 1F + G'Tlt_ 17-1~_ 1 G ,
At = [ Akt,Akw.t,Awt]',
(17)
c, ,~ N ( O , Q ) ,
(18)
[o
0
r h = rt -- E t _ 1(#",) •
O,~,,J
(20)
T h e a b o v e m o d e l is a r e p r e s e n t a t i o n o f ( 6 ) - ( 9 ) w i t h t i m e - v a r y i n g c o e f f i c i e n t s .
T h e m o d e l is a m o d i f i e d v e r s i o n o f C h o u et al. ( 1 9 9 2 ) e x t e n d e d to the b i v a r i a t e
s y s t e m . T h i s r e p r e s e n t a t i o n is the state s p a c e f o r m that can be r e c u r s i v e l y
e s t i m a t e d b y m e a n s o f the K a l m a n filter. T h e e l e m e n t s o f At are a l l o w e d to
i n t e r a c t t h r o u g h the o f f - d i a g o n a l e l e m e n t s o f the d i s p e r s i o n m a t r i x , Q. H e r e ,
h o w e v e r , all o f f - d i a g o n a l e l e m e n t s o f Q are set e q u a l to z e r o in o r d e r to r e d u c e
the n u m b e r o f p a r a m e t e r s to b e e s t i m a t e d .
T h e p r i c e o f risk p a r a m e t e r s ( t he state v a r i a b l e s ) are n o t d i r e c t l y o b s e r v a b l e and
t h e i r m o v e m e n t s are a s s u m e d to be g o v e r n e d b y a r a n d o m w a l k p r o c e s s . A l t h o u g h
the a s s u m p t i o n that t he p r i c e o f risk v e c t o r f o l l o w s a m u l t i v a r i a t e r a n d o m w a l k
p r o c e s s m a y n o t be p l a u s i b l e , it is not e n t i r e l y u n r e a s o n a b l e to the e x t e n t that the
p r i c e o f risk r e f l e c t s the c h a n g i n g i n v e s t m e n t o p p o r t u n i t y set and this o p p o r t u n i t y
set f o l l o w s a r a n d o m w a l k p r o c e s s . P l a u s i b l y , o n e w o u l d c h a n g e the e s t i m a t e s o f
the state v a r i a b l e s (the p r i c e o f risk v e c t o r ) o n l y w h e n n e w i n f o r m a t i o n b e c o m e s
a v a i l a b l e , thus s u g g e s t i n g the r a n d o m w a l k p r o c e s s . S i n c e the p a r a m e t e r s are no
l o n g e r c o n s t r a i n e d to h a v e a f i x e d m e a n , the v a l u e s t a k e n at the end o f the s a m p l e
K.-H. B a e / P a c i f i c - B a s i n F i n a n c e J o u r n a l 3 (1995) 1 - 2 9
10
p e r i o d m a y b e q u i t e d i f f e r e n t f r o m t h o s e at the b e g i n n i n g . T h u s , t h e m o d e l is a b l e
to a c c o m m o d a t e f a i r l y f u n d a m e n t a l c h a n g e s in s t r u c t u r e a n d m a y b e a t t r a c t i v e f o r
a r a p i d l y d e v e l o p i n g m a r k e t s u c h as K o r e a .
in this model, H t follows a modified GARCH process. The replacement of the
original innovation error vector, Et-1, with a newly-defined prediction error
v e c t o r , 7/t 1, in t h e v a r i a n c e e q u a t i o n is n e c e s s a r y s i n c e b o t h the c o e f f i c i e n t s a n d
e x p l a n a t o r y v a r i a b l e s are u n o b s e r v a b l e a n d n e e d to b e e s t i m a t e d . I f the e x p l a n a t o r y v a r i a b l e s are o b s e r v a b l e , the m o d e l r e d u c e s to the u s u a l t i m e - v a r y i n g
r e g r e s s i o n m o d e l . W i t h this r e p l a c e m e n t , the m o d e l is c o n d i t i o n a l l y G a u s s i a n , j u s t
as in the o r i g i n a l G A R C H m o d e l w i t h t i m e - i n v a r i a n t c o e f f i c i e n t s . T h i s m a y n o t b e
s a t i s f a c t o r y i f t h e G A R C H e f f e c t s are r e g a r d e d as s t e m m i n g f r o m Et_ 1T h e r e are t h r e e sets o f u n k n o w n s to b e e s t i m a t e d in the m o d e l : A t , t h e s t a t e
v a r i a b l e s ; He, the c o n d i t i o n a l v a r i a n c e s a n d c o v a r i a n c e s o f E~; a n d P , G , F , Q
a n d 0, t h e f i x e d p a r a m e t e r s . T h e e s t i m a t i o n is c a r r i e d o u t b y the K a l m a n f i l t e r a n d
the m a x i m u m l i k e l i h o o d e s t i m a t i o n s i m u l t a n e o u s l y . T h e l i k e l i h o o d f u n c t i o n c a n b e
o b t a i n e d d i r e c t l y f r o m the p r e d i c t i o n e r r o r d e c o m p o s i t i o n ( H a r v e y , 1 9 8 0 ) . T h e
l o g - l i k e l i h o o d f u n c t i o n f o r t h i s m o d e l c a n b e w r i t t e n in t e r m s o f the p r e d i c t i o n
e r r o r v e c t o r as
L,(qb)
:
1
1
-- l o g 2 " n - - - ~- I V t ( ~ ) I -- ~ r / ; ( q 0 ) V , - l ( q ~ ) ' r h ( q : ' ) ,
(21)
T
L(t/)) = Y~Lt(qb),
(22)
t=l
w h e r e Vt is the c o n t e m p o r a n e o u s v a r i a n c e a n d c o v a r i a n c e m a t r i x o f r/t.
I n i t i a l v a l u e s are r e q u i r e d f o r state, v a r i a n c e a n d c o v a r i a n c e v a r i a b l e s as w e l l as
f o r t h e f i x e d p a r a m e t e r s . V a l u e s f r o m e s t i m a t i n g the c o n s t a n t p r i c e o f r i s k m o d e l
are e m p l o y e d as initial v a l u e s . T h e m o d e l a l s o r e q u i r e s t h a t t h e d i s t r i b u t i o n o f t h e
initial state v a r i a b l e s b e k n o w n . A d i f f u s e p r i o r d i s t r i b u t i o n is a s s u m e d f o r the
initial s t a t e v a r i a b l e s : i.e., a l a r g e v a l u e ( 1 0 0 0 ) is a s s i g n e d f o r t h e i r v a r i a n c e s .
4. D a t a
and summary
statistics
T h e d a t a u s e d in this s t u d y are b a s e d o n t h e t i m e s e r i e s o f d a i l y s t o c k m a r k e t
i n d i c e s f o r the K o r e a n C o m p o s i t e S t o c k P r i c e I n d e x ( K O S P I ) o b t a i n e d f r o m t h e
K o r e a n S t o c k E x c h a n g e a n d the M o r g a n S t a n l e 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 )
w o r l d i n d e x f r o m J a n u a r y 1 9 8 0 to D e c e m b e r 1 9 9 0 . T h e K O S P I is a v a l u e - w e i g h t e d
i n d e x o f all c o m m o n s t o c k s l i s t e d o n the K o r e a n S t o c k E x c h a n g e . W e e k l y r e t u r n s
are e x a m i n e d as a c o m p r o m i s e b e t w e e n the m a n y d a i l y o b s e r v a t i o n s w i t h i n a
g i v e n c a l e n d a r t i m e a n d t h e less s e v e r e m e a s u r e m e n t e r r o r s in m o n t h l y r e t u r n s .
P r o b l e m s a r i s i n g f r o m n o n t r a d i n g w o u l d n o t b e as s e r i o u s in w e e k l y r e t u r n d a t a as
in d a i l y data. W e e k l y r e t u r n s are c o m p u t e d b y t a k i n g the d i f f e r e n c e o f t h e
logarithms of every Wednesday's closing price,
K. -H. B a e / P a c i f i c - B a s i n F i n a n c e J o u r n a l 3 ( 1 9 9 5 ) 1 - 2 9
11
Table 3
S u m m a r y statistics for the K O S P I and M S C I w o r l d index e x c e s s returns (in percent) f r o m J a n u a r y
1 9 8 0 to D e c e m b e r 1 9 9 0 . W e e k l y e x c e s s r e t u r n s a r e c o m p u t e d b y t a k i n g t h e l o g d i f f e r e n c e o f the
W e d n e s d a y c l o s i n g p r i c e s . D o l l a r - d e n o m i n a t e d e x c e s s r e t u r n s a r e net o f t h e t h r e e - m o n t h U . S . T r e a s u r y
bill yield, w h i l e W o n - d e n o m i n a t e d
e x c e s s r e t u r n s are n e t o f call m o n e y rate. T h e K o l m o g o r o v
D-statistic tests the null h y p o t h e s i s o f n o r m a l i t y . L B ( 6 ) and L B ( 1 2 ) are the L j u n g - B o x statistic for the
f i r s t 6 a n d 12 l a g s o f a u t o c o r r e l a t i o n f u n c t i o n s o f r a w e x c e s s r e t u r n s a n d t h e i r s q u a r e s . T h e p - v a l u e s
are for the X 2 distribution
Statistics
MSCI
($)
KOSPI
(Won)
MSCI
(Won)
A: Distributional statistics
NOBS
554
554
554
554
Mean(%)
80.1-90.12
80.1-85.6
85.7-90.12
0.0643
-- 0 . 0 5 7 6
0.1846
0.0745
-- 0 . 1 3 1 8
0.2778
Std. D e v , ( % )
80,1-90,12
80.1-85. 6
85.7-90.12
Skewness
Kurtosis
Range
D-statistic
(p-value)
KOSPI
($)
0.1238
-- 0 . 2 1 6 4
0.4592
2.7139
2.3306
3.0116
0.2419
0.1287
16.7680
0.9821
(0.1594)
1.8585
1.8284
1.8833
-- 0 . 1 2 7 3
0.8025
14.3862
0.9906
(0.9611)
2.6803
2.3172
2.9858
0.1860
0.1955
17.5660
0.9861
(0.6039)
0.0157
0.0288
0.0027
1.8085
1.7632
1.8552
--0.1960
1.0831
14.1385
0.9875
(0.7682)
Panel B: Autocorrelations of excess returns
Series: r t
P1
P2
P3
P4
Ps
P6
LB 6
(p-value)
L B 12
(p-value)
0.0459
0.0702
0.0910
0.0542
0.0121
0.0612
12.40
(0.05)
21.54
(0.04)
0.0740
0.0114
0.0582
0.0381
-- 0 . 0 1 2 1
-- 0 . 0 4 0 7
6.85
(0.33)
15.46
(0.22)
0.0195
0.0502
0.0683
0.0273
-- 0 . 0 1 0 8
0.0415
5.69
(0.46)
11.41
(0.49)
0.0512
-- 0 . 0 0 1 0
0.0620
0.0324
-- 0 . 0 1 3 4
-- 0 . 0 4 8 6
5.63
(0.47)
15.92
(0.20)
S e r i e s : rt 2
Pt
P2
03
P4
P5
,06
LB 6
(p-value)
L B 12
(p-value)
0.1550
0.1401
0.1132
0.1302
0.0841
0.0364
45.71
(0.00)
80.91
(0.00)
0.1198
0.1780
0.0072
0.0393
0.1159
0.0484
35.44
(0.00)
63.01
(0.00)
0.1492
0.1391
0.1114
0.1394
0.0837
0.0268
48,37
(0,00)
80.52
(0.00)
0.1245
0.1827
0.0117
0.0568
0.1354
0.0598
41.45
(0.00)
66.65
(0.00)
12
K.-H. B a e / P a c i f i c - B a s i n F i n a n c e J o u r n a l 3 (1995) 1 - 2 9
T h e m o d e l e s t i m a t i o n r e q u i r e s r i s k - f r e e r e t u r n d a t a to c o m p u t e e x c e s s r e t u r n s
s e r i e s . T h e p r o b l e m o f a s s u m i n g a r i s k - f r e e r a t e is t r o u b l e s o m e f o r t h e K o r e a n
s t o c k m a r k e t w h e r e a s h o r t - t e r m m o n e y m a r k e t r a t e s i m i l a r to t h e U . S . T - b i l l r a t e
is n o t r e a d i l y a v a i l a b l e . T h e c a l l m o n e y r a t e is u s e d as a p r o x y f o r t h e r i s k - f r e e
rate. T h e data are o b t a i n e d f r o m I n t e r n a t i o n a l F i n a n c i a l Statistics. O n l y m o n t h l y
data are available, the use of which implicitly assumes that the monthly call
money rate does not change over the month. Since Won-denominated
excess
returns include a p o o r p r o x y for the r i sk - f r e e rate, d o l l a r - d e n o m i n a t e d w e e k l y
excess returns are also examined; they are computed net of the three-month U.S.
T r e a s u r y b i l l y i e l d . T h e e x c h a n g e - r a t e d a t a to c o n v e r t W o n - d e n o m i n a t e d
returns
into dollar-denominated returns are obtained from the Bank of Korea. Given that
t h e p u r p o s e is to e x a m i n e t h e d i f f e r e n c e o f r i s k p r e m i u m s b e t w e e n t h e K o r e a n a n d
world capital markets, use of dollar excess returns would serve the purpose well
and may be more appropriate. The discussion of empirical results focuses on the
dollar excess returns.
T h e u s e o f c o m m o n c u r r e n c y e x c e s s r e t u r n s a s s u m e s t h a t t h e i n v e s t o r is
u n h e d g e d against e x c h a n g e rate risk. A l t e r n a t i v e l y , the issue o f e x c h a n g e risk c a n
b e s i m p l i f i e d a w a y b y a s s u m i n g a l o g a r i t h m i c u t i l i t y f u n c t i o n f o r all i n v e s t o r s .
U n d e r t h e s e c o n d i t i o n s , t h e p r i c e l e v e l a n d q u e s t i o n s r e l a t e d to p u r c h a s i n g p o w e r
parity become irrelevant for optimal portfolio choice (Adler and Dumas, 1983).
S i n c e b o t h a s s u m p t i o n s a r e o p e n to q u e s t i o n , o w n c u r r e n c y e x c e s s r e t u r n s a r e a l s o
e x a m i n e d . T h e i n t e r p r e t a t i o n o f t h i s a p p r o a c h , w h i c h is p i o n e e r e d b y S o l n i k
( 1 9 7 4 ) , is t h a t o n e g o e s s h o r t o n e u n i t o f f o r e i g n c u r r e n c y f o r e a c h p u r c h a s e o f o n e
unit of foreign currency stock. This approach may be unsatisfactory either when
m e c h a n i s m s to h e d g e a w a y e x c h a n g e - r a t e r i s k s a r e n o t e a s i l y a v a i l a b l e in t h e
K o r e a n m a r k e t o r w h e n e x c h a n g e c o n t r o l s a r e in e f f e c t . F u r t h e r m o r e , if m o v e m e n t s in s t o c k p r i c e s a n d e x c h a n g e r a t e s a r e c o r r e l a t e d , it w o u l d n o t b e p o s s i b l e to
c o m p l e t e l y h e d g e a g a i n s t e x c h a n g e risk.
Panel A of Table 3 presents summary statistics for the KOSPI and MSCI excess
returns. For the whole period, the KOSPI performs better than the MSCI with an
a v e r a g e d o l l a r e x c e s s r e t u r n s o f 0 . 1 2 % c o m p a r e d to 0 . 0 6 % f o r t h e M S C I w o r l d
i n d e x . T h e s t a n d a r d d e v i a t i o n o f e x c e s s r e t u r n s is m u c h h i g h e r f o r t h e K O S P I w i t h
2 . 7 1 % r e l a t i v e to 1 . 8 6 % f o r t h e M S C I . T h e s e f i g u r e s c o r r e s p o n d to a s t a n d a r d
deviation of 19.5% and 13.4% per year for each index. The breakdown of the
whole period shows that the mean excess returns over the second half of the
s a m p l e p e r i o d are m u c h h i g h e r than those o v e r the first h a l f for b o t h indices. T h e
c h a n g e in p e r f o r m a n c e is q u i t e d r a m a t i c w i t h t h e K o r e a n s t o c k m a r k e t f r o m
- - 0 . 2 2 % to 0 . 4 6 % in d o l l a r r e t u r n s . T h e M S C I e x c e s s r e t u r n s e x h i b i t s o m e
negative skewness, while the Korean index shows positive skewness. The magnit u d e o f e x c e s s k u r t o s i s is h i g h e r w i t h t h e M S C I . T h e K o l m o g o r o v D - s t a t i s t i c d o e s
not reject the null hypothesis of normality for both KOSPI and MSCI, although
significance levels are lower with the MSCI index.
A u t o c o r r e l a t i o n c o e f f i c i e n t s a r e p r e s e n t e d in P a n e l B f o r t h e r a w e x c e s s r e t u r n s
K.-H. Bae / Pacific-Basin Finance Journal 3 (1995) 1 - 2 9
13
and s q u a r e d r e t u r n s series. T h e K O S P I e x h i b i t s large a u t o c o r r e l a t i o n s at lag 2 a n d
3, e s p e c i a l l y in d o l l a r r e t ur ns , w h i l e the M S C I s h o w s a h i g h a u t o c o r r e l a t i o n at lag
1. T h e L j u n g - B o x statistic s t r o n g l y r e j e c t s the null h y p o t h e s i s o f w h i t e n o i s e f o r
the K O S P I e x p r e s s e d in dol l ar t er m s , s u g g e s t i n g the n e e d to c o n t r o l for serial
d e p e n d e n c e s in th e m o d e l e s t i m a t i o n . W h i l e the K O S P I in W o n t e r m s e x h i b i t s less
s e r i o u s a u t o c o r r e l a t i o n s , serial d e p e n d e n c e s are also c o n t r o l l e d up to lag 3. T h e
a u t o c o r r e l a t i o n s o f s q u a r e d series are s i g n i f i c a n t l y p o s i t i v e and d e c a y at a s l o w
rate, e s p e c i a l l y f o r the K O S P I , s u g g e s t i n g the p r e s e n c e o f t i m e - v a r y i n g v o l a t i l i t y .
T h e L j u n g - B o x statistics e a s i l y r e j e c t the null h y p o t h e s i s o f w h i t e n o i s e f o r b o t h
indices. T h e a u t o r e g r e s s i v e n a t u r e o f s q u a r e d r e t u r n s s u g g e s t s that the v a r i a n c e
p r o c e s s e s o f the e x c e s s r e t u r n s da t a w o u l d be w e l l a p p r o x i m a t e d b y the A R C H - t y p e
model.
5. E m p i r i c a l results
5.1. The c o n s t a n t p r i c e o f risk m o d e l
E s t i m a t e s f r o m the c o n s t a n t p r i c e o f risk m o d e l are p r e s e n t e d in T a b l e 4. 4 T h e
i n d i v i d u a l c o e f f i c i e n t e s t i m a t e s o f the d y n a m i c s o f v a r i a n c e - c o v a r i a n c e m a t r i x
f r o m Eq. (9) are d i f f i c u l t to interpret, but the s i g n i f i c a n c e o f the d i a g o n a l
c o e f f i c i e n t e s t i m a t e s in the P , G and F m a t r i c e s i m p l y a v e r y hi gh p e r s i s t e n c e o f
s h o c k s to the v a r i a n c e s in b o t h indices.
T h e e s t i m a t e s o f Ak, Akw, a n d Aw are 3.24, 4 . 6 6 and 2.71, r e s p e c t i v e l y , f o r the
w h o l e s a m p l e p e r i o d , w h i c h are all i ns i gn i fi cant . W o n a n d o w n - c u r r e n c y e x c e s s
r e t u r n s s h o w s i m i l a r results. T h e c o m p l e t e s e g m e n t a t i o n h y p o t h e s i s c a n n o t be
r e j e c t e d , in the s e n s e that the p r i c e o f c o v a r i a n c e risk is n e v e r s i g n i f i c a n t l y
p o s i t i v e . T h e l i k e l i h o o d ratio test d o e s not r e j e c t the null h y p o t h e s i s o f c o m p l e t e
s e g m e n t a t i o n at the u s u a l s i g n i f i c a n c e level. T h e full i n t e g r a t i o n h y p o t h e s i s is also
n o t r e j e c t e d , i n d i c a t i n g the m o d e l has no p o w e r to d i s c r i m i n a t e against c o m p e t i n g
h y p o t h e s e s . Fig. 2 s h o w s the p r e d i c t e d e x c e s s r e t u r n s f r o m the m o d e l f o r b o t h
i n d i c e s , u s i n g d o l l a r e x c e s s returns. Fig. 2 s h o w s no p a r t i c u l a r p a t t e r n o f t i m e v a r y i n g risk p r e m i u m s .
T h e l a c k o f s i g n i f i c a n c e o f the c o e f f i c i e n t s on the c o n d i t i o n a l v a r i a n c e s , Ak and
Aw, is t r o u b l e s o m e . O n e w o u l d t y p i c a l l y e x p e c t a p o s i t i v e r e l a t i o n b e t w e e n the
c o n d i t i o n a l e x p e c t e d e x c e s s r e t u r n on the m a r k e t p o r t f o l i o and the c o n d i t i o n a l
v a r i a n c e o f its r et ur n, e v e n if the capital asset p r i c i n g m o d e l d o e s n o t h o l d (see,
e.g., M e r t o n , 1 9 8 0 and F r e n c h et al., 1987). A p l a u s i b l e e x p l a n a t i o n is that the
4 T h e e m p i r i c a l r e s u l t s s h o w n in the f o l l o w i n g s e c t i o n s are o b t a i n e d b y e x c l u d i n g t h e o b s e r v a t i o n f o r
t h e w e e k o f t h e O c t o b e r 1987 m a r k e t c r a s h . T h e e s t i m a t e s o f p a r a m e t e r s o b t a i n e d i n c l u d i n g the
O c t o b e r m a r k e t c r a s h are s i m i l a r to t h o s e r e p o r t e d .
[ h~k'z
-0.1852
(-0.67)
[ - 1.92]
-0.1502
( - 0.57)
[ - 2.57]
-0.0705
( - 0.26)
[- 2.78]
Dollar
Own
Won
cq
Currency
0.0013
(0.01)
[0.00]
0.0070
(0,03)
[0.03]
0.2735
(1.34)
[1.50]
ctw
1.1795
(0.28)
[0.58]
3.2439
(0.76)
[1.25]
3.4391
(0.82)
[2.22]
Ak
5.7201
(0.50)
[0.46]
4.6569
(0,39)
[0.36]
-3.1239
( - 0.24)
[ - 0.27]
hkw
3.0208
(0.42)
[0.52]
2.7128
(0,37)
[0.40]
-6.7158
( - 1.01)
[ - 1.08]
hw
-0.0235
( - 0.55)
[ - 0.52]
0.0035
(0.08)
[0.08]
-0.0287
( - 0.66)
[ - 0.64]
Okl
hwt I and Ht=P'P+F'Ht_IF+G'e,_le;_IG
Panel A: Parameter estimates of the mean equation
~Wtl
rwt = aw q- A~h~t + Owlr~,t-1 + %t,
rkt = ctk + hkhk~ + Ak~,hkw,~+ Oklrk,t-1 + Ok2rk,t-2 + Ok3rk,t 3 -}- ~.kt,
0.0402
(0.90)
[0.92]
0.0601
(1.39)
[1.35]
0.0312
(0.69)
[0.72]
Ok2
0.0275
(0.64)
[0.62]
0.0438
(1.05)
[0.97]
0.0232
(0.53)
[0.54]
Ok3
0.1006
(2.24)
[2.22]
0.0984
(2.19)
[2.18]
0.0819
(1.92)
[1.75]
Owl
2693.36
R~ = 0.44%
R~ = 0.57%
2687.95
R~ = 1,11%
R~ = 0.38%
2709.95
R~ = 0.29%
R2~= 0.29%
logL
Table 4
Estimates from the fixed-parameterbivariate GARCH(1,1)-M model for the KOSPI and MSCI world index excess returns. Covariance dynamics specification
follows the formulation of BEKK ensuring the positive definiteness of the variance-covariance matrix in the GARCH model. Standard t-statistics are
presented in parenthesis and robust t-statistics computed with quasi-maximum likelihood method are in brackets. The model parameters are given by the
following system of equations. R~ and R2~ denote the ratio of the explained to total variation for the KOSPI and MSCI world index excess returns
I
I,o
r,
t%
t~
t~
"x.
t%
i
Own
Won
Dollar
Currency
- 0.4893
(-3.52)
[ - 3.72]
- 0.2030
( - 0,91)
[-1.16]
-0.4476
(-2.77)
[-3.30]
P22
- 0.2264
(-6.34)
[ - 6.08]
- 0.2775
( - 6.01)
[-8.58]
-0.2473
(-6.60)
[-6.34]
Gll
- 0.0278
(-0.07)
[ - 0.12]
- 0.0363
( - 0.16)
[-0.26]
-0.1131
(-0,37)
[-0.58]
P~2
Pll
0.2503
(1.72)
[1.69]
0.4101
(2.82)
[3.34]
0.3161
(2.75)
[2.26]
G
P
0.0003
(0.00)
[0.06]
0.0360
(0.57)
[0,94]
0.0005
(0.01)
[0.01]
G21
Panel B: Parameter estimates of the variance and covariance matrix
- 0.0789
(-2.54)
[ - 2.33]
- 0.1132
( - 4.45)
[-4.18]
-0.0776
(-2.52)
[-2.44]
GI2
- 0.2819
(-5.03)
[ - 6.13]
- 0.2094
( - 5.62)
[-5.32]
-0.2796
(-5.17)
[-6.12]
G22
0.9664
(92.04)
[77.97]
0.9430
(50.88)
[75.01]
0.9591
(80,17)
[66.36]
Fll
F
F21
0.0453
(1.13)
[2.39]
0.0926
(2.68)
[9.47]
0.0484
(1.18)
[1,88]
- 0.0314
(-2.37)
[ - 2.77]
- 0.0634
( - 5.52)
[-5.36]
-0.0313
(-2.29)
[-2.59]
F12
0,9161
(30.18)
[27.06]
0.9589
(52.85)
[45.67]
0.9216
(31.42)
[28,97]
F22
I
I,o
_,7,'
t~
K.-H. B a e ~ P a c i f i c - B a s i n F i n a n c e J o u r n a l 3 (1995) 1--29
16
1
0.8
0.6
0.4
c~
.~_
0.2
~
o
~
-0.2
-0.4
-0.6
KOSPI -
--MSCE]
F i g . 2. P r e d i c t e d e x c e s s r e t u r n s f r o m t h e c o n s t a n t p r i c e o f r i s k m o d e l .
p r i c e o f risk p a r a m e t e r s m a y be t i m e v a r y i n g . T o e x a m i n e a p o s s i b l e t i m e
v a r i a t i o n in the p r i c e o f risk p a r a m e t e r s , the m o d e l is r e e s t i m a t e d splitting t he
s a m p l e into t w o s u b p e r i o d s w i t h a d u m m y v a r i a b l e .
rkt = ot k + A k h k t q- A k w h k w . , + ( A~ hkt + A ~ w h k ~ . t ) O t + O'kZ'k,t_ 1 "t- Ekt ,
(23)
rwt = o~w + A w h w t + ( A* h w , ) D ,
+ O~Zw,,_ 1 + ew,.
(24)
D t t a k e s the v a l u e o f 0 b e f o r e 1 9 8 5 . 6 and the v a l u e o f 1 aft er 1985.6.
T a b l e 5 p r e s e n t s the e s t i m a t e d v a l u e s . A l l the e s t i m a t e s o f As s h o w a
s u b s t a n t i a l c h a n g e a c r o s s s u b p e r i o d s . T h e e s t i m a t e s o f the p r i c e s o f risk are
n e g a t i v e in the first s u b p e r i o d and b e c o m e p o s i t i v e in the s e c o n d s u b p e r i o d . W o n
a n d o w n - c u r r e n c y r e t u r n s s h o w s i m i l ar results. T h e i nst abi l i t y o f the e s t i m a t e d
c o e f f i c i e n t s a c r o s s the s u b s a m p l e p e r i o d s s u g g e s t s the n e e d to e x p l i c i t l y m o d e l the
t i m e v a r i a t i o n in the risk prices.
5.2. T h e t i m e - v a r y i n g p r i c e o f r i s k m o d e l
T a b l e 6 s h o w s the p a r a m e t e r e s t i m a t e s o f the t i m e - v a r y i n g p r i c e o f risk m o d e l .
T h e c o n v e r g e d v a l u e s f o r the p a r a m e t e r s in the v a r i a n c e e q u a t i o n s are c l o s e to the
e s t i m a t e s in the c o n s t a n t p r i c e o f risk m o d e l , s u g g e s t i n g the e s t i m a t e s o f the
c o n d i t i o n a l v a r i a n c e s a nd c o v a r i a n c e s in the t w o m o d e l s will al so be cl ose. T h e
o f f - d i a g o n a l c o e f f i c i e n t s in the G a n d F m a t r i c e s are m o s t l y s i g n i f i c a n t r e g a r d l e s s
o f the c u r r e n c y u s e d, s u g g e s t i n g the p o s s i b l e d e p e n d e n c e o f the K o r e a n s t o c k
m a r k e t o n the w o r l d m a r k e t .
T h e c o m p a r i s o n o f e x p l a n a t o r y p o w e r s s h o w s that the e x p l a i n e d v a r i a t i o n o f
e x c e s s r e t u r n s f r o m the t i m e - v a r y i n g p r i c e o f risk m o d e l is s u b s t a n t i a l l y h i g h e r
t h a n in the c o n s t a n t p r i c e o f r i s k m o d e l f or b o t h indices. R 2 s u b s t a n t i a l l y i n c r e a s e s
f r o m 1 . 1 1 % to 8 . 4 3 % f o r the K O S P I e x p r e s s e d in d o l l a r e x c e s s ret urns, a t r e n d
Ok3
Owl
log L
-0.0319 0.1985 -0.6250 -12.8476 -6,7689
(-0.12) (0.86)(-0.12)
(-0.64)
(-0.87)
[-0,58] [0.96] [-0.24] [-0.72]] [-0.88]
Okz
Own
0kl
-0.0453 0,3592 -0.2672 -18.8857 -10.5044 4.3506 21.5579 2.0011 -0.0284 0.0160 0.0194 0.0828 2712.14
(-0.17) (1.75)(-0.05)
(-0.90)
(-1.42)
(1.15) (0.83) (0.40) (-0.64) (0,35) (0.43) (1.95) R~ = 0.81%
[-2.53] [1.87] [-0.10] [-1.08]
[-1,38]
[1.21] [0.88] [0.50] [-0.66] [0.37] [0.47] [1.77] R2w= 0.34%
A~
3.4594 23.2970 7.6458 -0.0265 0.0292 0.0228 0.0971 2695.61
(0.95) (0,95) (1.61) (-0.61) (0.64) (0.51) (2.21) R~ = 0.84%
[0.94] [0.98] [1,60] [-0.64] [0.67] [0.54] [2.13] R2~,= 0,79%
7,1416 17.7695 6.5522 -0.0051 0.0471 0.0368 0.0965 2692.03
(1.75) (0.65) (1,38) (-0.11) (1.07) (0.86) (2.09)
= 2.50%
[1,69] [0.65] [1.46] [-0,11] [1.07] [0.84] [2.13] R2w~- 0.68%
A~
Won
-1.7664
(-0.22)
[-0.24]
A~
0.0540 -3.7503 -8.8509
(0.22) (-0.70) (-0.38)
[0,25] [-1.14] [-0.40]
Aw
0.0636
(0,23)
[3.37]
Akw
Dollar
Ak
and Hr = P'P + F'H, 1f + G'et_ 1e;_ IG.
oLw
hwt J
Currency otk
ekt " N(O,H t), where H t =
L~Wtl
lhwk,t
r,~, = ~,~ + Awh~t + ( A~hwt)O t + Owlrw,,_ 1 + ewt,
rkt = oLk -F Akh~t + Akwhkw,t + (h~ hi:t + A~whkw,t)D t + Oklrk,t_l -F Ok2rk,t_ 2 + Ok3rk,t_ 3 -F 'kt,
Table 5
Estimates from the dummy model for the KOSPI and MSCI world index excess returns, Covariance dynamics specification follows the formulation of BEKK
ensuring the positive definiteness of the variance-covariance matrix in the GARCH model. O t takes the value of 0 before 1985.6 and the value of 1 after
1985.6. Standard t-statistics are presented in parenthesis and robust t-statistics computed with quasi-maximumlikelihood method are in brackets. The model
parameters are given by the following system of equations. Only parameter estimates in the mean equations are reported. R~ and R~ denote the ratio of the
explained to total variation for the KOSPI and MSCI world index excess returns
I
r~
\
r
.~
.~
the,,,
[hk,
-0.1097
( - 0.31)
[-1.58]
- 0.1343
(-0.43)
[- 1.64]
- 0.0477
(-0.15)
[ - 2.62]
Dollar
Own
Won
ak
Currency
-0.1192
( - 0.43)
[-0.47]
0.1990
(0.89)
[0.97]
- 0.0665
(-0.25)
[- 0.28]
aw
-
L,Tw,]
r~,- E,_ ~(rw,)j
0.5476
(2.30)
[2.14]
0.3249
(2.00)
[1.98]
0.4356
(2.01)
[1.91]
Qak,
0.0067
(0.00)
[0.16]
0.0697
(0.01)
[0.20]
0.0020
(0.00)
[0.11]
Q~,~,
0.7056
(1.90)
[1.72]
0.4096
(1.58)
[1.31]
0.5776
(1.87)
[1.65]
Q~w,
-0.0270
( - 0.61)
[-0.59]
- 0.0256
(-0.55)
[-0.57]
- &0264
(-0.57)
[ - 0.58]
Ok1
0.0463
(1.00)
[1.02]
0.0302
(0.63)
[0.68]
0.0336
(0.71)
[0.74]
Ok:
0.0398
(0.91)
[0.87]
0.0267
(0.59)
[0.61]
0.0283
(0.63)
[0.62]
Ok3
['q,,]
r,,-E,-l(r,t)]
hkw t]
hw; and Ht= P'P + g'n t 1f + G'~t_l.;_lG, where
=
PandA: Parameter estimates of the mean equation
L,~, /
['kt] ~ g(O'Ht)' st =
/ / A~
L _1
At= A,_ a+ vt, where A, = iAkw,tl,vt ~ N(O,Q),
rwt ~ a,~ + Awthwt + Owlrw,t_a+ ~wt,
rkt = ak + Akthkt + Akw,thkw,t + Oklrk,t- 1 + Ok2rk,t 2 + Ok3rk,t- 3 + Ekt'
0.0796
(1.78)
I1.68]
0.0757
(1.77)
[1.55]
0.0902
(1.98)
[1.90]
Owl
2684.01
R~ = 8.43%
R2=4.15%
2703.03
R~ = 5.65%
R~ = 3.28%
2687.48
R~ = 6.93%
R~ = 3.79%
log L
Table 6
Estimates from the time-varying parameter bivariate GARCH(1,1)-M model for the KOSPI and MSCI world index excess returns. Standard t-statistics are
presented in parenthesis and robust t-statistics computed with quasi-maximum likelihood method are in brackets. The model parameters are given by the
following system of equations and the estimation is carried out by the Kalman filter and the maximum likelihood estimation simultaneously in the state space
model framework. R~ and R z denote the ratio of the explained to total variation for the KOSPI and MSCI world index excess returns.
\
L
Own
Won
Dollar
Currency
[1,91]
(2.14)
[1.04]
0.3772
(2.57)
[2,97]
0,2881
(0.89)
0.2095
-0.2225
(-0.49)
[ - 0.54]
-0.0111
( - 0.04)
[ - 0.07]
-0.1461
( - 0.45)
[ - 0.62]
-0.3344
(-1.11)
[ - 1.26]
-0.2539
( - 1,55)
[ - 1.84]
-0.4298
( - 2.48)
[ - 3.07]
-0.1912
(-5.21)
[ - 5.27]
-0.2562
( - 5.77)
[ - 8.42]
-0.2308
( - 6.24)
[ - 6.19]
GII
P22
PII
P12
G
P
0.0631
(1.00)
[1.05]
0.0475
(0.76)
[0.84]
0.0280
(0,38)
[0.49]
G21
Panel B: Parameterestimates of the variance and covariance matrix
-0.1001
(-4.01)
[ - 3.46]
-0.1078
( - 4.60)
[ 4.07]
-0.0776
( - 2.71)
[ - 2.57]
G12
-0.2212
(-5.01)
[ - 5.09]
-0.2046
( - 5.91)
[ - 5.01]
-0.2613
( - 5.35)
[ - 5.81]
G22
0.9712
(82.14)
[79.76]
0.9509
(56.69)
[82.11]
0.9632
(80.41)
[69.59]
Fll
F
0.0812
(2.34)
[2.39]
0,0861
(2.56)
[3.35]
0.0591
(1.46)
[1.87]
F21
-0.0380
(-3.47)
[ - 3.43]
-0,0580
( - 5.23)
[ - 5.06]
-0.0311
( - 2.56)
[ - 2.60]
F1z
0.9389
(37.25)
[37.18]
0.9564
(52.42)
[47.79]
0.9266
(32.25)
[32.99]
F22
7~
I
~2
t...,
,,,,,
20
K.-H. B a e / Pacific-Basin F i n a n c e J o u r n a l 3 (1995) 1 - 2 9
also s e e n in W o n a n d o w n - c u r r e n c y r e t u r n s . T h e e x p l a n a t o r y p o w e r a l s o i n c r e a s e s
f o r t h e M S C I , a l t h o u g h not as i m p r e s s i v e l y as f o r t h e K O S P I , f r o m 0 . 3 8 % to
4 . 1 5 % in d o l l a r e x c e s s r e t u r n s w i t h s i m i l a r r e s u l t s f o r the o t h e r c u r r e n c y r e t u r n s .
O v e r a l l , t h e r e is a s t r o n g e v i d e n c e t hat t he t i m e - v a r y i n g p r i c e o f ri sk m o d e l
provides m o r e accurate estimates of the e x p e c t e d excess returns.
T h e p r e d i c t e d r i s k p r e m i u m s f r o m t h e t i m e - v a r y i n g p r i c e o f ri sk m o d e l c a n b e
q u i t e d i f f e r e n t f r o m t h o s e e s t i m a t e d a s s u m i n g a c o n s t a n t p r i c e o f risk, as the p r i c e
o f r i s k v e c t o r , At, v a r i e s s i g n i f i c a n t l y o v e r t i m e . T h e d a t a s u g g e s t that A t i n d e e d
v a r i e s s i g n i f i c a n t l y f o r b o t h i n d i c e s . W h e n d o l l a r r e t u r n s are e m p l o y e d , t he
e s t i m a t e d v a l u e s f o r t he p a r a m e t e r s in the d i s p e r s i o n m a t r i x , Q, are 0. 55 f o r the
p r i c e o f v a r i a n c e risk s er i e s , 0 . 0 0 6 7 f o r t h e p r i c e o f c o v a r i a n c e ri sk a n d 0 . 7 0 f o r
t h e w o r l d p r i c e o f risk, r e s p e c t i v e l y , w h i c h are s i g n i f i c a n t at the 5 % l e v e l e x c e p t
f o r t he p r i c e o f c o v a r i a n c e r i s k series. 5 U s e o f W o n a n d o w n - c u r r e n c y r e t u r n s
s h o w s i m i l a r results. W h e n d o l l a r e x c e s s r e t u r n s are u s e d , Akt r a n g e s f r o m - - 9 . 1 6
to 17.88, Ak~,,t f r o m - - 8 . 2 7 to 2 7 . 7 9 , a n d Awt f r o m - - 3 0 . 2 2 to 2 1 . 9 6 f o r t he
w h o l e s a m p l e p e r i o d . T h e w i d e r a n g e in t he p r i c e s o f ri sk is m a i n l y d u e to t h e
K a l m a n f ilter e s t i m a t i o n t e c h n i q u e w h e r e a d i f f u s e p r i o r is i m p o s e d o n t h e
i n i t i a l i z e d v a l u e s o f t he state v a r i a b l e s .
T h e n e g a t i v e e s t i m a t e s o f t he r i s k p r i c e s p r e s e n t s o m e p r o b l e m s . W h i l e it is
p o s s i b l e f o r th e e s t i m a t e s o f the r i s k p r i c e s to b e n e g a t i v e , a s i m p l e e c o n o m i c
i n t u i t i o n s u g g e s t s that t h e e x p e c t e d e x c e s s r e t u r n o n the m a r k e t p o r t f o l i o m u s t b e
p o s i t i v e . T h e i d e a is that t he e x p e c t e d r e t u r n o n t h e m a r k e t p o r t f o l i o s h o u l d e x c e e d
t h e r i s k - f r e e r a t e if a g e n t s are r i s k - a v e r s e a n d t h u s w a n t c o m p e n s a t i o n f o r risk. 6
H e n c e , g i v e n this p r i o r i n f o r m a t i o n , e a c h o f t h e risk p r i c e s s h o u l d b e p o s i t i v e a n d
a n e g a t i v e v a l u e f o r r i s k p r i c e s is a b i a s e d e s t i m a t e . A s M e r t o n ( 1 9 8 0 , p. 3 5 4 )
n o t e s , " . . . th e n o n - n e g a t i v i t y r e s t r i c t i o n o n t h e e x p e c t e d e x c e s s r e t u r n s s h o u l d b e
e x p l i c i t l y i n c l u d e d as pa r t o f the s p e c i f i c a t i o n " to c i r c u m v e n t this p r o b l e m . F o r
i n s t a n c e , b y i m p o s i n g a p r i o r d i s t r i b u t i o n f o r t he p r i c e o f risk w h i c h is r e s t r i c t e d t o
b e n o n - n e g a t i v e , t h e n o n - n e g a t i v i t y r e s t r i c t i o n o f the e x p e c t e d e x c e s s r e t u r n s c a n
b e t a k e n in to a c c o u n t . T h i s a p p r o a c h is n o t p u r s u e d h e r e a n d l eft f o r f u t u r e s t u d y .
A g r a p h i c a l p r e s e n t a t i o n o f t he r e s u l t s is g i v e n in Fi gs. 3 a n d 4. T h e s e f i g u r e s
p l o t th e e s t i m a t e d p r i c e s o f risk s e r i e s and ri sk p r e m i u m s f r o m the t i m e - v a r y i n g
p r i c e o f r is k m o d e l , u s i n g d o l l a r r e t u r n s . Fig. 3 s h o w s an i m p r e s s i v e d e g r e e o f
c o v a r i a t i o n b e t w e e n the p r i c e o f v a r i a n c e risk a n d t he w o r l d p r i c e o f risk,
e s p e c i a l l y in the latter h a l f o f the s a m p l e p e r i o d . T h e w o r l d p r i c e o f ri sk p r i c e
s e r i e s r e m a i n l o w until the m i d - 1 9 8 0 s , b e c o m e s i g n i f i c a n t l y p o s i t i v e a n d r e m a i n at
a h i g h e r l e v e l s i n c e 1985, a n d t h e n d r o p b a c k to a l o w e r l e v e l a f t e r 1989. S t a r t i n g
5 T h e e s t i m a t e o f Q o b t a i n e d in C h o u et al. (1992) u s i n g the m o n t h l y N Y S E v a l u e - w e i g h t e d i n d e x
f o r the p e r i o d 1 9 2 6 - 1 9 8 5 is 0.032.
6 A r e c e n t p a p e r b y B o u d o u k h et al. (1993), h o w e v e r , r e p o r t s e v i d e n c e that the e x a n t e risk
p r e m i u m is n e g a t i v e in s o m e states o f the w o r l d w h i c h are r e l a t e d to p e r i o d s o f h i g h e x p e c t e d i n f l a t i o n
and e s p e c i a l l y to d o w n w a r d - s l o p i n g t e r m structures.
21
1(.--1-1. B a e ~ P a c i f i c - B a s i n F i n a n c e J o u r n a l 3 (1995) 1--20
3o
"
0
-10
80E113
-
' ~
-20
-30
_,o
/
{
l
KOSPI: Variance risk ~
\
~ Covariance risk - - M S C I ]
Fig. 3. Prices of risk from the time-varying price of risk model.
f r o m 1986, the p r i c e o f v a r i a n c e risk series in the K o r e a n m a r k e t b e c o m e
s i g n i f i c a n t l y p o s i t i v e a n d the m a g n i t u d e s are b e c o m i n g c l o s e to t h o s e o f the w o r l d
p r i c e o f risk. T h e p r i c e o f c o v a r i a n c e risk series r e m a i n s i n s i g n i f i c a n t l y p o s i t i v e
f o r m o s t o f the s a m p l e p e r i o d a n d t h e n b e c o m e m a r g i n a l l y s i g n i f i c a n t in the later
s a m p l e p e r i o d . 7 T h i s b e h a v i o r o f the p r i c e o f c o v a r i a n c e risk, c o u p l e d w i t h t he
b e h a v i o r o f the p r i c e o f v a r i a n c e risk, is c o n s i s t e n t w i t h the v i e w that the K o r e a n
s t o c k m a r k e t has b e c o m e m o r e i n t e g r a t e d w i t h t he w o r l d m a r k e t in r e c e n t years.
O n e p o s s i b l e s o u r c e o f this t i m e - v a r y i n g p a t t e r n o f t he risk p r i c e s r e l a t e s to t he
d e g r e e o f g o v e r n m e n t r e g u l a t i o n . In the latter h a l f o f 1980s, w i t h t he o u t s t a n d i n g
p e r f o r m a n c e o f the K o r e a n e c o n o m y and the r a p i d e x p a n s i o n o f the capital m a r k e t ,
t h e K o r e a n g o v e r n m e n t p u s h e d f o r w a r d w i t h the capital m a r k e t i n t e r n a t i o n a l i z a tion process. The K o r e a n g o v e r n m e n t continued expanding indirect investment
o p p o r t u n i t i e s w i t h the e n l a r g e m e n t o f the f o r e i g n i n v e s t m e n t f u n d s and an i n c r e a s e
in o v e r s e a s s e c u r i t i e s issues b y d o m e s t i c c o r p o r a t i o n s . T h e g o v e r n m e n t also
r e l a x e d r e s t r i c t i o n s on t r a d i n g c o n v e r t e d st ocks, rai sed l i m i t a t i o n s on f o r e i g n
s h a r e h o l d i n g in d o m e s t i c s e c u r i t i e s c o m p a n i e s , and a l l o w e d a g r e a t e r n u m b e r o f
f o r e i g n s e c u r i t i e s to o p e n b r a n c h e s in K o r e a . A l t h o u g h f o r e i g n e r s w e r e not
p e r m i t t e d to d i r e c t l y i n v e s t in the K o r e a n s t o c k m a r k e t in this p e r i o d , the g r a d u a l
capital m a r k e t l i b e r a l i z a t i o n p r o c e s s c a r r i e d out b y the K o r e a n g o v e r n m e n t a p p e a r s
to be c o n s i s t e n t w i t h the i dea that the g o v e r n m e n t d e r e g u l a t i o n m a y be a s o u r c e o f
t h e v a r i a t i o n s in the p r i c e o f risk p a r a m e t e r s .
Fig. 4 p lo ts the p r e d i c t e d risk p r e m i u m s and r e v e a l s a si m i l ar t i m e - v a r y i n g
p a t t e rn . M e a n risk p r e m i u m s f o r the K O S P I and M S C I are 0 . 1 7 % and 0 . 0 5 % ,
r e s p e c t i v e l y , w h i c h are c l o s e to r e a l i z e d m e a n e x c e s s ret urns ( 0 . 1 2 % a n d 0 . 0 6 %
7 Given a significant correlation between hkt and hk~,t (0.49 in dollar returns), the true covariance
effect may be understated due to multicollinearity.
K.-H. B a e / P a c i f i c - B a s i n F i n a n c e J o u r n a l 3 (1995) 1--29
22
-1 .B
-2
~
\
/
Fig. 4. P r e d i c t e d e x c e s s returns f r o m the t i m e - v a r y i n g price o f risk m o d e l .
f o r e a c h in d ex ) . T h e m a g n i t u d e s o f risk p r e m i u m s are m u c h h i g h e r f o r the K O S P I ,
e s p e c i a l l y f o r the latter h a l f o f the eighties. T h e m e a n d i f f e r e n c e in risk p r e m i u m s
is statistically s i g n i f i c a n t 0 . 1 2 % w i t h a t-statistic o f 4.22. S t u l z ' s ( 1 9 8 1 b ) m o d e l
w i t h i n v e s t m e n t b a r r i e r s s u g g e s t s that the d i f f e r e n c e b e t w e e n e q u i t y p r e m i u m s can
b e i n t e r p r e t e d as t he " t a x r a t e " e q u i v a l e n t o f i n t e r n a t i o n a l i n v e s t m e n t barriers. T o
the e x t e n t that th e d i f f e r e n c e b e t w e e n m e a n e q u i t y p r e m i u m s m e a s u r e s t he d e g r e e
o f s e g m e n t a t i o n , the results i m p l y that the K o r e a n m a r k e t is s e g m e n t e d f r o m t he
world market. 8
P r e v i o u s studies s u g g e s t that a l o o s e n i n g o f i n t e r n a t i o n a l i n v e s t m e n t r e s t r i c t i o n s
s h o u l d b e a s s o c i a t e d w i t h a fall in the e x p e c t e d e x c e s s r e t u r n s o f K o r e a n equi t i es.
Alternatively, a relaxation of investment restrictions would imply a narrowing of
m e a n e q u i t y p r e m i u m d i f f e r e n c e s b e t w e e n the K o r e a n and w o r l d m a r k e t s . Fig. 4
s h o w s that th er e is s o m e e v i d e n c e in the later s a m p l e p e r i o d that risk p r e m i u m s
d e c l i n e to a rate that is c l o s e to t h o s e o n the w o r l d e q u i t y m a r k e t , as o n e w o u l d
e x p e c t if the K o r e a n m a r k e t is b e c o m i n g m o r e i n t e g r a t e d into the w o r l d capital
m a r k e t . T h e m e a n e q u i t y p r e m i u m d i f f e r e n c e after the 1 9 8 8 l i b e r a l i z a t i o n pl an is
0 . 0 6 % w i t h a t-statistic o f 1.42. T h i s result is c o n s i s t e n t w i t h the i dea that r e l a x i n g
g o v e r n m e n t - i m p o s e d b a r r i e r s is a s s o c i a t e d w i t h a d e c r e a s e in m e a n e q u i t y p r e m i u m s , s u g g e s t i n g that the l i b e r a l i z a t i o n p r o c e s s r e d u c e s the cost o f capi t al f o r local
firms. 9
8 M e a n "difference in risk p r e m i u m s during the first h a l f o f the s a m p l e p e r i o d is statistically
insignificant. This d o e s not n e c e s s a r i l y m e a n i n s i g n i f i c a n t i n v e s t m e n t barriers but m a y reflect l o w
K o r e a n s t o c k returns and inactive asset trade.
9 T h i s interpretation is at b e s t tentative g i v e n the relatively short s a m p l e p e r i o d u s e d to e s t i m a t e
e x p e c t e d e x c e s s returns. T h e d e c r e a s e in m e a n equity risk p r e m i u m s after the a n n o u n c e m e n t o f capital
c o n t r o l relaxation m a y be a p h e n o m e n o n particular to the s a m p l e p e r i o d e x a m i n e d in this study and
may h a v e no relation to the liberalization p r o c e s s .
K. -H. Bae / Pacific-Bas• Finance Journal 3 (1995) 1 - 2 9
23
5.3. T e s t o f i n t e g r a t i o n vs. s e g m e n t a t i o n
T h e p r e v i o u s s e c t i o n s h o w s that i m p l i e d risk p r e m i u m s can be f o r e c a s t m o r e
p r e c i s e l y by a l l o w i n g the price o f risk to c h a n g e o v e r t i m e a n d that the K o r e a n
stock m a r k e t exhibits a t i m e - v a r y i n g b e h a v i o r o f the risk prices and p r e m i u m s
close to the w o r l d capital m a r k e t . In this section, a test for the i n t e g r a t i o n vs.
s e g m e n t a t i o n h y p o t h e s i s is presented. For the sake o f e x p o s i t i o n , Eq. (12) is
reexpressed below:
rkt = cek + A k t h k t + Akw,thkw,t + O'kZk,t-1 -]- Ekt"
(25)
In principle, b y u s i n g m u l t i p l i c a t i v e p a r a m e t e r s in the m e a n e q u a t i o n that can
be c h o s e n to h a v e a v a l u e o f zero to e x c l u d e the risk p r e m i u m term f r o m the
m o d e l , a test c o n c e r n i n g the i n t e g r a t i o n and s e g m e n t a t i o n h y p o t h e s e s can be
c o n d u c t e d . U n f o r t u n a t e l y , the i n t r o d u c t i o n o f m u l t i p l i c a t i v e p a r a m e t e r s in the
m e a n e q u a t i o n leads to the p r o d u c t o f t w o free p a r a m e t e r s to be estimated,
resulting in an i d e n t i f i c a t i o n p r o b l e m a n d m a k i n g this p r o c e d u r e impractical. T h e
t i m e - v a r y i n g price o f risk m o d e l c o n s i d e r e d here d o e s not p r o v i d e a w a y to test
the c o m p l e t e s e g m e n t a t i o n or the full i n t e g r a t i o n h y p o t h e s i s as a special case o f a
m o r e g e n e r a l h y p o t h e s i s . T h u s , the usual l i k e l i h o o d ratio test, w h i c h can o n l y be
applied to test n e s t e d h y p o t h e s e s , is not f e a s i b l e in the f r a m e w o r k c o n s i d e r e d in
this study.
A s an alternative, D a v i d s o n and M a c K i n n o n ' s C-test is u s e d to c o m p a r e the
m i l d s e g m e n t a t i o n h y p o t h e s i s against each o f the c o m p l e t e s e g m e n t a t i o n and full
i n t e g r a t i o n h y p o t h e s e s . T h e C-test s u g g e s t e d by D a v i d s o n a n d M a c K i n n o n (1981)
i n v o l v e s c o m p u t i n g the t-statistic f r o m a regression:
r~, = (1 -- o t ) • + crg, + G or r k , - - ~ = ( g , --3~) + G,
(26)
w h e r e ft is the e s t i m a t e d e x c e s s return for the K o r e a n m a r k e t p o r t f o l i o u n d e r the
null h y p o t h e s i s and ~t u n d e r the n o n - n e s t e d alternative h y p o t h e s i s . I f the null
h y p o t h e s i s is true, then the true v a l u e o f or w o u l d be zero. T h e c o m p l e t e
s e g m e n t a t i o n m o d e l is e s t i m a t e d b y restricting the price o f c o v a r i a n c e risk to be
zero, w h i l e the i n t e g r a t i o n m o d e l is e s t i m a t e d b y restricting the price o f v a r i a n c e
risk to be zero.
T a b l e 7 g i v e s the test results. Panel A p r e s e n t s a c o m p a r i s o n o f the integration
h y p o t h e s i s against the m i l d s e g m e n t a t i o n h y p o t h e s i s . W h e n the full integration
h y p o t h e s i s is m a i n t a i n e d as the null h y p o t h e s i s , the null is s t r o n g l y rejected in
f a v o r o f the alternative regardless o f the c u r r e n c y used; w h e n the m i l d s e g m e n t a tion h y p o t h e s i s is m a i n t a i n e d as the null, the m o d e l is not rejected. P a n e l B s h o w s
the test results b e t w e e n the c o m p l e t e s e g m e n t a t i o n and m i l d s e g m e n t a t i o n hypotheses. W h e n dollar returns are e m p l o y e d , the m i l d s e g m e n t a t i o n h y p o t h e s i s is
f a v o r e d w i t h a t-statistic o f 2.89 ( s e g m e n t a t i o n as the null) c o m p a r e d to the
t-statistic o f - - 1 . 7 5 ( m i l d s e g m e n t a t i o n as the null) at the 5% s i g n i f i c a n c e level.
T h e s u b s a m p l e a n a l y s i s s h o w s that n e i t h e r h y p o t h e s i s is c h o s e n as a p r e f e r r e d
K. -H. B a e / P a c i f i c - B a s i n F i n a n c e J o u r n a l 3 (1995) 1--29
24
Table 7
T h e D a v i d s o n a n d M a c K i n n o n ' s ( 1 9 8 1 ) C - t e s t in c o m p a r i n g t h e m i l d s e g m e n t a t i o n h y p o t h e s i s a g a i n s t
each of the complete segmentation and full integration hypotheses. The C-test suggested by Davidson
and MacKinnon involves computing the t-statistic from a regression:
w h e r e 3~ is t h e e s t i m a t e d e x c e s s r e t u r n s f o r t h e K o r e a n m a r k e t p o r t f o l i o u n d e r t h e n u l l h y p o t h e s i s a n d
g t u n d e r t h e n o n - n e s t e d a l t e r n a t i v e h y p o t h e s i s . I f t h e n u l l h y p o t h e s i s is t r u e , t h e n t h e t r u e v a l u e o f ce 1
is z e r o . T h e c o m p l e t e s e g m e n t a t i o n m o d e l is e s t i m a t e d b y r e s t r i c t i n g t h e p r i c e o f c o v a r i a n c e r i s k to b e
z e r o , w h i l e t h e i n t e g r a t i o n m o d e l is e s t i m a t e d b y r e s t r i c t i n g t h e p r i c e o f v a r i a n c e r i s k to b e z e r o . T h e
t-statistics reported are White's heteroskedasticity-consistent
Currency
Null hypothesis
80.1-90.12
t-stat
80.1-85.6
Adj-R z
85.7-90.12
t-stat
Adj-R z
t-stat
Adj-R 2
0.0218
-- 0 . 0 0 1 1
0.0442
0.0016
0.0523
0.0057
2.87
-- 1 . 4 7
2.31
-- 0 . 5 7
2.28
-- 1 . 1 2
0.0288
0.0043
0.0157
-- 0 . 0 0 2 5
0.0298
0.0048
2.28
-- 0 . 1 1
4.11
-- 1 . 3 3
4.18
-- 1 . 6 4
0.0149
-- 0 . 0 0 3 6
0.0542
0.0028
0.0611
0.0069
0.0199
0.0058
0.0366
0.0177
0.0403
0.0228
1.09
-- 0 . 2 0
1.29
-- 0 . 7 2
1.57
-- 0 . 9 2
0.0007
-- 0 . 0 0 3 6
0.0025
-- 0 . 0 0 1 8
0.0054
-- 0 . 0 0 0 6
3.07
-- 1 . 7 6
4.20
-- 3 . 0 7
4.41
-- 3 . 4 6
0.0320
0.0123
0.0562
0.0292
0.0621
0.0381
0.0093
0.0004
0.0233
-- 0 . 0 0 0 6
0.0287
-- 0 . 0 0 0 8
2.75
-- 1.33
2.00
-- 0 . 2 8
2.13
-- 1.01
0.0229
0.0026
0.0110
-- 0 . 0 0 3 0
0.0217
0.0024
1.23
1.38
2.61
-- 0 . 6 5
2.74
-- 0 . 3 4
0.0029
0.0045
0.0225
-- 0 . 0 0 1 9
0.0274
-- 0 . 0 0 3 1
P a n e l A : Integration vs. mild segmentation
Dollar
Integration
Mild segmentation
Integration
Mild segmentation
Integration
Mild segmentation
Won
Own
3.23
-- 0 . 5 6
4.59
-- 1 . 2 2
5.05
-- 1 . 8 3
P a n e l B : S e g m e n t a t i o n vs. m i l d segmentation
Dollar
Segmentation
Mild segmentation
Segmentation
Mild segmentation
Segmentation
Mild segmentation
Won
Own
2.89
-- 1.75
4.19
-- 2 . 9 6
4.23
-- 3 . 2 0
P a n e l C: Integration t,s. segmentation
Dollar
Integration
Segmentation
Integration
Segmentation
Integration
Segmentation
Won
Own
model
in the first
against
the
what
one
years
from
since
recent
When
cut.
Both
half
complete
would
mild
of the
expect
other
sample
segmentation
stronger
d a t a . 10
the
2.10
0.93
3.44
-- 0 . 7 4
3.64
-- 0 . 6 3
if the
evidence
currency
segmentation
l0 I t h a n k a n a n o n y m o u s
period,
in the
while
second
Korean
market
for
mild
excess
and
the
returns
complete
the
mild
segmentation
half.
This
result
became
segmentation
are
employed,
segmentation
referee for suggesting subsample analysis.
more
integrated
hypothesis
the
is favored
is consistent
results
hypotheses,
in
is
are
with
recent
obtained
not
when
clear
main-
K. -H. Bae / Pacific-Basin Finance Journal 3 (1995) 1 - 2 9
25
t a i n e d as the null h y p o t h e s i s , are r e j e c t e d in f a v o r o f the a l t e r n a t i v e h y p o t h e s i s .
T h e m i l d s e g m e n t a t i o n m o d e l s e e m s to be p r e f e r r e d g i v e n that the c o m p l e t e
s e g m e n t a t i o n m o d e l is m o r e s t r o n g l y r e j e c t e d w h e n it is m a i n t a i n e d as the null
h y p o t h e s i s . M o r e o v e r , the c o m p a r i s o n o f the a d j u s t e d R e r e v e a l s that the m i l d
s e g m e n t a t i o n m o d e l has h i g h e r e x p l a n a t o r y p o w e r than the s e g m e n t a t i o n m o d e l . 11
P a n e l C p r e s e n t s the test r e s ul t s o f the i n t e g r a t i o n v e r s u s the s e g m e n t a t i o n
h y p o t h e s i s . C o n s i s t e n t w i t h p r i o r e x p e c t a t i o n s , the i n t e g r a t i o n m o d e l is s t r o n g l y
r e j e c t e d o v e r the c o m p l e t e s e g m e n t a t i o n m o d e l . O v e r a l l , the e v i d e n c e s e e m s to
s u g g e s t that the K o r e a n s t o c k m a r k e t is i n f l u e n c e d b y the w o r l d m a r k e t in p r i c i n g
its s e c u r i t i e s and is c o n s i s t e n t w i t h the v i e w that it has b e c o m e m o r e i n t e g r a t e d
w i t h the w o r l d m a r k e t a l t h o u g h its m a r k e t s t r u c t u r e a p p e a r s to be m o r e s e g m e n t e d
than i n t e g r a t e d .
6. F u r t h e r
tests
6.1. A l t e r n a t i v e s p e c i f i c a t i o n a n d e s t i m a t i o n m e t h o d
A n i m p o r t a n t e l e m e n t in the e m p i r i c a l i m p l e m e n t a t i o n o f the m o d e l c o n s i d e r e d
in this s t u d y is the s p e c i f i c a t i o n o f t he d y n a m i c s o f c o n d i t i o n a l v a r i a n c e s a n d
c o v a r i a n c e s o v e r time. T o see the s e n s i t i v i t y o f results to an a l t e r n a t i v e s p e c i f i c a tion, the m o d e l o f B o l l e r s l e v et al. ( 1 9 8 8 ) ( B E W ) is e x a m i n e d . B E W ' s s p e c i f i c a tion a s s u m e s that the c o n d i t i o n a l v a r i a n c e s d e p e n d o n l y on past s q u a r e d r e s i d u a l s
and c o v a r i a n c e s on past p r o d u c t s o f residuals. T h i s s p e c i f i c a t i o n is thus r e s t r i c t e d
r e l a t i v e to that o f B E K K w h e r e the c o n d i t i o n a l v a r i a n c e s and c o v a r i a n c e s o f the
t w o s t o c k m a r k e t s are a l l o w e d to i n f l u e n c e e a c h o t h e r in s u f f i c i e n t g e n e r a l i t y .
A b i v a r i a t e t i m e - v a r y i n g p a r a m e t e r G A R C H m o d e l r e q u i r e s the r e p l a c e m e n t o f
the o r i g i n a l d i s t u r b a n c e e r r o r s w i t h the K a l m a n filter p r e d i c t i o n errors. T h i s m a y
n o t b e s a t i s f a c t o r y c o n s i d e r i n g that G A R C H e f f e c t s are s t e m m i n g f r o m the
o r i g i n a l d i s t u r b a n c e errors. T o i n v e s t i g a t e the s e n s i t i v i t y o f the results to e s t i m a tion m e t h o d , an a l t e r n a t i v e t w o - s t e p p r o c e d u r e is e m p l o y e d to e s t i m a t e the p r i c e s
o f risk series. First, the c o n d i t i o n a l v a r i a n c e and c o v a r i a n c e series are g e n e r a t e d
a s s u m i n g c o n s t a n t c o n d i t i o n a l m e a n s . T h e n the p r i c e o f risk series are o b t a i n e d
u s i n g K a l m a n filter e s t i m a t i o n .
Final results c o n c e r n i n g the s e g m e n t a t i o n vs. i n t e g r a t i o n h y p o t h e s i s are pres e n t e d in T a b l e 8. T h e test results are s i m i l a r to t hose s h o w n in T a b l e 7. P a n e l A
s h o w s that the i n t e g r a t i o n m o d e l is s t r o n g l y r e j e c t e d agai nst the m i l d s e g m e n t a t i o n
m o d e l r e g a r d l e s s o f the a l t e r n a t i v e s p e c i f i c a t i o n o f v a r i a n c e - - c o v a r i a n c e d y n a m i c s
a n d e s t i m a t i o n m e t h o d . P a n e l B also i n d i c a t e s that the m i l d s e g m e n t a t i o n m o d e l is
11 T h i s a r g u m e n t f o r t h e m i l d s e g m e n t a t i o n h y p o t h e s i s is r a t h e r t e n u o u s as o n e r e f e r e e p o i n t e d out.
O n e c a n i n t e r p r e t the r e s u l t s as s u g g e s t i n g that b o t h m o d e l s are i n a d e q u a t e ,
26
K.-H. B a e / P a c i f i c - B a s i n F i n a n c e J o u r n a l 3 (1995) 1 - 2 9
Table 8
T h e D a v i d s o n a n d M a c K i n n o n ' s ( 1 9 8 1 ) C - t e s t in c o m p a r i n g the m i l d s e g m e n t a t i o n h y p o t h e s i s a g a i n s t
e a c h o f t h e c o m p l e t e s e g m e n t a t i o n a n d full i n t e g r a t i o n h y p o t h e s e s u n d e r the a l t e r n a t i v e s p e c i f i c a t i o n
a n d e s t i m a t i o n m e t h o d . B E W d e n o t e s t h e m o d e l o f B o l l e r s l e v et al. ( 1 9 8 8 ) w h e r e e a c h e l e m e n t o f t h e
v a r i a n c e - c o v a r i a n c e m a t r i x d e p e n d s o n its p a s t v a l u e s a l o n e . I n the t w o - s t e p e s t i m a t i o n m e t h o d , the
c o n d i t i o n a l v a r i a n c e a n d c o v a r i a n c e s e r i e s are g e n e r a t e d first, a s s u m i n g that c o n d i t i o n a l m e a n s are
c o n s t a n t . T h e n t h e p r i c e s o f r i s k s e r i e s are e s t i m a t e d f r o m t h e K a l m a n filter e s t i m a t i o n . A l l t e s t s are
b a s e d o n the d o l l a r - d e n o m i n a t e d e x c e s s r e t u r n s , T h e C - t e s t s u g g e s t e d b y D a v i d s o n a n d M a c K i n n o n
involves c o m p u t i n g the t statistic f r o m a regression:
w h e r e j~ is the e s t i m a t e d e x c e s s r e t u r n s f o r t h e K o r e a n m a r k e t p o r t f o l i o u n d e r t h e n u l l h y p o t h e s i s a n d
gt u n d e r the n o n - n e s t e d a l t e r n a t i v e h y p o t h e s i s . I f the n u l l h y p o t h e s i s is true, t h e n t h e t r u e v a l u e o f ~ l
is z e r o . T h e c o m p l e t e s e g m e n t a t i o n m o d e l is e s t i m a t e d b y r e s t r i c t i n g t h e p r i c e o f c o v a r i a n c e r i s k to be
z e r o , w h i l e the i n t e g r a t i o n m o d e l is e s t i m a t e d b y r e s t r i c t i n g the p r i c e o f v a r i a n c e r i s k to b e z e r o . T h e
t - s t a t i s t i c s r e p o r t e d are W h i t e ' s h e t e r o s k e d a s t i c i t y - c o n s i s t e n t
Model
Null hypothesis
80.1--90.12
80.1--85.6
t-stat
t-stat
Adj-R 2
t-stat
0.0230
0.0024
0.0606
0.0029
1.98
-- 0.35
3.19
-- 1.79
0.0106
-- 0 . 0 0 3 3
0.0468
0.0133
3.10
-- 1.58
4.34
-- 1.24
0.0299
0.0054
0.0615
0.0022
0.0170
0.0068
0,0195
0.0068
-- 0 . 1 7
0.82
0,86
-- 0 . 0 8
-- 0 . 0 0 3 6
--0.0012
0,0028
-- 0 . 0 0 3 7
3.64
-- 1.78
3,15
-- 1.24
0.0409
0.0137
0.0353
0.0168
0.0087
-- 0 . 0 0 1 8
0,0452
-- 0 . 0 0 0 5
2.15
-- 0 . 4 3
3,15
-- 1.61
0.0132
-- 0 . 0 0 3 0
0.0392
0.0082
1.42
0.15
3.34
-- 0.33
0.0036
-- 0 . 0 0 3 5
0.0384
-- 0 . 0 0 3 2
Adj-R 2
85.7-90.12
Adj-R 2
P a n e l A : Integration ~'s. mild segmentation
BEW
Two-step
estimation
Integration
Mild segmentation
Integration
Mild segmentation
3.58
-- 1.46
5.56
-- 1.48
P a n e l B: S e g m e n t a t i o n ~,s. mild segmentation
BEW
Two-step
estimation
Segmentation
Mild segmentation
Segmentation
Mild segmentation
2.90
-- 1.95
2.57
-- 1.62
P a n e l C: Integration ~'s. segmentation
BEW
Two-step
estimation
Integration
Segmentation
Integration
Segmentation
2.24
-- 0 . 1 2
4.86
-- 0 . 8 6
p r e f e r r e d to the c o m p l e t e s e g m e n t a t i o n m o d e l . T h e s u b s a m p l e a n a l y s i s also
p r e s e n t s e v i d e n c e s u p p o r t i n g the m i l d s e g m e n t a t i o n h y p o t h e s i s as a p r e f e r r e d
m o d e l to e x p l a i n the asset p r i c i n g m e c h a n i s m o f the K o r e a n s t o c k m a r k e t .
6.2. Residual diagnostics
T a b l e 9 r e p o r t s s o m e d i a g n o s t i c s o f the s t a n d a r d i z e d r e s i d u a l s f r o m the
t i m e - v a r y i n g p r i c e o f risk m o d e l . T h e s t a n d a r d i z e d residuals, uit, are o b t a i n e d
f r o m the r a w r e s i d u a l s b y setting uit = T ~ i t f ~
w h e r e r/i t is the p r e d i c t i o n e r r o r
f r o m the m o d e l f o r the ith m a r k e t and V,i,t is the ith d i a g o n a l e l e m e n t o f the
K. -H. B a e / P a c i f i c - B a s i n F i n a n c e J o u r n a l 3 ( 1 9 9 5 ) 1--29
27
Table 9
Residual diagnostics for time-varying GARCH models for the KOSPI and MSCI world index returns
from January 1980 to December 1990. The standardized residuals are obtained by scaling the raw
residuals by the estimated conditional variances. The Kolmogorov D-statistic tests the null hypothesis
o f n o r m a l i t y . L B ( 6 ) a n d L B ( 1 2 ) a r e t h e L j u n g - B o x s t a t i s t i c f o r t h e f i r s t 6 a n d 12 l a g s o f a u t o c o r r e l a t i o n f u n c t i o n s o f r a w e x c e s s r e t u r n s a n d t h e i r s q u a r e s . T h e p - v a l u e s a r e f o r t h e X2 d i s t r i b u t i o n .
Statistics
Model 1
KOSPI($)
MSCI($)
KOSPI(Won)
MSCI(Won)
KOSPI(Won)
MSCI($)
NOBS
Mean(%)
Std. D e v ( % )
Skewness
Kurtosis
D-statistic
p-value
551
-- 0 . 0 0 6 7
0.9911
0.2418
0.4483
0.9854
(0.52)
551
0.0011
1.0001
--0.1188
0.5518
0.9941
(0.99)
551
-- 0 . 0 1 3 5
0.9819
0.2110
0.4109
0.9862
(0.63)
55 l
-- 0 . 0 1 4 0
0.9954
--0.1226
0.5859
0.9930
(0.99)
551
-- 0 . 0 0 9 4
0.9882
0.2469
0.4782
0.9865
(0.65)
551
-- 0 . 0 0 0 2
0.9939
--0.1424
0.4943
0.9933
(0.99)
S e r i e s : t~
Pa
P2
P3
to4
P5
P6
LB 6
(p-value)
L B 12
(p-value)
0.0362
0.0021
0.0015
0.0190
-- 0 . 0 2 6 0
0.0281
1.75
(0.94)
5.08
(0.95)
-- 0 . 0 0 0 4
0.0056
0.0248
0.0122
-- 0 . 0 2 4 8
-- 0 . 0 3 1 1
1.33
(0.97)
9.32
(0.67)
0.0263
0.0174
0.0137
0.0115
-- 0 . 0 2 9 8
0.0307
1.76
(0.94)
4.54
(0.97)
-- 0 . 0 0 2 9
0.0050
0.0327
0.0093
-- 0 . 0 1 8 9
-- 0 . 0 2 3 6
1.18
(0.97)
11.35
(0.50)
0.0296
0.0125
0.0078
0.0089
-- 0 . 0 3 2 1
0.0275
1.65
(0.95)
5.00
(0.96)
-- 0 . 0 0 8 6
0.0082
0.0257
0.0140
-- 0 . 0 2 3 4
-- 0 . 0 2 9 3
1.35
(0.96)
9.41
(0.66)
S e r i e s : ut^2
Pl
P2
P3
Pa
P5
P6
LB 6
(p-value)
L B 12
(p-value)
-- 0 . 0 0 5 0
-- 0 . 0 0 3 1
0.0535
0.0807
-- 0 . 0 3 9 1
-- 0.0422
7.09
(0.31)
10.46
(0.57)
0.0319
0.0664
-- 0 . 0 2 2 3
-- 0 . 0 4 1 7
0.0319
-- 0 . 0 1 4 0
4.95
(0.55)
9.16
(0.69)
-- 0 . 0 1 9 7
0.0089
0.0504
0.0568
-- 0 . 0 5 7 3
-- 0 . 0 6 0 9
7.39
(0.28)
9.96
(0.62)
0.0517
0.0741
-- 0 . 0 1 4 5
-- 0 . 0 4 2 4
0.0275
-- 0 . 0 1 8 0
6.27
(0.39)
9.73
(0.64)
-- 0 . 0 1 5 3
-- 0 . 0 0 1 4
0.0555
0.0794
-- 0 . 0 4 2 6
0.0491
7.74
(0.26)
11.38
(0.49)
0.0254
0.0524
-- 0 . 0 2 4 9
-- 0 . 0 4 5 7
0.0358
-- 0 . 0 1 2 7
4.20
(0.65)
7.79
(0.82)
variance-covariance
icant
deviations
tions
observed
statistics
large
lag
show
matrix
from
in
no
In general,
4, the
the
the
the
raw
of
are
Ljung-Box
estimated
r/t. The
Model 3
Kolmogorov
normality
for
excess
returns
significant
autocorrelations
3 and
Model 2
serial
still
obtained
are
seems
from
do
not
D-statistic
index.
no
correlations
statistics
model
either
for
the
to survive
longer
lags
squared
reject
The
confirms
significant
present.
up
to
12.
residuals
the
assumption
most
diagnostic
no
signif-
autocorrela-
The
Ljung-Box
While
relatively
of the
KOSPI
of white
checks.
at
noise.
28
K.-1t. B a e / P a c i f i c - B a s i n F i n a n c e J o u r n a l 3 (1995) 1--29
7. C o n c l u s i o n
This s t u d y i n v e s t i g a t e s the t i m e - v a r y i n g b e h a v i o r o f the risk p r e m i u m s in the
K o r e a n s t o c k m a r k e t a n d its r e l a t i o n s h i p w i t h the w o r l d capital m a r k e t , e m p l o y i n g
a bivariate G A R C H - M m o d e l for the K o r e a n C o m p o s i t e S t o c k Price I n d e x
( K O S P I ) and M S C I w o r l d index d u r i n g the period 1980 to 1990. T h e e v i d e n c e
indicates the i m p o r t a n c e o f a l l o w i n g for the t i m e - v a r y i n g price o f risk, in that it
p r o v i d e s m o r e a c c u r a t e e s t i m a t e s o f risk p r e m i u m s relative to those e s t i m a t e d
f r o m the c o n s t a n t price o f risk m o d e l .
The empirical results s h o w that w h i l e the K o r e a n s t o c k m a r k e t c o m m a n d s
h i g h e r risk p r e m i u m s than the w o r l d m a r k e t , there is s o m e e v i d e n c e in the later
s a m p l e p e r i o d that risk p r e m i u m s decline to a rate close to t h o s e o f the w o r l d
e q u i t y m a r k e t as g o v e r n m e n t - i m p o s e d barriers b e c o m e less stringent. T h i s result
s u g g e s t s that r e l a x i n g g o v e r n m e n t - i m p o s e d barriers is a s s o c i a t e d w i t h a d e c r e a s e
in e q u i t y p r e m i u m s , i n d i c a t i n g that the liberalization p r o c e s s r e d u c e s the cost o f
capital for local firms.
T h e test results are c o n s i s t e n t w i t h the p r e d i c t i o n s o f the m i l d s e g m e n t a t i o n
h y p o t h e s i s w h e r e b o t h d o m e s t i c and i n t e r n a t i o n a l f a c t o r s are i m p o r t a n t in p r i c i n g
K o r e a n equities. Overall, the e v i d e n c e s u g g e s t s that the K o r e a n e q u i t y m a r k e t has
b e c o m e m o r e i n t e g r a t e d w i t h the w o r l d capital m a r k e t in recent years, a l t h o u g h its
m a r k e t structure, if a n y t h i n g , s e e m s m o r e s e g m e n t e d than integrated.
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