Von Wielligh, J. F.C.; Smi , E. V.D.M.
A icle
Pe sis ence in he pe o mance o Sou h A ican uni us s
Sou h A ican Jou nal o Business Managemen
P o ided in Coope a ion wi h:
Uni e si y o S ellenbosch Business School (USB), Bell ille, Sou h A ica
Sugges ed Ci a ion: Von Wielligh, J. F.C.; Smi , E. V.D.M. (2000) : Pe sis ence in he pe o mance o
Sou h A ican uni us s, Sou h A ican Jou nal o Business Managemen , ISSN 2078-5976, A ican
Online Scien i ic In o ma ion Sys ems (AOSIS), Cape Town, Vol. 31, Iss. 3, pp. 120-129,
h ps://doi.o g/10.4102/sajbm. 31i3.742
This Ve sion is a ailable a :
h ps://hdl.handle.ne /10419/218230
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120
S.A .J.Bus.Manage.2000,31())
Pe sis ence
in
he pe o mance
o
Sou h A ican uni us s
J.F.C.
on
Wielligh
&
E.
d
M.
Smi
G adua e
School
o
Business,
Uni e si y
o
S ellenbosch,
P.O.
Box
610,
Bell ille,
7535
Sou h A ica
Recei ed
May
2000
The
pe sis ence o
pe o mance
o
he
Gene al
Equi y
Uni
T us s
and
All
Uni
T us s
ha
aded
in
Sou h A ica du ing
he
pe iod
Janua y
1988
o
Decembe
1997
and
Janua y
1993
o
Decembe
1997,
is
analysed
using
h ee models
o
pe o m-
ance
measu emen ,
namely
he
Capi al
Asse
P icing
Model,
a wo- ac o A bi age P icing Theo y
model
and
a h ee- ac-
o
A bi age
P icing
Theo y
(AP )
model
de eloped
in
his
s udy.
The
Capi al
Asse
P icing
Model
does
no
explain
he
ela i e e u ns
o
he
di e en
po olios.
Bo h
AP
models
accoun
o
almos
all
o
he
c oss-sec ional a ia ion
in
ex-
pec ed
e u ns.
I
is
shown
ha
he e
is
e idence
o
bo h
sho - e m
and
long- e m
pe sis ence
in
pe o mance o
Sou h
A -
ican
uni
us s.
I
appea s
ha
he
wo s
pe o ming
uni
us
po olio
ends
o
s ay
he
wo s
pe o me . The po olio o
uni
us s
wi h
an
a e age
mon hly
e u n
may
e en ually
become
he
op
pe o ming po olio, while he
op
pe o me
o e
ime
ends
o
becomes
an
a e age
pe o ming
po olio.
In oduc ion
The aim
o
his s udy
is
o de ennine whe he e idence
o
pe sis ence
in
pe onnance exis s amongs Sou h A ican uni
us s. F om he li e a u e e iew
in
he second sec ion
i
is
clea ha he pe iods
o
analyses and he ya ds ick used o
de ennine pe onnance, ha e an in luence on all conclusions.
Fou da a se s a e discussed
in
he hi d sec ion which allow
analyses o e a i e-yea and a en-yea pe iod as well as o
bo h Gene al Equi y Uni T us s and All Uni T us s.
The ou h sec ion deals wi h he h ee models
o
pe onn-
ance measu emen which a e employed
in
he analyses o en-
su e mo e han one ya ds ick. These a e he Capi al Asse
P icing Model (CAPM), a wo- ac o A bi age P icing The-
o y (APT) model and a h ee- ac o APT model.
Sho - enn pe sis ence
o
pe o mance as well as long- e m
pe sis ence
o
pe o mance
o
uni us s a e s udied
in
he
i h sec ion. The pe onnance
o
pas -winne s
is
also exam-
ined. The s udy
is
concluded wi h a summa y
o
he cen al
indings.
Li e a u e
e iew
O e he yea s di e en esea che s ha e de i ed di e en
conclusions abou he pe sis ence
o
pe onnance
o
uni
us s and speci ically Sou h A ican uni us s. Knigh &
Fi e (1989) p esen e idence ha o e he pe iod 1977 o
1986, us s ha e pe o med ei he consis en ly well o con-
sis en ly poo ly. Smi h & Chapman (1994), Bige & Page
{1994) and Old ield & Page (1997), amongs o he s, conclude
ha he e
is
li le e idence
o
ma ke iming abili y amongs
po olio manage s
o
Sou h A ican uni us s. They could
no ind any e idence
o
skills
in
selec ing and swi ching
secu i ies wi hin each asse class. Ga in concu s:
'Fund manage s we e no able o consis en ly ou pe -
onn he ma ke , nei he did any manage consis en ly
pe onn wo se han he ma ke . The e
is
e y li le
"pe sis ence"
in
pe o mance amongs und manage s.
In
o he wo ds,
i
a und manage pe onned well
in
one pe iod
i
does no imply ha he will pe o m well
in he subsequen pe iod' (1995: 104).
On he o he hand The on ( 1996) and De Lange (
1996)
a -
gue ha he e
is
some e idence
o
pe sis ence
o
pe o mance
o
uni us s
in
Sou h A ica. They ad ise ha
i
is
impo an
o in es
in
one
o
he be e pe o me s, which
in
he
long
un
can make a signi ican di e ence
in
e u ns.
I
in es ed
in
he
op qua ile
o
bes pe o me s, one will consis en ly
ob ain
posi i e e u ns. Howe e , acco ding o he
Uni
T us
Hand-
book
( 1997) only one
in
i e
o
he unds in he op qua ile
o
a i e-yea league able a e likely o emain
in
he op
qua ile
o e he nex i e yea s.
Meye (1997) examines he pe sis ence
o
Sou h
A ican
uni us s using he Jensen measu e oge he wi h he
secu i y
ma ke line and he All Sha e Index o e ou -yea ,
wo-yea
and one-yea in e als. Meye (1997) concludes ha
he
e-
sul s a e compa able o hose ob ained
in
much bigge
ma -
ke s and ha some pe sis ence
in
pe o mance
o
uni us s
in
he Sou h A ican en i onmen does ex'is . The epea
winne
phenomenon exis s o e wo-yea pe iods o o al
e u ns
and he epea lose phenomenon
is
p esen o e
one-yea ,
wo-yea and ou -yea ime pe iods a a much highe
e-
quency. Meye concludes ha :
'Pe sis ence
in
pe o mance seems o exis and
i
appea s o be a guide o bea he pack
in
he long
un.
The longe he e alua ion pe iod, he be e he esul s'
(1997: II).
Mos esea ch done on mu ual unds
in
he USA poin
o-
wa ds posi i e pe sis ence
in
pe o mance. G inbla &
Ti -
man (1992), Hend icks, Pa el & Zeckhause
(1993),
Goe zmann & Ibbo son (1994), B own & Goe zmann (1995),
El on, G ube & Blake (1996) and Ca ha (1997) all
ag ee
ha he e
is
some e idence
o
pe sis ence
in
mu ual und
pe -
o mance.
The conclusions eached
in
any one s udy, howe e ,
a e
model and benchma k dependen (see Page, 1993). The e o e,
in
o de o add o he obus ness
o
he cu en s a e
o
knowl-
edge abou pe sis ence
in
pe o mance
in
he Sou h A ican
ma ke , due o he ac ha mos esea ch
is
CAPM based,
he
APT amewo k is u ilised
in
he cu en s udy.
S.A .J.Bus.Manage.2000,31(3)
The
Capi al Asse P icing Model (CAPM)
is
he equa ion
o
he
secu i y ma ke line showing he ela ionship be ween
he
expec ed e u n and be a. A bi age P icing Theo y (APT)
is
based
on ewe and less es ic i e assump ions han he
CAPM
and
is
also a mo e gene al model allowing o mo e
han
one
isk ac o o unde lie sha e e u ns. The APT
is
based
on
he assump ions ha ma ke s a e pe ec ly compe i-
i e
and
ic ionless and ha in es o s p e e mo e weal h o
less
weal h and a e isk a e se.
In~i iduals sh~ e he ~elie ha o he se
o
asse s being
conside ed, he ime se ies p ocess unde lying he gene a ion
o secu i y e u ns can be ep esen ed by he ollowing linea
k- ac o model:
K
R,,
= E(R;,) + L
Balk,+
E;,
k = I
(I)
whe e:
R;,
ealised e u ns ea ned by asse i
in
ime pe iod
,
whe e i =
1,2
...
n and =
1,2
...
T;
E(R,J=
he expec ed a e
o
e u n
o
asse i o pe iod a
he beginning
o
pe iod ;
a coe icien ha measu es he sensi i i y
o
R,,
o
mo emen s
in
k,;
he
k h
isk ac o ha impac s on asse i's e u n,
whe e k = 1,2
...
K.
All isk ac o s ep esen unex-
pec ed mo emen s
in
pe asi e economic o ces and
ha e an expec ed alue
o
ze o; and
a no mally dis ibu ed andom e o which meas-
u es he unexplained esidual e u n
o
asse i
in
pe iod
.
Page
(1985) concludes ha in compa ing he APT and he
CAPM,
he APT was ound o be subs an ially be e wi h e-
ga d
o he explana ion
o
a iabili y
in
Sou h A ican sha e
e u ns
and ha he unde lying mac oeconomic a iables de-
ennining he e u n gene a ion p ocess can be di ided in o
hose
ha p ima ily in luence he mining sec o and hose ha
a ec
he indus ial sec o o a g ea e ex en .
.
Acc_o ding
o Ross ( 1976) a bi age heo y equi es essen-
ially
iden ical expec a ions and ag eemen on he be a coe i-
cien_ s
i_
he iden i ica ion
o
ex an e belie s wi h ex pos
eahsa 1ons
is
o p o ide empi ically ui ul esul s. Page
(1989)
and Ba (1989) bo h conclude ha a wo- ac o model
is
he
bes benchma k o use
in
measu ing secu i y p ice pe -
onnance
in
Sou h A ica. Da idson (1993) concu s ha he
CAPM
is
no an app op ia e model o use on he JSE, bu a
he
same ime a gues ha he APT is a om ope a ional.
Reese
(1993) con i ms ha
in
e ms
o
he JSE as a whole,
wo
o h ee ac o s appea
o
be p iced, al hough he esea ch
on
a ya ds ick o uni us s' pe o mance by Bige & Page
(1993)
poin s owa ds an app op ia e model con aining h ee
o
i e
ac o s.
,
Va~
Rensbu g & Slaney ( 1997) a gue ha a wo index
mul i-ma ke model' when employing he JSE All Gold and
~dus ial Indices as explana o y a iables, aids he economic
m e p e a ion
o
he esul s as well as in oducing conside a-
ble
e iciency
in
he ensuing c oss-sec ional es ima ion p oce-
du es.
I also p o ides a model ha
is
mo e easily applied
by
p ac i ione s and bypasses he well-documen ed di icul ies
121
associa ed wi h ac o analysis. They conclude ha he di e -
en
so_u ces
o
isk a e ewa ded wi h isk p emia
o
di e en
magni udes and ha he la ge majo i y
o
JSE sha es a e in-
luenced
by
ei he he Mining o Indus ial Indices bu seldom
by.
~o h_
o an equal deg ee. The wo- ac o APT model has
~ncmg implica ions no compa ible wi h he CAPM employ-
ing he JSE All Sha e Index as he ma ke p oxy.
Van
Rensbu g (1998) s udies he e ec
o
economic o ces
on he JSE a~d. concludes ha he i ual 'poo ly speci ied
ma ke po olio appeal will always be he las un es able de-
ense
o
he CAPM. Howe e , his esul s indica e ha he
CA~M, as con en ionally speci ied
by
Sou h A ican aca-
demics and p ac i ione s (i.e. using he JSE All Sha e Index
~s
a ma ke p oxy),
is
se iously lawed. The ela i e supe io -
i y
o
he Slaney (1995) wo-index APT model is demon-
s a ed
by
using he Indus ial and All Gold Indices as
obse able p oxies.
I
is
a gued ha no only does his p oce-
du e signi ican ly imp o e he explana o y powe
o
models
using p e-speci ied mac oeconomic a iables, bu also ha i s
omission leads o upwa d bias
in
he a iances
o
he coe i-
cien es ima o s
o
hese models.
Da a
and
sample
selec ion
Fo~ samples
o
da a a e used, namely all en Gene al Equi y
Uni T us s ha aded
in
Sou h A ica o e he pe iod
Janua y 1988 o Decembe 1997 ( i s sample), he Gene al
Equi y Uni T us s ha aded
in
Sou h A ica o e he pe iod
Janua y 1993 o Decembe 1997 (second sample) and all Uni
T us s ha aded
in
Sou h A ica du ing hese pe iods a e
used
in
he hi d and ou h samples
(21
and 42) espec i ely.
T us s ha we e
in
exis ence o e he en i e i e- and en-yea
pe iods a e included
in
he ou samples espec i ely.
Mon hly da a was used. Selling p ices we e ob ained om
he Money Ma e da abank. Mon hly a es
o
e u ns we e cal-
cula ed using he ollowing equa ion:
(2)
whe e:
R,,
= he mon hly a e o e u n
o
uni us i
in
pe iod
;
P
11
= he mon hly selling p ice
o
uni us i
in
pe iod ; and
P,
1•1 = he mon hly selling p ice
o
uni us i
in
pe iod -1.
The yield
on
he h ee-mon h T easu y Bill is used o ep e-
sen he isk- ee a e
o
e u n. The da a
is
ob ained om
1-
Ne o he pe iod Janua y 1988 o Decembe 1997 on a
mon hly basis as a yea ly a e
o e um.
The mon hly isk ee
a e
o
e u n o e he en-yea pe iod was ecalcula ed on a
mon hly basis. The mon hly excess a e
o
e u n o he ou
samples we e calcula ed by sub ac ing he isk ee a e om
he mon hly a e
o
e u n as de e mined by equa ion 2.
Th ee models
o
pe o mance measu emen we e em-
ployed: he Capi al Asse P icing Model as desc ibed
in
Ross,
Wes e ield & Jo dan (1993), a wo- ac o A bi age P icing
Theo y model (Van Rensbu g & Slaney, 1997) and a h ee-
ac o A bi age P icing Theo y model de eloped
in
his
s udy and sugges ed by
Van
Rensbu g.
122
Capi al Asse
P icing
Model
(CAPM)
The i s model
o
pe onnance measu emen
is
he CAPM,
speci ied as
PORTF;,
= a;y+
I};,,.
ASHARE,
+&;,
= I, 2 ... T ... (3)
whe e:
PORTF = he a e age mon hly excess1 e u n o po olio
II
i
in
pe iod ;
ASHARE = he mon hly a e
o e um
o
he All Sha e
Index2
in
pe iod
;
and
= he s ochas ic e o enn
o
uni us i
in
pe iod
.
Two- ac o
model
The wo- ac o APT model has he ollowing speci ica ion:
PORTFi
=
aiT
+
JliT
AGOLD1 + cIT INDUST1 +
&i
= 1,2...T (4)
whe e:
A
GOLD,=
he mon hly a e
o e um
o
he All Gold Index
in
pe iod ; and
INDUST,= he mon hly a e
o
e u n
o
he Indus ial Index
in
pe iod
.
Da a on a mon hly basis o he en-yea pe iod
is
ob ained
o he All Sha e Index, he All Gold Index and he Indus ial
Index, om I-Ne . The mon hly e u ns a e calcula ed using
he same me hod as o he po olios.
This model
is
based on he indings
o
Van
Rensbu g &
Slaney who claim ha
'The empi ical indings s ongly sugges ha a wo
index model, employing he JSE Indus ial and All
Gold Indices as "p esc ibed ac o s",
is
a mo e app o-
p ia e app oach o adop
in
asse p icing applica ions
such as po olio pe onnance e alua ion and calcula -
ing Sou h A ican companies' cos
o
equi y capi al'
(1997: 20).
S.
A .J.
Bus.
Manage.2000,31(3)
Th ee- ac o
model
This model con ains an addi ional ac o in ended o
p ice
isk
explici y:
PORTF;
1 =
aiT
+
3iT
AGOLD
1 + ciT
IND
UST,+
d;T
STDEV;
1 +
&;
1
(S)
=
1,2
... T
whe e:
STDEV = he s anda d de ia ion
o
he mon hly a e o e-
" um
o
po olio i
in
pe iod .
Summa y s a is ics o he ac o po olios epo ed
in
Ta-
ble I indica e ha he wo- ac o model can explain
conside -
able a ia ion
in
e u ns o bo h he i e- and
en-yea
pe iods. Fi s , no e he ela i e high a iance
o
he A
GOLD
and he INDUST and hei low co ela ions wi h each
o he .
This sugges s ha he wo- ac o model can explain
sizeable
ime-se ies a ia ion. Second, he low c oss-co ela ions
im-
ply ha mul icollinea i y does no subs an ially a ec
he
es i-
ma ed wo- ac o model loadings.
Empi ical
esul s
Pe sis ence
in
he
cu en yea e u n
so ed
uni
us
po olios
(base
case)
Fo all ou da a samples (All Uni T us s and Gene al
Equi y
Uni T us s o e en- and i e-yea pe iods), h ee
equally
weigh ed po olios
o
uni us s ha e been o med
based
on
he cu en yea 's excess e u n using a modi ied
e sion
o
he me hodology
o
Hend icks, Pa el & Zeckhause
(1993).
On he i s
o
Janua y
o
each yea , h ee equally
weigh ed
po olios
o
uni us s, using epo ed yea ly e u ns
o
he
cu en yea , a e onned. The op pe o me s a e included
in
po olio I (PO
RTF
I), he a e age pe o me s
in
po olio 2
(PORTF2) and he wo s pe o me s
in
po olio 3
(PORTF3).
The po olios a e held o one yea a e which hey
a e
e·
o med. F om his, ime se ies
o
mon hly excess e u ns
o
each
o
he h ee po olios a e ob ained om Janua y
1989
o
Decembe 1997 o he wo en-yea samples (All Uni
T us s
and Gene al Equi y Uni T us s) and Janua y 1993
o
Decem·
be 1997 o he wo i e-yea samples (All Uni T us s
and
Gene al Equi y Uni T us s).
Table
1
Pe o mance
measu emen
model
summa y
s a is ics
FIVE-
YEAR
PERIOD
(Janua y
1993
-Decembe
1997)
Fac o po olio
A e age
mon hly
S anda d C oss-co ela ions
e u n
de ia ion
A
SHARE
AGOLD
INDUST
AS
HARE
1.177%
4.504%
1.000
AGOLD
0.641%
11.363%
0.600
1.000
INDUST 0.979% 4.303%
0.850
0.198 1.000
TEN-
YEAR
PERIOD
(Janua y
1988
-Decembe
1997)
Fac o po olio
A e age
mon hly
S anda d C oss-co ela ions
e u n
de ia ion
AS
HARE
A GOLD
IN
DUST
AS
HARE
1.173%
4.840%
1.000
A
GOLD
0.621%
10.140%
0.588
1.000
INDUST
1.350%
4.670% 0.857 0.217
1.000
S.A .J.Bus.Manage.2000,31 (3)
Mul iple eg ession analyses a e pe onned wi h he h ee
po olios' e u ns as he dependan a iables. Fo each
o
he
ou
samples h ee mul iple eg ession analyses a e un pe -
aining
o
each
o
he h ee models
o
pe onnance measu e-
men .
A o al
o
36 mul iple eg ession analyses a e epo ed
on
in
Tables 2 and 3. The po olios
o
bo h All Uni T us s
and
Gene al Equi y Uni T us s demons a e s ong a ia ion
in
mean
e u ns, as shown
in
hese ables.
The
mean mon hly excess e u ns
o
he h ee po olios de-
cline
wi h po olio ank o all ou samples. Because he
po olios
a e onned on he basis
o
he cu en yea 's pe -
o mance
his pa e n is expec ed. The dispe sions
o
he ou
samples
indica e sizeable annualized sp eads
in
e u ns
o
ap-
p oxima ely 9%
in
he case
o
he Gene al Equi y Uni T us s
and
30%
in
he case
o
All Uni T us s. C oss-sec ional a ia-
ion
in
e u n is conside ably la ge among he po olios
o
All
Uni
T us s han Gene al Equi y Uni T us s and also
la ge
among he po olios
in
he en-yea samples han he
i e-yea
samples
in
h ee
o
he ou samples.
In
all ou
samples
he op po olio (PO RTF I) exhibi s posi i e excess
e u ns,
while he wo s pe onne s (PORTF3) show nega i e
e u ns.
123
In
he case
o
he Gene al Equi y Uni T us po olios, he
CAPM be as o he h ee po olios a e almos iden ical and
hey consis en ly dec ease om PORTFI o PORTF3, excep
o he i e-yea pe iod. Fo he All Sha e Uni T us po o-
lios, he CAPM be as consis en ly dec ease om PO
RTF
I o
PORTF3 indica ing a highe isk o he po olios wi h he
highe excess e u ns.
In
all he samples he a e age po olio
(PORTF2) shows he bes co ela ion wi h he All Sha e In-
dex (ASHARE). Du ing he i e-yea pe iod, he Gene al
Eq-
ui y Uni T us po olios co ela e be e wi h ASHARE han
he All Sha e Uni T us po olios, while du ing he en-yea
pe iod he opposi e
is
ue.
The esul s
o
wo- ac o model indica es ha he Gene al
Equi y Uni T us po olios a e less sensi i e o he All Gold
Index (AGOLD) han he All Sha e Uni T us po olios. The
opposi e
is
ue o he Indus ial Index
(INOusn.
No e he
small eg ession coe icien s o he PORTF3's
o
he All Uni
T us po olios. High adjus ed R-squa e alues indica e a
good i be ween he pe onnance
o
he po olios and he
wo- ac o model, especially
in
he case
o
he high and me-
dium e u n po olios.
The h ee- ac o model does no do subs an ially be e han
he wo- ac o model
in
enns
o
he adjus ed R-squa e alues
Table 2 Po olios
o
gene al equi y uni us s o med on he cu en yea e u ns
FIVE-YEAR PERIOD TEN-YEAR PERIOD
Po olio PORTFI PORTF2 PORTF3 PORTFI PORTF2 PORTF3
(High) (Med) (Low) (High) (Med) (Low)
Mean mon hly excess e u n 0.723% 0.069% -0.004% 0.564% 0.061% -0.269%
S d de ia ion 3.480% 3.493% 3.384% 3.898% 3.807% 4.681%
Alpha -0.122% -0.799% -1.205% -0.317% -0.801% -1.113%
-S a -0.697 -5.498 -6.796 -2.271 -5.944 -3.579
CAPM
ASHA
RE
0.717 0.738 0.692 0.751 0.735 0.719
I-S a 19.015 23.445 18.033 26.671 27.045 11.472
Adj R-sq 0.859 0.903 0.846 0.869 0.872 0.550
OW-S a 2.160 2.211 2.347 2.197 2.475 2.979
Alpha 0.028% -0.658% -1.082%
-0.369"Ai
-0.873% -1.108%
-S a 0.133 -3.996 -5.792 -2.153 -6.088 -3.314
A
GOLD
0.072 0.080 0.065 0.088 0.092 0.114
2-Fac o
I-S a 3.884 5.497 3.922 5.305 6.621 3.499
Mod l
IN DUST 0.663 0.690 0.664 0.687 0.687 0.616
-S a 13.612 17.984 15.249 18.981 22.693 8.721
Adj R-sq 0.795 0.873 0.826 0.808 0.859 0.494
OW-S a
2.111
2.118 2.412 2.562 2.300 2.901
Alpha -1.380% 0.228% -0.765% -0.800% -0.327% -1.630%
-S a -2.799 0.466 -1.767 -2.329 -1.015 -5.073
A GOLD 0 073 0.077 0.067 0.083 0.093 0.107
-S a 4.261
5354
3.993 4.882 6.752 3.611
3-Fac o
IN
DUST 0.656 0.703 0.664 0.678 0.698 0.626
Model I-S a 14.454 18.453
15.201
18.609 22.932 9.785
STOEY 1.006 0.793 -0.258 0.365 0.545 0.304
-S a 3.107 -1.919 -0.810 1.446 -1.886 4.874
Adj R-sq 0.822 0.979 0.825 0.810 0.862 0.584
2.051 2.408 2.632 2.296 2.814
OW-S a 2.279

124
S.A .J.Bus.Manage.2000,31(3)
Table
3 Po olios
o
All Uni T us s o med
on
he cu en yea e u ns
FIVE-YEAR PERIOD TEN-YEAR PERIOD
Po olio PORTFI PORTF2
(High) (Med)
Mean mon hly excess e u n 1.039% 0.035%
S d de ia ion 4.000% 3.337'%
Alpha 0.069% -0.791%
-S a 0.344 -5.481
CAPM
A SHARE 0.823 0.702
-S a 18.857 22.464
Adj R-sq 0.857 0.895
OW-S a 1.684 2.185
Alpha 0.369% -0.663%
-S a 1.450 -4.412
A GOLD 0.188 0.077
2-F•c o
-S a 8.384 5.839
Model INDUST 0.561 0.662
-S a 9.454 18.900
Adj R·sq 0.769 0.884
OW-S a
1.831
2.220
Alpha -0.474% -0.112%
I-S a -0.964 -0.223
A GOLD 0.173 0.073
-S a 7.423 5.207
J.F•c o
INDUST
0.559
0.661
Model I-S a 9.673 18.912
STD EV 0.351 -0.380
-S a 1.985 -1.151
Adj R-sq 0.781 0.885
OW-S a 1.796 2.184
which he STOEY a iable
is
equen ly insigni ican and un-
s able
in
enns
o
i s sign.
Pe sis ence
in
one-yea e u n-so ed uni us po -
olios
The pu pose
o
his sec ion
is
o de ennine whe he sho -
enn pe sis ence exis s
in
he pe onnance
o
Sou h A ican
uni us s. Once again o all ou da a samples (All Uni
T us s and Gene al Equi y Uni T us s o e en- and i e-yea
pe iods), h ee equally weigh ed po olios
o
uni us s ha e
been onned. Fo hese analyses he po olios ha e been
onned on he basis
o
lagged one-yea e u ns, hus e-
plica ing he me hodology
o
Hend icks e
al.
(1993). On he
i s
o
Janua y
o
each yea , h ee equal weigh ed po olios
o
uni us s a e onned, using epo ed yea ly e u ns
o
he
p e ious yea . The op pe onne s a e included
in
po olio I
(PORTF l ), he a e age pe o me s
in
po olio 2 (PORTF2)
and he wo s pe o me s in po olio 3 (PORTF3).
The po olios a e held o one yea a e which hey a e e-
onned. Once again a o al
o
36 mul iple eg ession analyses
ha e been un using he h ee models
o
pe o mance meas-
u emen . Summa ies
o
he esul s
o
he mul iple eg ession
PORTF3 PORTFI PORTF2 PORTF3
(Low) (High) (Med) (Low)
-1.740% 0.782% -0.007% -1.430%
3.608% 4.314% 3.727% 4.077%
-2.344% -0.163% -0.857% -2.200o/o-
-6.290 -0.893 -6.815 -8.657
0.514 0.806 0.724 0.656
6.368 21.833 28.582 12.810
0.401 0.816 0.884 0.604
1.632 1.707 2.608 2.374
-2.160% -0.033% -0.883% -2.037%
-6.048 -0.149 -5.971
-7800
0.153 0.193 0.111 0.196
4.844 9.031 7.689 7.724
0.329 0.594 0.644 0.441
3.958 12.802 20.607 7.987
0.442 0.742 0.844 0.593
1.698 1.893 2.364 2.410
-0.833% -1.205% -0.425% -2.462%
-2.749 -2.599 -1.251 -7.481
0.106 0.172 0.106 0.199
4.633 7.802 7.280 7.941
0.440 0.587 0.641 0.438
7.336 13.032 20.618 8.064
-0.352 0.586 -0.292 0.167
-7.764 2.846 -1.496 2.068
0.726 0.759 0.846 0.605
2.308 2.022 2.351 2.394
analyses pe aining o he Gene al Equi y Uni T us s
and
All
Uni T us s a e shown
in
Tables 4 and 5 espec i ely.
Once again a ia ions
in
mean e u ns be ween he
po o-
lios a e demons a ed, al hough no as p onounced
as
in
he
base case.
In
he case
o
Gene al Equi y Uni T us s,
PORTFI
shows he highes mon hly excess e u ns and PORTF2
he
lowes .
In
he case
o
All Uni T us s, he mon hly excess
e-
u ns
o
he h ee po olios inc ease wi h po olio ank
o de .
PORTFI has he lowes (nega i e) mon hly excess e u ns o
all po olios. The ou samples indica e annualised sp eads o
app oxima ely 3% o he Gene al Equi y Uni T us s and be·
ween wo and 14% o All Uni T us s. C oss-sec ional a ia-
ion
in
e u ns
is
conside ably la ge among he po olios o
All Uni T us s han Gene al Equi y Uni T us s and
also
la ge amongs he po olios in he en-yea samples han
he
i e-yea samples.
The CAPM does no explain he ela i e e u ns
o
hese
po olios. The e
is
no consis en ela ion be ween he
CAPM
be as and he e u ns on he h ee po olios. The CAPM
be as
should be highe o highe e u ns indica ing a highe isk
o
he po olios wi h he highe excess e u ns. In all he sam·
pies he a e age po olio (PORTF2) shows he bes co ela-
ion wi h he All Sha e Index (ASHARE), while du ing
he
s.A .J.Bus.Manage.2000,31 (3)
12S
Table
4 Po olios
o
Gene al Equi y Uni T us s o med
on
lagg d
e one yea e u
-
ms
FIVE-YEAR PERIOD TEN-YEAR PERIOD
Po olio PORTFI PORTF2
(High) (Med)
Mean mon hly excess e u n 0.310% 0.000%
S d de ia ion 3.291% 3.540%
Alpha -0.463% -0.883%
-S a -2.392 -6.225
CAPM
AS HARE 0.657 0.751
I-S a 15.675 24.431
Adj R-sq 0.806 0.910
DW-S al
2085
2.339
Alpha -0.353% -0.732%
-S a -1.
761
-4.311
A
GOLD
0.049 0.087
2-Fac o
-S a 2.751 5.778
Model
IN
DUST 0.645 0.691
-S al 13.820 17.453
Adj R-sq 0.789 0.869
OW-S a 2.076 2.242
Alpha -0.988% -0.601%
-S a -2.216 -1.307
A
GOLD
0.047 0.087
-S a 2.700 5.732
J-Fac o
INDUST 0.649 0.693
Model -S a 14.072 17.025
STD
EV 0.484 -0.1
IO
-S a 1.590 -0.307
Adj R-sq 0.794 0.867
DW-S a I 2.092 2.242
i e-yea
pe iod, he Gene al Equi y Uni T us po olios co -
ela e
be e wi h he All Sha e Index (ASHA RE) han he All
Sha e
Uni T us po olios. Du ing he en-yea pe iod, he
opposi e
holds.
In
Tables 4 and 5 he same phenomena a e obse ed as
in
he
base
case. Using he wo- ac o model, i ollows ha he
Gene al
Equi y Uni T us po olios a e less sensi i e o he
All
Gold Index (AGOLD) han he All Sha e Uni T us po -
olios,
while he opposi e holds o he Indus ial Index (IN-
DUST).
High adjus ed R-squa e alues indica e a good
co ela ion be ween he pe onnance
o
he po olios and he
wo- ac o model in mos cases. In all ou samples he
~ORTF2's ha e he highes adjus ed R-squa e alues, which
IDlplies
ha he pe onnance
o
he a e age po olios can
bes
be
desc ibed by his model.
The
h ee- ac o model does no do subs an ially be e han
he
wo- ac o model, as he alues
o
he s anda d de ia ion
o
he
po olios (STDEV) a e no signi ican
in
a numbe
o
cases.
In
summa y, he esul s show ha sho - e m pe sis ence
does
no exis o he All Sha e Uni T us po olios.
In
he
case
o
he Gene al Equi y Uni T us po olios, howe e ,
PORTF3 PORTFI PORTF2 PORTF3
(Low) (High) (Med) (Low)
0.246% 0.217% 0.057% 0.083%
3.676% 4.601% 3.864% 3.907%
-0.765% -0.602% -0.826% -0.769"/o
-5.175 -1.939 -6.407 -5.523
0.737 0.698 0.752 0.749
23040
11.158 28.945 26.792
0.900 0.536 0.887 0.861
2.154 2.860 2.420 1.965
-0.615% -0.633% -0.871% -0.846%
-3431 -1.925 -5.693 -5.011
0.080 0.093 O.I02 0.096
5.045 2.915 6.839 5.866
0.681 0.626 0.682 0.683
16.292 9.006 21.111 19.172
0.850 0.493 0.844 0.815
2.169 2.795 2.315 2.378
-0.472% -1.194% -0.330% -0.976%
-0.975 -3.744 -0.853 -3.352
0.079 0.087 O.I03 0.096
4.941 3.008 6.952 5.816
0.679 0.634 0.684 0.684
16.011
I0.078 21.286 19.115
-0.104 0.369 -0.468 0.119
-0.318 4.914 -1.521 0.552
0.848 0.584 0.846 0.819
2.136 I 2.713 2.295 2.378
he e is e idence
o
pe sis ence. The op po olio (PO RTF I)
emains he po olio wi h he highes a e age mon hly excess
e u n. PORTF2 and PORTF3 change posi ions bu s ill e ain
posi i e excess e u ns. Mos
o
he pe sis ence can
be
ex-
plained
by
common- ac o sensi i i ies.
Pe o mance
on
pas -winne uni us s
(1
yea lag)
To
u he in es iga e he pe sis ence
o
pas -winne s, he
ollowing me hod
is
used - o he en-yea pe iods (bo h o
he All Uni T us s and Gene al Equi y Uni T us s), h ee
equally weigh ed po olios ha e been o med
in
each yea
based on he p e ious yea 's yea ly excess e u ns. The op
pe o me s a e included in po olio I (PORTFI), he a e age
pe o me s
in
po olio 2 (PORTF2) and he wo s pe onne s
in
po olio 3 (PORTF3).
The po olios emain unchanged o he en i e pe iod and
he a e age mon hly excess e u ns a e calcula ed o each
po olio o he o ma ion yea and
in
each
o
he nex i e
yea s a e o ma ion. Figu es 1 and 2 show he pos - o ma-
ion e u ns on he Gene al Equi y Uni T us po olios so ed
on lagged one-yea e u ns and he pos - onna ion e u ns on
126
S
.A
.J
.Bus.Manage.2000,3
l(l)
Table
5
Po olios
o
All
Uni
T us s
o med
on
lagged
one-yea e u ns
FIVE-YEAR
PERIOD
TEN-YEAR PERIOD
Po olio
PORTFI
PORTF2
(High)
(Med)
Mean
mon hly
excess
e u n
-0.913%
0.007%
S d
de ia ion
3.857% 3.373%
Alpha
-1.623% -0.821%
-S a
-4.401
-5.241
CAPM
ASHARE
0.603 0.703
-S a
7.558
20.737
Adj
R-sq
0.488
0.879
OW-S a
1.626 1.916
Alpha
-1.426% -0.707%
-S a
-3.932
-4.659
A
GOLD
0.154 0.064
2-Fac o -S a
4.810
4.805
Model
INDUST
0.423
0.686
-S a
5.010
19.416
Adj
R-sq
0.496 0.885
OW-S a
1.668
2.184
Alpha
-0.340% -0.624%
-S a
-1.032
-1.554
A
GOLD
0.111
0.065
-S a
4.325 4.758
J-Fac o
IN
DUST
0.533
0.689
Model
I-S a
7.880
18.249
STDEV
-0.285
-0.057
I-S a
-6.279
-0.223
Adj
R-sq
0.699
0.883
OW-S a
1.859
2.188
he
All
Uni
T us
po olios so ed
on
lagged
one-yea
e u ns
espec i ely.
F om
bo h
igu es
i
is
clea ha
he
ela i e highe
e u ns
o
he
op
po olios
a e
sho -li ed.
I
can
also
be
seen
ha
u, 0.80%
E
~
0.80%
ig
0.40%
§Cl)
0.20%
~
0.00%
; -0.20%
C)
!!!
-0.40%
g?
<(
-0.60%
A
1/.···~
....
~
,'/
-
....
_
,,,
.
~~
-
...
,
z
~
Cl) Cl)
0
~
~
j::
i >
+ >
e
"'
~
+
I ---PORTF1
-PORTF2
--
/'
'"'.:.:-
•
~
~
'~
Cl) Cl)
~
I
T
• • • • •
·PORTF3
I
Figu e I
Pos - o ma ion
e u ns
on
he
Gene al
Equi y
Uni
T us
po olios
so ed
on
lagged
one-yea
e u ns
PORTF3
PORTFI
PORTF2
PORTF3
(Low) (High) (Med) (Low)
0.246%
-0.330% -0.190% -0.135%
3.676% 4.405% 3.706% 4.085%
-0.614% -1.206% -1.030% -0.984%
-2.796 -4.808 -7.907 -4.725
0.731
0.746 0.716 0.724
15.372
14.758
27.264
17
247
0.800
0.670 0.874 0
735
1.360
2.163 2.451
1.475
-0.313% -1.137% -1.056% -0.760%
-1.355
-4.295 -6.254 -3.666
0.203
0.169 0.093 0.238
9.966
6.554
5.681
11.792
0.438
0.590 0.637 0.452
8.145
10.544
17.857
10.329
0.776
0.641
0.798 0.744
1.780
2.208
2.404
1.688
-0.587% -1.520% -0.201% -0.462%
-1.379 -4.753
-0.564 -1.124
0.200
0.171
0.095 0.240
9.598
6.733
5.952
11.799
0.438
0.588 0.666 0.453
8.123
10.667 18.338
10.326
0.101
0.170 -0.567 -0.116
0.769
2.067 -2.697 -0.840
0.774
0.652 0.806
0.743
1.824
2.145
2.354
1.660
he
one-yea pe o mance pe sis ence
is
mos ly
elimina ed
a ·
e
one
o
wo
yea s.
Fo bo h he Gene al
Equi y
Uni
T us s
and
he
All
Uni
T us s a end
o
pe sis en
unde -pe o m-
ance
o
he
wo s po olio (PORT3)
is
no able. I
appea s
ha
0.80%
J)
E 0.60%
i 0.40%
sCI):
0.20%
0.00%
>.
i;
-0.20%
c
~
-0.40%
-0.60%
g?
-0.80%
< -1.00%
-
---...------
.,,.--
...
..
,(
/'
·,
..
,,
/
' '
,,.
__/
'
': -!-L--"" .
/"'
..
'(
' '
I
+
I
+
I-
-
-PORTF1
--PORTF2
• • • • • ·PORTFD
Figu e 2 Pos - o ma ion e u ns
on
All
Uni
T us
po olios
so ed
on
lagged
one-yea e u ns
S.A .J.Bus.Manage.2000,31 (3)
e
2.00%
- ---,----,----,----,-----,
!
1~%+----c-~-
..
~.-
..
-._--+----+----+----.
~
100%+--_,.. >-..:
............
,--~
...
-+----+----+----.
= '
...
~·.
9
050%
-1----1--.>.,,,---,.--~---+----+------<
G)
'
..
~
000%
~··..:.·..::·.
I
-050%
.1----+----+---- >-..~~~,+.-
..
-~
Ill .100%
.l----l----+----+---__::1'=:,~--l
e
-1.50%
-1--------------'
.........
---l
<(
·2.00%
.L---.L.---'----'----'------'
z
a:: a:: a:: a::
Q < < <
;li
I-
w w w
<
>- >-
>- >-
N 7
...
~
+ + +
a::
0
u.
- - -
PORTF1
--PORTF2
• · · • • PORTFJ
Figu e J Pos - o ma ion e u ns on he Gene al Equi y Uni T us
po olios
so ed on lagged i e-yea e u ns
he
a e age
po olio (PORTF2)
in
he
case
o
Gene al
Equi y
Uni
T us s
gene a es
he
bes a e age mon hly excess
e u ns
in
mos
pos - o ma ion yea s.
Pe sis ence
in i e-yea e u n-so ed uni us po -
olios
To
de e mine
whe he e idence
can
be
ound
o
longe
e m
2.50%
"'
E
2.00%
~
150%
"'
1.00%
~
050%
CD
0.00%
>,
:j;
-0.50%
~
·100%
-1.50%
-2.00%
1
-2.50%
-3.00%
!}...
;
...
127
,...._
·:~
-~
·-~'- -
'" .
_-,,<"
---...:
'.'
;.
'
~
~
I
+ + +
Figu e 4 Pos - o ma ion e u ns on All Uni T us po olios so ed
on lagged i e-yea e u ns
pe sis ence
in
pe o mance,
po olios o
All
Uni
T us s
and
Gene al
Equi y
Uni
T us s
a e
o med
on
lagged
i e-yea
yea ly
e u ns.
This
is
done
o
he
en-yea da a samples
only.
Once
again
he
me hodology
o
Hend icks
e
al.
(1993)
is
used.
On
he
i s
o
Janua y
o
each
yea ,
h ee equally
Table
6 Po olios
o
Gene al Equi y Uni T us s and All Uni T us s o med
on
lagged i e-yea
e u ns o e a en-yea pe iod
GENERAL EQUITY UNIT TRUSTS ALL UNIT TRUSTS
Po olio PORTFI PORTF2 PORTF3 PORTFI PORTF2 PORTF3
(High) (Med) (Low) (High) (Med) (Low)
Mean mon hly excess e u n 0.032% 0.185% -0.011% 0.155% 0.199% -0.766%
S d de ia ion 3.510% 3.425% 3.609% 3.531~0 3.525% 4.265%
Alpha -0.835% -0.661% -0.878% -0.722% -0.672% -1.661%
I-S a -5.398 -4.369 -4.584 -4.853 -4.372 -4.870
CAPM
A SHARE 0.737 0.718 0.736 0.745 0.740 0.762
-S a 21.990 21.946 17.762 23.135 22.238 10.309
Adj R-sq 0.891 0.891 0.842 0.901 0.893 0.641
DW-S a 2.308 2.247 2.282 2.266 1.839 · 1.844
Alpha -0.683% -0.524% -0.732% -0.545% -0.435% -1.362%
I-S a -3.807 -3.118 -3.389 -2.774 -1.926 -5.172
AGOLD
0.091 0.077
O.Q75
0.099 0.136 0.258
2-Fac o
-S a 5.731 5.171 3.957 5.718 6.839 11.081
Model
INDUST 0.670 0.674 0.686 0.650 0.558 0.441
I-S a 16.036 17.195 13.642 14.188 10.609 7.183
Adj R-sq 0.851 0.863 0.796 0.823 0.767 0.783
DW-S a 2.361 2.337 2.217 2.237 1.949 1.745
Alpha -0.632% -0.530% -0.578% -0.466% -1.261% -0.675%
I-S a -1.679 -1.523 -1.325 -0.986 -2.598 -1.455
A
GOLD
0.090 0.077 0.077 0.099 0.134 0.266
-S a 5.613 5.115 3.944 5.656 6.903 11.419
J.Fac o
INDUST 0.670 0.674 0.687 0.651 0.560 0.457
Model
-S a 15.898 16.466 13.547 13.938 10.898 7.500
STDEV -0.049 0.005 -0.159 -0.048 0.416 -0.235
-~ a -0.153 0.019 -0.408 -0.185 1.912 -1.782
Adj R-sq 0.849 0.860 0.793 0.820 0.777 0.791
DW-S a 2.356 2.338 2.166 2.236 2.021 1.705