efficiencies of the DAX, MDAX, SDAX and ASE indices. By ..... Asia-Pacific Capital Markets School of Economics and Finance, Curtin. University of Technology ... Voit, J. (2001), 'The Statistical Mechanics of Financial Markets', Springer,. Berlin.
M arket E f f i ci ency w i t hi n t he German S t ock M arket : A comparat i ve s t udy of t he rel at i ve efficiencies of the DAX, MDAX, SDAX and ASE indices By A dmi n S t arcevi c and T i mot hy R odg ers
Ab s tra ct
It can b e i m p l i ed fro m t h e effi ci en t m ark et h yp o t h es i s t h at t h e m o re t ran s p aren t a m ark et i s , t h en t h e m o re l i k el y i t i s t h at t h e m ark et wi l l b e effi ci en t . Th i s p ap er i s a s t u d y o f wh et h er t h e d i fferen t t ran s p aren cy s t an d ard s ap p l i ed t o t h e d i fferen t i n d i ces q u o t ed o n t h e Germ an s t o ck m ark et h av e an y i m p act o n t h ei r rel at i v e effi ci en ci es . Th e s t u d y u s es ru n s t es t s an d s eri al co rrel at i o n t es t s t o ex am i n e wh at p ro p o rt i o n o f t h e s t o ck s o n each i n d ex fo l l o w a ran d o m wal k . In ad d i t i o n , t h e s t u d y s earch es fo r an y d i fferen ces b et ween t h e P ri m e S t an d ard i n d i ces i n res p ect t o cal en d ar an o m al y effect s . It i s fo u n d t h at t h e d i fferen ces i n t ran s p aren cy s t an d ard s h av e an i m p act o n m ark et effi ci en cy.
Th e cas e fo r h i gh l ev el o f m ark et
effi ci en cy i n res p ect t o t h e P ri m e S t an d ard i n d ex s t o ck s i s rei n fo rced b y t h e ad d i t i o n al fi n d i n g t h at cal en d ar an o m al y effect s ap p ear t o h av e o n l y l i m i t ed s t at i s t i cal s i gn i fi can ce.
2
1 . I n tro d u cti o n
M o s t o f t h e ev i d en ce av ai l ab l e i n d i cat es t h at acad em i cs t ren d t o s u p p o rt t h e effi ci en t m ark et s h yp o t h es i s (EM H) i n s o m e fo rm o r o t h er wh i l s t p ract i t i o n ers t en d n o t t o (S ee, fo r ex am p l e, Fl an egi n an d R u d d , 2 0 0 5 ). Th i s p ap er at t em p t s t o t ak e t h i s d eb at e fu rt h er b y ex am i n i n g t h e i m p act o n m ark et
effi ci en cy
of
the
d i fferen ces
in
i n fo rm at i o n al
req u i rem en t s
(t ran s p aren cy s t an d ard s ) fo r s t o ck s l i s t ed o n t h e s en i o r an d j u n i o r s t o ck m ark et s i n Germ an y.
Fam a (1 9 9 1 ) i d en t i fi ed t h at d i fferen t l ev el s o f
i n fo rm at i o n fl o wi n g i n t o a m ark et wi l l res u l t i n d i fferen t l ev el s o f m ark et effi ci en cy.
Th i s s t u d y ap p l i es ru n s t es t s an d s eri al co rrel at i o n t es t s t o
i d en t i fy wh at p ro p o rt i o n o f t h e p ri ces o f s t o ck s l i s t ed o n t h e d i fferen t i n d i ces fo l l o w a ran d o m wal k . In ad d i t i o n , a rel at ed s eco n d ary s t u d y o f m ark et effi ci en cy i s u n d ert ak en b y ex am i n i n g wh et h er o r n o t t h ere are d i fferen ces b et ween t h e P ri m e S t an d ard i n d i ces i n res p ect t o cal en d ar an o m al y effect s .
S ect i o n 2 o f t h i s s t u d y i n t ro d u ces t h e co n cep t o f m ark et effi ci en cy an d s u b s eq u en t l y S ect i o n 3 i d en t i fi es t h e d i fferen t i n fo rm at i o n req u i rem en t s m ad e o f co m p an i es l i s t i n g o n t h e d i fferen t Germ an i n d i ces . Th i s i s fo l l o wed i n S ect i o n 4 b y an ex am i n at i o n o f t h e m et h o d o l o gy an d d at a u s ed . Th e em p i ri cal res u l t s are p res en t ed an d d i s cu s s ed i n S ect i o n 5 an d fi n al l y, co n cl u s i o n s are d rawn i n S ect i o n 6 .
3
2 . Ma rk et E f f i ci en cy
M ark et effi ci en cy i m p l i es t h at fu t u re ret u rn s are u n p red i ct ab l e fro m p as t ret u rn s an d t h erefo re as n ew i n fo rm at i o n en t ers t h e m ark et , s t o ck p ri ces wi l l
fo l l o w
a
ran d o m
wal k .
Gl en
(1 9 9 8 )
i d en t i fi ed
grap h i cal l y t h e
rel at i o n s h i p b et ween t h e l ev el o f m ark et effi ci en cy an d t h e way t h at n ew i n fo rm at i o n i m p act s o n m ark et p ri ces . Th i s i s s h o wn i n Fi gu re 1 . O v e r r e a c t i o n f o l l o we d b y d e f l a t i o n Anticipatory price
S h are P ri ce
movements through information leak.
Days -1 5
-1 0
-5
0
5
10
15
P u b l i cat i o n o f New In fo rm at i o n Effi ci en t M ark et (Tru e C o m p an y’s Val u e o v er Ti m e) In v es t o r’s p erm an en t o v er react i o n o n t h e s h are p ri ce In v es t o r’s
slow
react i o n
on
the
i n fo rm at i o n ,
al l o ws
i n v es t o rs t o m ak e ex ces s ret u rn s aft er t h e an n o u n cem en t P ers i s t en t In effi ci en cy Figure 1: T he impact on new information on stock prices (adapted from Glen 1998)
If t h e m ark et
is
effi ci en t
t h en
t h e i m p act
o f t h e n ew (p rev i o u s l y
u n k n o wab l e) i n fo rm at i o n o n p ri ce i s i m m ed i at e an d p ri ce m o v em en t s o v er t i m e s h o u l d b e ran d o m an d n o t p red i ct ab l e. If h o wev er t h e p ro ces s o f p ri ce ad j u s t m en t t o n ew i n fo rm at i o n fo l l o ws a regu l ar p at t ern (fo r ex am p l e, as s h o wn i n Fi gu re 1 , res u l t i n g fro m t h e s l o w react i o n o f m ark et s t o t h e n ew i n fo rm at i o n ) t h en fu t u re s h are p ri ces wi l l b e t o s o m e ex t en t p red i ct ab l e an d t h e m ark et wi l l n o t b e co m p l et el y effi ci en t . 4
Fam a (1 9 7 0 ) i d en t i fi ed d i fferen t l ev el s o f m ark et effi ci en cy. Th e weak fo rm o f t h e EM H req u i res t h at fu t u re p ri ces can n o t b e p red i ct ed fro m h i s t o ri cal p ri ce d at a. Th i s d o es n o t req u i re t h e m ark et p ri ce t o b e eq u al t o t h e t ru e v al u e at ev ery p o i n t i n t i m e b u t i t d o es req u i re t h at erro rs i n t h e m ark et p ri ce are ran d o m an d u n b i as ed .
If t h e d ev i at i o n s fro m t h e t ru e
v al u e are ran d o m i t fo l l o ws t h at n o i n v es t o r s h o u l d b e ab l e t o i d en t i fy u n d er o r o v er v al u ed s t o ck s fro m p as t p ri ce d at a.
Th i s m ean s t h at p ri ce
m o v em en t s s h o u l d fo l l o w a ran d o m wal k wh i ch M al k i el (2 0 0 3 , p . 1 ) d efi n es as : “ (t h e) i d ea t h at i f t h e fl o w o f i n fo rm at i o n i s u n i m p ed ed an d i n fo rm at i o n i s i m m ed i at el y refl ect ed i n s t o ck p ri ces t h en t o m o rro w’s p ri ce ch an ge wi l l refl ect o n l y t o m o rro w’s n ews an d wi l l b e i n d ep en d en t o f p ri ce ch an ges t o d ay”. A n u m b er o f s t u d i es h av e b een u n d ert ak en o f t h e DAX i n d ex s u gges t i n g t h at i t d o es i n d eed fo l l o w a ran d o m wal k an d i s t h erefo re weak fo rm effi ci en t . Fo r ex am p l e, Vo i t (2 0 0 1 ), Fran s es an d Van Di j k (2 0 0 0 ).
If a m ark et i s effi ci en t an d fo l l o ws a ran d o m wal k t h en i t s h o u l d n o t b e p o s s i b l e t o fi n d ’cal en d ar an o m al i es ’ wi t h i n s t o ck p ri ce d at a (fo r ex am p l e, h i gh er ret u rn s are m ad e i n J an u ary).
Th ere are, h o wev er, a s i gn i fi can t
n u m b er o f s t u d i es i n t h e l i t erat u re t h at s u gges t cal en d ar an o m al i es ex i s t . Fo r ex am p l e, S i egel (2 0 0 2 ) an d Cornett et al (1995). Th es e t yp es o f an o m al i es are i n co n s i s t en t wi t h effi ci en t m ark et s as i n v es t o rs s h o u l d n o t b e ab l e t o fi n d p at t ern s i n fu t u re s t o ck p ri ces wi t h t h e h el p o f h i s t o ri cal d at a (Faws o n et a l 1 9 9 5 ).
Al t h o u gh t h e s t u d i es ci t ed ab o v e s u gges t t h at t h ere i s
ev i d en ce o f t h e DAX fo l l o wi n g a ran d o m wal k , t h ere are al s o a n u m b er o f s t u d i es wh i ch s u gges t t h at cal en d ar an o m al i es can b e fo u n d i n t h e Germ an m ark et s . Fo r ex am p l e, Han s en an d Lu n d e (2 0 0 3 ).
Th i s s t u d y at t em p t s t o i d en t i fy wh et h er o r n o t t h e d i fferen ces i n t h e t ran s p aren cy s t an d ard s (i n fo rm at i o n req u i rem en t s ) ap p l i ed t o t h e d i fferen t i n d i ces o f t h e Germ an m ark et h av e an i m p act o n t h ei r rel at i v e effi ci en ci es . Th e m et h o d o l o gy ap p l i ed i s t o ex am i n e h o w cl o s el y s t o ck s wi t h i n t h es e i n d i ces fo l l o w a ran d o m wal k an d wh et h er o r n o t t h e ret u rn s t o t h es e s t o ck s s h o w ev i d en ce o f cal en d ar an o m al i es . 5
3 . T ra n s p a ren cy req u i remen ts i n th e Germa n S to ck Ma rk et
Th e Germ an s t o ck m ark et h as d i fferen t t ran s p aren cy s t an d ard s fo r acces s t o d i fferen t el em en t s o f i t s cap i t al m ark et . Th es e are: t h e P ri m e S t an d ard , t h e Gen eral S t an d ard an d t h e En t ry S t an d ard . Th e fi rs t t wo fu l fi l t h e h i gh es t i n t ern at i o n al t ran s p aren cy req u i rem en t s an d are req u i rem en t s fo r s t o ck s l i s t ed o n t h e DAX, M DAX, TEC DAX an d S DAX. Th e En t ry S t an d ard p ro v i d es s m al l t o m ed i u m s i z ed co m p an i es fas t an d co s t effi ci en t acces s t o t h e cap i t al m ark et . It req u i res co m p an i es t o p u b l i s h s i gn i fi can t l y l es s d et ai l ed p erfo rm an ce-rel at ed i n fo rm at i o n t h an t h e P ri m e S t an d ard an d i t can t h erefo re b e argu ed t h at t rad i n g o n t h i s m ark et i s l i k el y t o b e l es s effi ci en t .
Th e co n s t i t u en t s o f t h e DAX i n d ex are t h e 3 0 l arges t Germ an co m p an i es i n t erm s o f t u rn o v er an d m ark et cap i t al i z at i o n . Th e M DAX i n d ex co n t ai n s t h e n ex t 5 0 l arges t co m p an i es b y way o f t u rn o v er an d m ark et cap i t al i z at i o n an d t h e S DAX t h e s u b s eq u en t 5 0 l arges t co m p an i es . Th e Al l S h are En t ry (AS E) i n d ex co n s t i t u en t s are t h e co m p an i es t h at are t rad ed o n t h e b as i s o f t h e En t ry S t an d ard req u i rem en t s . Th es e t en d t o b e co m p an i es t h at are rel at i v el y n ew an d l es s wel l es t ab l i s h ed an d t en d t o b e s i gn i fi can t l y s m al l er i n t erm s o f t u rn o v er an d m ark et cap i t al i s at i o n 1.
1
Further information on German stock market transparency standards and performance indicators is
available on the German stock market homepage (http://deutsche-boerse.com).
6
4 . Meth o d o l o g y a n d Da ta
Meth o d o l o g y Th e p ri m ary o b j ect i v e o f t h i s p ap er i s t o i d en t i fy an y d i fferen ces i n t h e l ev el s o f effi ci en cy o f t h e P ri m e S t an d ard an d En t ry S t an d ard i n d i ces o f t h e Germ an s t o ck m ark et . Th e s t u d y t es t s fo r t h e p res en ce o f ran d o m wal k s wi t h i n s t o ck p ri ces u s i n g b o t h ru n s t es t s an d s eri al co rrel at i o n t es t s (wi t h a s i n gl e l ag).
Th i s d u al ap p ro ach i s fo l l o wed t o ex am i n e fo r co n s i s t en cy
wi t h i n t h e t es t res u l t s .
Th e t es t s are u n d ert ak en o n a ran d o m l y s el ect ed
n u m b er o f s t o ck s fro m each i n d ex 2.
C al en d ar an o m al y effect s are al s o t es t ed fo r i n o rd er t o p ro v i d e ad d i t i o n al ev i d en ce. Th es e t es t s u s e b o t h d ai l y an d m o n t h l y d at a. Th e m et h o d ap p l i ed i s t o i d en t i fy an y s t at i s t i cal l y s i gn i fi can t d i fferen ces i n t h e m ean ret u rn s b et ween t h e rel ev an t p eri o d (d ay o r m o n t h ) an d t h e rem ai n i n g p eri o d s i n t h e cal en d ar. In ad d i t i o n , fu rt h er ev i d en ce i s p res en t ed i n t h e fo rm o f t h e ret u rn s fro m s i m u l at ed t rad i n g s t rat egi es b as ed o n t h es e effect s .
Da ta Th e s o u rce o f t h e d at a u s ed i n t h i s s t u d y i s Yah o o Fi n an ce 3.
Th e s eri al
co rrel at i o n t es t s , ru n s t es t s an d d ay-o f-t h e-week effect t es t s u s e d ai l y d at a o n i n d i v i d u al co m p an y s t o ck p ri ces co v eri n g t h e p eri o d 1 s t J an u ary 2 0 0 5 t o 1 s t J an u ary 2 0 0 7 . M o n t h o f t h e year effect s are ex am i n ed o v er t h e p eri o d 1 s t J an u ary 2 0 0 1 t o 1 s t J an u ary 2 0 0 7 . Th e n u m b er o f o b s erv at i o n s fo r s eri al co rrel at i o n t es t s , ru n s t es t s an d d ay-o f-t h e-week effect s t es t s i s 5 0 8 fo r t h e m aj o ri t y o f co m p an i es 4.
Th e n am es o f t h e i n d i v i d u al s t o ck s u s ed
fo r t h es e t es t s can b e fo u n d i n Ap p en d i x 1 . Th e an al ys i s o f m o n t h -o f-t h eyear effect s u s es 7 2 m o n t h l y o b s erv at i o n s .
2
10 stocks are used from the DAX index, 14 stocks from the SDAX and 15 stocks from each of the
MDAX and ASE indices. These represent one third of the constituents of the DAX, 28% of the SDAX, 30% of the MDAX and 20% of the ASE. 3
(http://uk.finance.yahoo.com).
4
T h e r e w e r e f e w e r o b s e r v a t i o n s a v a i l a b l e f o r HII Hanseatische Immobilien Invest AG, NanoFocus AG and
ZertifikateJournal AG.
7
5 . E mp i ri ca l Res u l ts
5 a . S eri a l co rrel a ti o n tes ts Th e s t at i s t i cal s i gn i fi can ce o f an y fi rs t o rd er 5 s eri al co rrel at i o n i d en t i fi ed was es t i m at ed u s i n g t -t es t s . Th e v al u es o f t h e es t i m at ed t -s t at i s t i cs are s h o wn o n t h e y-ax i s i n Fi gu re 2 . R ej ect i o n o f t h e n u l l h yp o t h es i s at t h e 5 % s i gn i fi can ce l ev el (gi v en b y an ap p ro x i m at e v al u e o f t ≥ 2 ) i d en t i fi es t h at a s t o ck p ri ce i s n o t fo l l o wi n g a ran d o m wal k i.
Figure 2: Significance of serial correlation tests on individual stocks
Fi gu re 2 i d en t i fi es t h at t h e h yp o t h es i s o f n o s eri al co rrel at i o n i s rej ect ed fo r rel at i v el y few o f t h e P ri m e S t an d ard i n d ex s t o ck s (aro u n d 1 0 %) b u t fo r a rel at i v el y l arge p ro p o rt i o n o f t h e En t ry S t an d ard i n d ex co m p an y s t o ck s (4 7 %). Th i s i s i n d i cat i v e o f t h e P ri m e S t an d ard m ark et s b ei n g m o re effi ci en t t h an t h e En t ry S t an d ard m ark et .
5
Serial correlation tests with up to a lag of 5 were produced. As the first lag produced the strongest
evidence of correlation by a substantial margin only these results are reported.
8
W i t h i n t h e P ri m e S t an d ard t h ere are s i gn i fi can t d i fferen ces . As i d en t i fi ed i n Fi gu re 2 , al l o f t h e DAX s t o ck s fo l l o w a ran d o m wal k wh i l s t t h e res p ect i v e fi gu re fo r t h e M DAX i s 7 % an d fo r t h e S DAX 2 1 %. Th es e can b e co n t ras t ed wi t h t h e 4 7 % o f En t ry S t an d ard s t o ck s t h at d o n o t fo l l o w a ran d o m wal k . Th es e res u l t s s u gges t t h e co n cl u s i o n t h at t h e m o re s en i o r t h e m ark et , an d t h e m o re wi d el y t rad ed t h e s t o ck , t h en t h e m o re effi ci en t t h e m ark et wi l l b e.
Fu rt h er t es t s were u n d ert ak en t o t es t fo r t h e s t at i s t i cal s i gn i fi can ce o f t h e d i fferen ces b et ween t h e n u m b ers o f i n d i v i d u al s t o ck s i n each i n d ex fo l l o wi n g a ran d o m wal k ii.
Th e res u l t s o f t h es e t es t s , p res en t ed i n Fi gu re
2 a, s u gges t t h at t h e d egree t o wh i ch t h e En t ry S t an d ard AS E i s l es s effi ci en t t h an t h e o t h er i n d i ces i s s t at i s t i cal l y s i gn i fi can t 6.
Test Statistic
Differences between Indices - Serial Correlation 2.715
2.598
MDAX - ASE
DAX - ASE
1.992 1.658 0.758
0.843
MDAX - SDAX
DAX - SDAX
0.338 0.000 DAX - MDAX
Figure
2a:
Statistical
significance
of
SDAX - ASE
b e t we e n - i n d e x
differences
in
the
serial
correlation tests
6
At the 5% level, where t ≥ 1.658. A 1-tail test is used to test whether the efficiency of the senior
market is significantly higher statistically than that of the junior market.
9
5 b . Ru n s tes ts
Th e
ru n s
t es t
ex am i n es
wh et h er
t h ere
is
a
s t at i s t i cal l y
s i gn i fi can t
d i fferen ce b et ween t h e act u al an d ‘ex p ect ed ’ 7 n u m b ers o f ru n s o f a s p eci fi c l en gt h .
Fi gu re 3 i d en t i fi es t h at fo r m o s t o f t h e i n d i v i d u al co m p an i es
an al ys ed , t h e act u al n u m b er o f ru n s t o b e h i gh er t h an t h e ‘ex p ect ed ’ n u m b er.
Th ere are al s o cl ear d i fferen ces b et ween En t ry S t an d ard an d
P ri m e S t an d ard co m p an i es .
Th e t es t s u n d ert ak en iii
i n d i cat e t h at t h e
h yp o t h es i s o f s t o ck p ri ces fo l l o wi n g a ran d o m wal k can b e rej ect ed at t h e 5 % l ev el (z ≥ 1 . 9 6 ) fo r al l o f t h e En t ry S t an d ard an d S DAX co m p an i es .
Figure 3: Statistical significance of runs tests on individual companies
Th es e res u l t s s u gges t cl ear d i fferen ces b et ween t h e m ark et effi ci en ci es o f co m p an i es i n t h e s en i o r P ri m e S t an d ard i n d i ces an d t h o s e i n t h e j u n i o r En t ry S t an d ard (AS E) i n d ex . Th e p ercen t age o f co m p an i es i n each i n d ex wh ere t h e ran d o m wal k h yp o t h es i s i s rej ect ed was 5 0 % fo r t h e DAX, 6 7 % fo r t h e M DAX an d 1 0 0 % fo r b o t h S DAX an d AS E.
7
The number of consecutive (positive and negative) runs in stock prices that would be expected if
stock prices follow a random walk.
10
Th e rel at i v el y h i gh effi ci en cy fo u n d i n t h e DAX i n d ex an d t h e rel at i v el y l o w l ev el s o f effi ci en cy fo u n d i n t h e AS E an d t h e S DAX i n d i ces are s i m i l ar t o t h e fi n d i n gs o f t h e s eri al co rrel at i o n t es t s . Fi gu re 3 a ex am i n es t h e s t at i s t i cal s i gn i fi can ce 8 o f t h e d i fferen ces b et ween t h e n u m b ers o f i n d i v i d u al s t o ck s i n each i n d ex fo l l o wi n g a ran d o m wal k iv. Th es e s u gges t t h at t h e d egree t o wh i ch t h e En t ry S t an d ard AS E an d t h e S DAX i n d ex are l es s effi ci en t t h an t h e o t h er t wo i n d i ces i s s t at i s t i cal l y s i gn i fi can t .
Differences between Indices - Runs Test -6.632 Test Statistic
-5.71 -4.92
-4.974 -3.90 -2.85
-3.316
-1.658
-2.71
-1.06 DAX - MDAX
MDAX - SDAX
DAX - SDAX
SDAX - ASE
MDAX - ASE
0.000
F i g u r e 3 a : S i g n i f i c a n c e o f b e t we e n - i n d e x d i f f e r e n c e s f o r r u n s t e s t s
8
A 1-tail test is undertaken, as with Figure 2b.
11
DAX - ASE
I mp l i ca ti o n s o f th e s eri a l co rrel a ti o n tes ts a n d ru n s tes ts f i n d i n g s Th e s eri al co rrel at i o n res u l t s s u gges t h i gh er l ev el s o f m ark et effi ci en cy t h an t h e res u l t s i n d i cat ed b y t h e eq u i v al en t ru n s t es t s . Bo t h s et s o f t es t s h o wev er,
show
t h at
the
P ri m e
S t an d ard
i n d i ces ,
wi t h
t h ei r
h i gh er
t ran s p aren cy s t an d ard s , are s u b s t an t i al l y m o re effi ci en t t h an t h e En t ry S t an d ard i n d ex 9. Bo t h s et s o f t es t s al s o s u gges t t h at wi t h i n t h e P ri m e S t an d ard , t h e s en i o r DAX i n d ex i s s u b s t an t i al l y m o re effi ci en t t h an t h e s m al l cap i t al i s at i o n S DAX i n d ex .
In ad d i t i o n t o t h e ru n s t es t s an d t h e s eri al co rrel at i o n t es t s , Au gm en t ed Di ck ey-Fu l l er (ADF) t es t were u n d ert ak en t o i d en t i fy u n i t ro o t s (ran d o m wal k s ) wi t h i n t h e d at a. Al t h o u gh t h es e t es t s are n o t s t ri ct l y co m p arab l e 10, t h ei r res u l t s rei n fo rce t h e ab o v e fi n d i n gs as t h ey i n d i cat ed t h at wh i l s t s t o ck s i n t h e P ri m e S t an d ard fo l l o wed a ran d o m wal k , a s i gn i fi can t p ro p o rt i o n o f t h e AS E s t o ck s d o n o t .
Th e res u l t s fro m t h i s s t u d y are co m p arab l e t o d i fferen ces fo u n d i n t h e C h i n es e s t o ck m ark et 11 b et ween ‘A’ an d ‘B’ s h ares b y S h i gu an g M a (2 0 0 4 ). S eri al co rrel at i o n t es t s i n t h i s s t u d y fo u n d 1 2 % o f s t o ck s i n t h e A-S h ares i n d ex d i d n o t fo l l o w a ran d o m wal k (t h i s co m p ares wi t h an av erage o f 1 4 % i n t h i s s t u d y fo r P ri m e S t an d ard s t o ck s ). Fo r C h i n es e B-S h ares t h e rej ect i o n rat e ro s e t o 4 5 % (co m p ared t o 4 7 % i n t h i s s t u d y fo r t h e Germ an En t ry S t an d ard s t o ck s ). R u n s t es t s u n d ert ak en b y t h e s am e au t h o r al s o p ro d u ced res u l t s co m p arab l e wi t h t h i s s t u d y. Th es e i n d i cat ed ab o u t 3 5 % o f A-S h ares d i d n o t fo l l o w a ran d o m wal k (co m p ared wi t h 5 0 % o f DAX s h ares i n t h i s s t u d y). Fo r C h i n es e B-S h ares t h e rej ect i o n rat e i n creas ed t o 7 5 % (co m p ared t o 1 0 0 % fo r t h e Germ an En t ry S t an d ard s h ares i n t h i s s t u d y).
9
It sh ou ld b e n ot ed t h a t , i n a d d i t i on t o t ra n sp a ren c y effec t s, d i fferen c es i n effi c i en c y levels b et ween
indices could also, in part, be due to different trading frequency in the junior markets. 10
The statistical power of the standard ADF test is relatively weak given that unlike the runs and
serial correlation tests, the null hypothesis is for the existence of a unit root (i.e. random walk). The null is only rejected in the standard test if there is less than 5% chance of this outcome being true. 11
Based on a composite study of the Shanghai and Shenzhen markets.
12
5 c. T es ts f o r ca l en d a r a n o ma l y ef f ects
If s t o ck p ri ces fo l l o w a ran d o m wal k t h en i n v es t o rs s h o u l d n o t b e ab l e t o m ak e m o n ey b y ex p l o i t i n g cal en d ar an o m al i es . Ho wev er t h ere i s s i gn i fi can t em p i ri cal ev i d en ce t o s u gges t t h at p ro fi t o p p o rt u n i t i es fro m s u ch an o m al i es d o ex i s t . Th i s s ect i o n o f t h e p ap er rep o rt s t h e res u l t s o f t es t s fo r d ay-o ft h e-week an d m o n t h -o f-t h e-year an o m al i es i n t h e Germ an m ark et .
Th e
m et h o d o l o gy u s ed i s t o ex am i n e wh et h er o r n o t t h e m ean ret u rn s m ad e o n o n e s p eci fi c d ay o f t h e week (o r m o n t h ) are s t at i s t i cal l y s i gn i fi can t l y d i fferen t fro m t h e ret u rn s m ad e o n t h e o t h er d ays i n t h e week (m o n t h s i n t h e year).
Dat a l i m i t at i o n s wi t h AS E s t o ck s 12 m ean t t h at t h es e t es t s are
u n d ert ak en fo r P ri m e S t an d ard In d i ces o n l y.
Da y -o f -th e-w eek -ef f ects Th e d at a s h o ws t h ere t o b e cl ear b et ween -i n d ex d i fferen ces i n t h e m ean d ai l y ret u rn s . Fo r ex am p l e, M o n d ays p ro d u ce h i gh er ret u rn s fo r t h e DAX, wh ereas Fri d ays p ro d u ce h i gh er ret u rn s fo r t h e M DAX an d S DAX. Tu es d ays , gen eral l y ap p ear t o p ro d u ce t h e l o wes t ret u rn s fo r al l i n d i ces . It i s i d en t i fi ed t h at fo r s t o ck s l i s t ed o n t h e DAX, d ay-o f-t h e-week effect s were s t at i s t i cal l y s i gn i fi can t at t h e 5 % l ev el fo r o n l y 2 % o f o b s erv at i o n s (a s i n gl e co m p an y i n t h e s am p l e o n a s i n gl e d ay). Fo r t h e m o re j u n i o r i n d i ces o f t h e P ri m e S t an d ard t h i s p ro p o rt i o n i s s l i gh t l y h i gh er. Th e effect s were fo u n d t o b e s i gn i fi can t fo r 4 % o f o b s erv at i o n s fro m t h e M DAX an d 1 0 % o f o b s erv at i o n s fro m t h e S DAX. Det ai l s o f t h e s i gn i fi can ce l ev el s fo r t h e i n d i v i d u al s t o ck s u s ed i n t h e s am p l e are s h o wn i n Fi gu re 4 v.
12
A number of the stocks in the ASE sample were not listed on the market over the full 6 year period.
13
DAX - Day of the Week
2.5 2.0
Test Statistic
1.5 1.0 0.5 0.0 -0.5
Monday
Tuesday
Wednesday
Thursday
Friday
Thursday
Friday
Thursday
Friday
-1.0 -1.5 -2.0
MDAX - Day of the Week
2.5 2.0
Test Statistic
1.5 1.0 0.5 0.0 -0.5
Monday
Tuesday
Wednesday
-1.0 -1.5 -2.0 -2.5
SDAX - Day of the Week
3.0
Test Statistic
2.0 1.0 0.0 -1.0
Monday
Tuesday
Wednesday
-2.0 -3.0
Figure 4:
S t a t i s t i c a l s i g n i f i c a n c e o f m e a n r e t u r n b a s e d d a y - o f - t h e - we e k e f f e c t s
(individual stocks)
14
Th e res u l t s fo u n d i n t h i s s t u d y are co m p arab l e wi t h t h o s e o f S h i gu an g M a (2 0 0 4 )
wh o
al s o
fo u n d
cl ear,
but
s t at i s t i cal l y
i n s i gn i fi can t ,
d ai l y
d i fferen ces i n C h i n a. Li k e t h e Germ an m ark et , C h i n es e m ark et s were fo u n d t o p ro d u ce t h ei r l o wes t ret u rn s o n a Tu es d ay, an d l i k e t h e M DAX an d S DAX, t h e h i gh es t ret u rn s were fo u n d o n a Fri d ay.
Al t h o u gh t h e res u l t s fro m t h i s s t u d y s u gges t t h at d ay-o f-t h e-week effect s are gen eral l y n o t s t at i s t i cal l y s i gn i fi can t , s i m u l at ed t rad i n g t es t s s h o w t h at i n s o m e cas es a t rad i n g s t rat egy b as ed o f t h i s ap p ro ach can o u t p erfo rm a b u y-an d -h o l d s t rat egy 13. Ex cl u d i n g t ran s act i o n s co s t s , t h e ret u rn s o n 2 0 % o f DAX s t o ck s u s i n g a d ay-o f-t h e-week s t rat egy o u t p erfo rm ed a b u y-an d h o l d s t rat egy. Th e fi gu res fo r t h e M DAX an d S DAX were 5 3 % an d 5 7 % res p ect i v el y 14.
Mo n th -o f -th e-y ea r-ef f ects A n u m b er o f s t u d i es s u gges t t h e ex i s t en ce i s a p o s i t i v e J an u ary effect , wh i l s t o t h ers s t u d i es s u gges t t h e ex i s t en ce n egat i v e s u m m er an d Oct o b er effect s (S i egel 2 0 0 2 ). Th e d at a i n t h i s s t u d y i n d i cat es t h at , fo r t h e DAX at l eas t , m o s t s t o ck s d o n o t ex h i b i t p o s i t i v e m ean ret u rn s i n J an u ary. Al l o f t h e i n d i ces s u gges t t h at n egat i v e ret u rn s are m ad e i n Au gu s t an d t h at p o s i t i v e ret u rn s are m ad e i n S ep t em b er. R es u l t s fo r m o n t h -o f-t h e-year effect s were s t at i s t i cal l y s i gn i fi can t at t h e 5 % l ev el fo r b et ween 7 %-1 0 % o f o b s erv at i o n s acro s s t h ree i n d i ces vi. Det ai l s fo r t h e s i gn i fi can ce l ev el s fo r t h e i n d i v i d u al s t o ck s u s ed i n t h e s am p l e are s h o wn i n Fi gu re 5 .
13
For each stock, the buying day is identified as the day during the week that produces the lowest
mean return. The selling day is the day in the week that produced the highest mean return. The returns from buying and selling once a week on this basis were compared with the returns from buy the stock at the start of the period of the study and holding it until the end of this period. 14
On the inclusion of transactions costs (buying costs 1.5% and selling costs 1%) all profits from this
trading strategy were eliminated.
15
DAX - Month of the Year 4.0 3.0
Test Statistic
2.0 1.0 0.0 January
February
March
April
May
June
July
August
September
October
November December
August
September
October
November December
August
September
October
November December
-1.0 -2.0 -3.0 -4.0
MDAX - Month of the Year
4.0 3.0
Test Statistic
2.0 1.0 0.0 January
February
March
April
May
June
July
-1.0 -2.0 -3.0 -4.0
SDAX - Month of the Year
4.0 3.0
Test Statistic
2.0 1.0 0.0 January
February
March
April
May
June
July
-1.0 -2.0 -3.0 -4.0
Figure 5: Statistical significance of mean return based month-of-the-year effects (individual stocks)
Al t h o u gh o n l y a few o f t h e o b s erv at i o n s are s t at i s t i cal l y s i gn i fi can t , m o n t h -o f-t h e-year effect s ap p ear t o b e d i s cern ab l e i n Fi gu re 5 . Th e d at a s u gges t s t h at t h e p eri o d fro m Ap ri l t o Au gu s t p ro d u ces gen eral l y l o wer ret u rn s an d t h at S ep t em b er t o Decem b er p ro d u ces gen eral l y h i gh er ret u rn s . Th e cas e fo r t h e wel l d o cu m en t ed ‘J an u ary effect ’ i s h o wev er weak as p o s i t i v e ret u rn s i n t h i s m o n t h ap p ear m ai n l y l i m i t ed t o M DAX s t o ck s . Th es e fi n d i n g can b e co n t ras t ed wi t h t h o s e o f S h i gu an g M a (2 0 0 4 ) wh o 16
fo u n d s t ro n gl y n egat i v e an d s i gn i fi can t Decem b er an d J an u ary effect s an d , i n m ark ed co n t ras t t o Germ an y, wh ere Au gu s t was t h e wo rs t p erfo rm i n g m o n t h , i n C h i n a Au gu s t was t h e b es t p erfo rm i n g m o n t h .
Fu rt h er s i m u l at ed t rad i n g t es t s were u n d ert ak en t o i d en t i fy wh et h er a t rad i n g s t rat egy b as ed o n t h e m o n t h -o f-t h e-year effect s i d en t i fi ed ab o v e wo u l d o u t p erfo rm a b u y-an d -h o l d s t rat egy 15. Ex cl u d i n g t ran s act i o n s co s t s , 9 0 % o f s t o ck s o u t p erfo rm ed b u y-an d -h o l d fo r t h e DAX. Th e fi gu res fo r t h e M DAX an d S DAX were 7 3 % an d 8 0 % res p ect i v el y.
Th e i m p l i cat i o n s o f t h es e fi n d i n gs fo r m ark et effi ci en cy are m i x ed . Th e l i m i t ed s t at i s t i cal s i gn i fi can ce o f cal en d ar an o m al y effect s fo u n d i n t h i s s t u d y ad d s cred en ce t o t h e cl ai m t h at t h e P ri m e S t an d ard i n d i ces are rel at i v el y effi ci en t .
Ho wev er, t h e res u l t s p res en t ed i n Fi gu re 5 a an d al s o
t h e res u l t s fro m t h e as s o ci at ed m o n t h -o f-t h e-year s i m u l at ed t rad i n g t es t s s u gges t t h at a cas e can b e m ad e fo r s o m e el em en t o f i n effi ci en t i n t h e m ark et .
It m ay v ery wel l b e t h at t h e o l d Bri t i s h m ark et ad age o f ‘s el l i n
M ay an d go away d o n ’t co m e b ack u n t i l S t Leger Day’ al s o h as s o m e cred en ce i n t h e Germ an m ark et .
15
For each stock, the buying month is identified as the month that produces the lowest mean return.
The selling month is the one which produced the highest mean return. The returns from buying and selling once a year on this basis were compared with the returns from buy the stock at the start of the period and holding it until the end of this period. Dividends received are added to the return for the buy and hold strategy. Unlike with day-of-the-week effects, transactions costs are of minor importance.
17
6 . Co n cl u s i o n
Us i n g b o t h s eri al co rrel at i o n an d ru n s t es t s t h i s p ap er h as fo u n d cl ear ev i d en ce o f d i fferen ces i n effi ci en cy l ev el s b et ween P ri m e S t an d ard an d En t ry S t an d ard s t o ck s o n t h e Germ an s t o ck m ark et . It h as b een s u gges t ed i n t h i s p ap er t h at t h es e d i fferen ces are p o s s i b l y d u e t o d i fferen ces i n t h e t ran s p aren cy req u i rem en t s o f t h es e d i fferen t i n d i ces .
Al t h o u gh t h e s eri al co rrel at i o n t es t s u n d ert ak en gi v e a s t ro n ger i n d i cat i o n t h an t h e ru n s t es t s t h at P ri m e S t an d ard s t o ck s fo l l o w a ran d o m wal k , b o t h s u gges t t h at o n av erage t h e i n d i v i d u al s t o ck s fo u n d i n t h e DAX are m o re l i k el y t o fo l l o w a ran d o m wal k t h an t h e i n d i v i d u al s t o ck s fo u n d i n t h e M DAX an d t h e S DAX. Th i s i n d i cat es t h at t h ere are p ro b ab l y fact o rs i n ad d i t i o n t o t ran s p aren cy s t an d ard effect s t h at d et erm i n e t h e l ev el o f effi ci en cy wi t h i n Germ an m ark et s .
Th e s t u d y fo u n d o n l y l i m i t ed ev i d en ce o f s t at i s t i cal l y s i gn i fi can t cal en d ar an o m al y
effect s .
Th i s
ad d s
cred en ce
to
the
fi n d i n gs
of
the
s eri al
co rrel at i o n s an d ru n s t es t s o f h i gh l ev el s o f effi ci en cy am o n gs t P ri m e S t an d ard s t o ck s . Ho wev er, a cav eat n eed s t o b e ad d ed wh i ch cal l s t h i s fi n d i n g i n t o q u es t i o n .
S i m u l at ed t rad i n g t es t s b as ed o n a m o n t h -o f-t h e-
year cal en d ar s t rat egy ap p ear t o s u gges t t h at i n s o m e ci rcu m s t an ces t rad i n g s t rat egi es b as ed o n m o n t h -o f-t h e-year effect s m i gh t b e p ro fi t ab l e.
18
Ap p en d i x 1 : In d i v i d u al co m p an i es u s ed i n t h e s t u d y DAX companies used ALLIANZ N ALTANA Bayer AG DEUTSCHE TELEKOM N DT.LUFTHANSA N E.ON AG THYSSENKRUPP TUI N VOLKSWAGEN BASF MDAX companies used AAREAL BANK AMB GENERALI HOLDIN AWD HOLDING BAYR.HYPO-U.VERBK BEIERSDORF IVG IMMOBILIEN IWKA K+S AG KARSTADT QUELLE KRONES SUEDZUCKER TECHEM VOSSLOH SGL Carbon AG Puma AG SDAX companies used comdirect bank AG CeWe Color Holding AG BALDA BAYWA AG VINK.N Dyckerhoff AG Vz FIELMANN FUCHS PETROLUB VZ elexis AG GFK TAG TEGERNSEE IMMO TAKKT THIEL LOGISTIK Sixt AG St VIVACON ASE companies used ACTIVA RESOURCES AG Agnico-Eagle Mines Ltd. AMITELO AG Aragon AG Artec technologies AG Ecotel communication ag Elite Model Management Lux. S.A. HII Hanseatische Immobilien Invest AG HYDROTEC Gesellschaft für Wassertechnik AG ifa systems AG Mox Telecom AG NanoFocus AG trading-house.net AG UNYLON AG ZertifikateJournal AG
19
Ref eren ces C o rn et t , M . M . , S ch warz , T. V. an d S z ak m ary, A. C . (1 9 9 5 ), ‘S eas o n al i t i es an d i n t rad ay ret u rn p at t ern s i n t h e fo rei gn cu rren cy fu t u res m ark et ’, J o u rn al o f Ban k i n g an d Fi n an ce, Vo l . 1 9 , p p . 8 4 3 -8 6 9 . Fam a, E. F. (1 9 9 1 ), ‘Effi ci en t C ap i t al M ark et s : II’, J o u rn al o f Fi n an ce, Vo l . 4 6 (5 ), p p . 1 5 7 5 -1 6 1 7 . Fam a, E. F. (1 9 7 0 ) ‘effi ci en t cap i t al m ark et s : a rev i ew o f t h eo ry an d em p i ri cal wo rk ’, J o u rn al o f Fi n an ce, Vo l . 2 5 (2 ), p p . 3 8 3 -4 1 7 . Faws o n , C . , Gl o v er, T. , Fan g, W . an d C h an g, T. (1 9 9 5 ), ‘Th e weak -fo rm effi ci en cy o f t h e Tai wan s h are m ark et ’, Ap p l i ed Eco n o m i cs Let t ers , Vo l . 3 , p p . 6 6 3 – 6 6 7 . Fl an egi n , F. R . an d R u d d , D. P . (2 0 0 5 ), ‘S h o u l d i n v es t m en t s p ro fes s o rs j o i n t h e cro wd ’, M an ageri al Fi n an ce, Vo l . 3 1 ( 5 ) p p : 2 8 -3 7 . Fran s es , P . H. an d Van Di j k , D. (2 0 0 0 ), No n l i n ear Ti m e S eri es M o d el s i n Em p i ri cal Fi n an ce, C am b ri d ge Un i v ers i t y P res s . Gl en , A. (1 9 9 8 ), ‘C o rp o rat e Fi n an ci al M an agem en t ’, Lo n d o n : Fi n an ci al Ti m es P i t m an P u b l i s h i n g. Han s en , P . R . an d Lu n d e, A. (2 0 0 3 ), ‘Tes t i n g t h e s i gn i fi can ce o f cal en d ar effect s ’, Eco n o m i cs W o rk i n g P ap er s eri es n o . 1 4 3 , Un i v ers i t y o f Aarh u s , Den m ark . KrLak o n i s h o k , J . an d S m i d t , S . (1 9 8 8 ), ‘Are S eas o n al An o m al i es R eal ? : A Ni n et y-year P ers p ect i v e’, R ev i ew o f Fi n an ci al S t u d i es , Vo l . 1 3 , p p . 4 3 5 -4 4 5 . M al k i el , B. (2 0 0 3 ), ‘Th e Effi ci en t M ark et Hyp o t h es i s an d i t s cri t i cs ’, J o u rn al o f Eco n o m i c P ers p ect i v es , Vo l . 1 7 , p p . 5 9 – 8 2 . S h i gu an g, M . (2 0 0 4 ), ‘Th e Effi ci en cy o f C h i n a’s S t o ck M ark et ’, C en t re fo r As i a-P aci fi c C ap i t al M ark et s S ch o o l o f Eco n o m i cs an d Fi n an ce, C u rt i n Un i v ers i t y o f Tech n o l o gy, P ert h S i egel , J . J . (2 0 0 2 ), ‘S t o ck s fo r t h e Lo n g R u n ’, 3 r d Ed i t i o n , M cGraw-Hi l l , New Yo rk . Vo i t , J . (2 0 0 1 ), ‘Th e S t at i s t i cal M ech an i cs o f Fi n an ci al M ark et s ’, S p ri n ger, Berl i n .
20
∑(Y −Y)⋅(Y n
i
Serial correlation is estimated as follows:
αk = t=k+1
t−k
t
−Y)
, where: Yt=current rate of return,
∑(Y −Y) n
t=1
2
t
Y = m e a n r a t e o f r e t u r n , k = n u m b e r o f l a g s . T h e a s s o c i a t e d t - s t a t i s t i c s a r e e s t i m a t e d b y : tI =
ii
T h e t e s t s t a t i s t i c s f o r F i g u r e 2 b w e r e c a l c u l a t e d a s f o l l o w s : TI =
Ri − Rk
αk ⋅ n − 2 1 - α k2
, where R-bar is mean
si2 sk2 + ni nk
percentage of stocks following a random walk for each index.
iii
The test statistics for the runs test are estimated as follows:
where: number of runs=R, standard deviation=
ZI =
R I − E (R )
σR
,
σR
E(R ) =
2 ⋅ N1 ⋅ N 2 + 1, w h e r e : n u m b e r o f p o s i t i v e c h a n g e s = N 1 , n u m b e r o f n e g a t i v e c h a n g e s = N 2 N
σR =
2 ⋅ N1 ⋅ N 2 ⋅ (2 ⋅ N 1 ⋅ N 2 − N ) N 2 ⋅ (N − 1)
iv
See endnote ii above for formula.
v
See endnote ii above for formula, where Ri and RK represent the mean returns for the individual day
of the week and the mean return for the sum of the rests of the days of the week respectively.
vi
See endnote ii above for formula, where Ri and Rk represent the mean returns for the individual
month of the year and the mean return for the sum of the rest of the months of the year respectively.
21
