Ca e , K. J.; A leck-G a es, J. F.; Money, A. H.
A icle
Uni us s and po olio selec ion on he Johannesbu g
S ock Exchange
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: Ca e , K. J.; A leck-G a es, J. F.; Money, A. H. (1982) : Uni us s and po olio
selec ion on he Johannesbu g S ock Exchange, 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. 13, Iss. 4,
pp. 169-175,
h ps://doi.o g/10.4102/sajbm. 13i4.1194
This Ve sion is a ailable a :
h ps://hdl.handle.ne /10419/217812
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I_
Uni
us s
and po olio
selec ion
on
he
Johannesbu g
S ock
Exchange
KJ.
Ca e
Allan
G ay
In es men Counsel, Cape Town
J.F.
A leck-G a es
Depa men
o
Ma hema ical S a is ics, Uni e si y o Cape Town
A.H.
Money
G adua e
School
o
Business, Uni e si y o Cape Town
The
applica ion o he s anda d echniques
o
po olio
selec ion
on
he
34
sec o s comp ising he JSE All Sha e index is unde aken o
he
h ee equal non-o e lapping i e-yea pe iods be ween Feb ua y
1965
and
Janua y
1980.
E icien
po olios
in each pe iod which ca y
he
same
isk as he ma ke index a e seen o ou pe o m he ma ke
subs an iaily. Po olios chosen a andom o span he e icien
on ie
in
each pe iod e eal he consis en ine iciency o
10
sec o s
o e
he 15-yea pe iod. Th ee
o
hese sec o s, namely Mining
Holding, Mining Houses and Indus ial Holding a e shown o be
a ou ed
in
he Associa ion
o
Uni T us s
po olio
ela i e
o
hese
sec o s' p opo ion
o
he ma ke . On he p esump ion ha uni us
manage s
a emp
o
ac
e icien ly, holding hese sec o s is only
jus i ied i he measu e
o
isk used in he
po olio
selec ion
algo i hm, namely s anda d de ia ion
o
expec ed e u n, is less
app op ia e han o he measu es
o
isk such as ea nings ola ili y. I
s anda d de ia ion o expec ed e u n is a mo e app op ia e measu e
o
isk
in
he selec ion
o
e icien
po olios,
i
mus be concluded
ha he la ge sophis ica ed in es o s managing he uni us s ac
ine icien ly.
S.
A .
J.
Bus. Mgm . 1982, 13:
169-175
S andaa d egnieke an po e eulje-seleksie
ui
die 34 sek o e waa ui
die
Johannesbu gse E ek ebeu s bes aan, is op die d ie nie-
oo een allende y -jaa pe iodes ussen Feb ua ie 1965
en
Janua ie
1980
oegepas. Daa is ge ind da doel e ende po e euljes -wa
diesel de isiko as die ma kindeks d a -in elke ydpe k baie be e as
die ma k p es ee . Po e euljes is willekeu ig gekies om die g ense an
doel e endheid
('e icien
on ie ') e dek
en
ydens elke ydpe k he
die deu lopende ondoel e endheid an
10
sek o e oo die 15-jaa
pe iode aan die lig gekom. Daa is bewys da d ie an hie die sek o e,
naamlik mynbehee , mynhuise en nywe heidsbehee , deu die
po e eulje
an
die Ve eniging an E ek e us s beguns ig wo d in
e houding
o
hie die sek o e se aandeel an die ma k. lndien daa
an
die s andpun ui gegaan wo d da die bes uu de s an die
e ek e us s daa na s ee om doel e end e unksionee , kan die
hou
an
hie die sek o e in po e euljes alleenlik ge eg e dig wo d as
die isiko ak o be okke by die
algo i me
an po e eulje-seleksie,
naamlik s andaa da wyking an e wag e opb engs, minde oepaslik
as
ande isiko ak o e, soos e diens e-onbes endigheid, is. lndien
s andaa da wyking an e wag e opb engs 'n geskik e isikomaa s a
by
die seleksie an doel e ende po e euljes is, moe daa a gelei
wo d
da die g oo geso is ikee de belegge s, deu wie die
e ek e us s behee wo d, ondoel e end unksionee .
S.-A . Tydsk .
Bed y sl.
1982, 13:
169-175
K.J.
Ca e ,• J.F. A l k-G a es
ud
A.H.
Money
Allan
G ay
In es men
Counsel, Sou he n Li e Building,
IOI
S
Geo ge's
S ee ,
Cape
Town
8001.
Republic
o
Sou h
A ica
•To
whom
co espondence
should
be
add essed
Recei ed
June
1982;
accep ed
Sep embe
1982
Following an amendmen
o
he Uni T us Con ol Ac ,
he i s Sou h A ican uni us was launched in June
1965
wi h asse s o alling
R600
000.
A p esen he e a e
12
uni
us s in exis ence, which a e con olled
by
six
managemen
companies. These managemen companies a e each
pan
o
one
o
he coun y's majo inancial ins i u ions. A
Decembe 31, 1980, he o al equi y asse s unde
managemen by he mo emen o alled R566,3 million,
accoun ing o
1,490/o
o
he ma ke capi aliza ion
o
he
JSE All Sha e index a he same da e.
The Associa ion
o
Uni T us s was es ablished in
1967
o ep esen he join in e es s
o
i s membe us s and hei
uni holde s in dealing wi h he au ho i ies, o p omo e he
common in e es s
o
he indus y, and o main ain
communica ion wi h he media. 1 Fo he pu poses
o
his
pape , he Associa ion
o
Uni T us s po olio
<n.
which
is
a combined pon olio
o
he
12
unde lying us s,
is
signi ican in ha i
is
he la ges p o essionally managed
po olio, he cons i uen s
o
which a e public knowledge.
In his pape , he s uc u e
o
his po olio a Decembe
31, 1980
is
analysed and discussed wi h espec
o
he
selec ion
o
e icien po olios on he Johannesbu g S ock
Exchange (JSE) o e he pas
15
yea s.
The JSE
Ac ua ies
index
and
he
Associa ion
o
Uni
T us s
po olio
Compa a i ely ecen ly, a comp ehensi e se
o
sha e p ice
indices has been p oduced o he JSE,
2 p o iding a
mon hly p ice his o y
o
he JSE om Janua y
1960
o
Sep embe
1978
and daily he ea e . Since hese indices a e
weigh ed
by
ma ked capi aliza ion, a use ul guide o a
po olio's s uc u e
is
p o ided by compa ing he
p opo ion
o
he po olio in es ed in each sec o wi h he
p opo ion ha sec o ep esen s
o
he JSE All Sha e index.
Clea ly a highe ela i e weigh ing
o
a sec o
in
he po olio
o he ma ke indica es a a ou able expec ed ou come
in
u u e pe o mance
o
ha sec o ela i e o he ma ke .
while a ela i e exposu e
o
less
han uni y indica es expec ed
u u e unde:-pe o mance ela i e o he ma ke . A ela i,e
exposu e
o
uni y indica es a neu al pe o man1:e
expec a ion ela i e o he ma ke . Table I shows he T
po olio ep esen ed in his way ela i e o he JSE All
Sha 1:
index a Decembe 31, 1980.
170
Table
1 Associa ion o Uni T us s Po olio ela i e
o he JSE All Sha e indexa
Rela i e
p opo ion
P opo ion P opo ion Uni T us s
o
JSE
o
Uni o JSE
All
Sec o
All
Sha e T us s Sha e
1.
Gold -Rand 0,0242 0,0047 0,1942
2.
Gold -E ande 0,0142 0,0040 0,2817
3.
Gold -Kle ksdo p
0,0729.
0,0288 0,3951
4.
Gold -OFS 0,076S... 0,0144 0,1882
S.
Gold -W. Wi s 0,1424 0;0117 0,0822
6.
Coal 0,0365 0,0605 l,6575
7.
Diamonds 0,0696 0,0818 1,1753
8.
Pla inum
0,0251
0,0183 0,7291
9.
Coppe , Tin, o he s 0,0209 0,0070 0,3349
10.
Mining Holding 0,0600 0,0389 0,6483
I I. Mining House 0,1350 0,1537 l,1385
12.
In . T us s 0,0072. 0,0070 · 0,9722
13.
Insu ance 0,0057 0,0079 1,3860
14.
P ope y 0,0054 · 0,0004 ·
.0.0741
IS. Banks 0,0305 0;0695 . 2,2787
16.
Ind. Holding 0,0639 0,1452 . 2,2723
17.
Be e ages
6,0lOQ,
0,0609 3,0450
18.
Building ·
0,0122"
0,0143
·,:
1,1721
19.
Chemicals
0,0611
o,04S9. 0,7512.
20. Clo hing 0,0054
,.
0,0026 .
o.48..is
21.
Elec ical 0,0071
...
·.
0,0083
1,'1691
22.
Enginee ing 0,0154 0,0171 1,1104
23.
Fishing 0,0010
24.
Food 0,0143
·•
0,0181 1,2797
25. Fu ni u e
o,cxnL
'·
0,0243 . 3,ISS8
26.
Mo o s 0,0048· 0,0013 0,2708
27. Pape , Packaging 0,0146 0,0192 · 1,315)
28.
Pha maceu ical 0,0015 ,0,0021 l,4000
29.
P in ing 0,0009
30.
S eel 0,0063 0,0072 I,
1429
31.
S o es 0,0169. 0,0861 S,0947
32.
Suga 0,0073 0,0006 0,0822
33.
Tobacco 0,0078 0,0361 4,6282
34.
T anspo 0,0057 0,0019 0,3333
1,0000 1,0000
"The JSE
All
Sha e index has been exp essed excluding P ope y T us s
which only appea ed om Janua y
1976:
A Decembe 31, 1980 i was
0,32%
o
he JSE All Sha e index.
I can
be
seen ha wo sec o s, namely Fishing and P in-
ing, we e no p esen in he po olio and he e o e ca ied
he lowes ela i e exposu e a ze o. The highes ela i e ex-
posu e was S o es a 5,09, ollowed by Tobacco, Be e ages
and Fu ni u e, he o me o e ou imes, and he la e
wo mo e han h ee imes he ma ke p opo ion o hese
sec o s. The gold sec o s all ca ied a low ela i e weigh ing.
The app op ia eness
o he
weigh ings e ealed in Table l
will
be
discussed la e in his pape .
Selec ion
o
e clan
po olios
In
1952
Ma kowi z published a now amous pape
on
po -
olio selec ion,
3 om which a whole heo y
o
po olio
S.-A .
Tydsk .
Bed y sl.
1982,
l3(
4)
selec ion has been de i ed. The basic no ion
is
ha
only
wo
ac o s need be conside ed in choosing a po olio,
namely
he e u n
an
in es o can expec o ecei e om
holding
he po olio and he unce ain y associa ed wi h
his
e u n.
Fo he pu poses
o
his pape he gene ally
accep ed
measu es
o
hese a iables ha e been used and
hey
a e,
espec i ely, he weigh ed a e age mon hly e u n o
he
componen s
o
he po olio, and he s anda d
de ia ion
o
he mon hly e u n
on
he po olio (bo h exp essed
in
pe ,
cen pe mon h). Any po olio may hus be ep esen ed
by
· a poin in a isk/ e u n plane. In ac all easible
(i.e.
a -
ainable) po olios
will
ill some egion in his plane.
o
pa -
Jcula , a se
o
po olios, known as he e icien
se ,
can
-be. ound which will domina e all o he po olios,
because
o hese po olios i
is
no possible o ob ain ei he a
g ea e
..
expec ed e u n wi hou incu ing g ea e isk o
.ob ain
s nalle isk wi hou dec easing expec ed e u ns ..
4
The e o e
in es o s will only wish
o
hold po olios belong hg
o
he
· e icien se
and
each in es o
is
le o .choose he
single
. .
oq_e
po olio (i.e. ade
o
he le els
o
isk
and,
e u n)
o
himsel .
S anda d echniques
a e
a ailable o choosing he
e i-
. cien se ,5 and his has been done
on
he JSE.6•7 Fo
his
paJ)e , h ee equal, non-o e lapping ime pe iods
o
mon hly in e als we e chosen o s udy, nam~ly: ·
Feb ua y
1965
o
Janua y
197Q
-.
Pe iod 1
·
· ~ ua y
1970 o
Janua y
1975 -Pe iod 2 ·
Feb ua y
1975
o
Janua y
1980-'- Pe iod 3.
I
mus be s essed
ha
hese h ee ime pe iods
we e
no
chosen because
o
any ma ke
o
economic conside "1ion.
They we e chosen me ely
o
di ide he da a se in o
h ee
equal non-o e lapping ime pe iods.
The
34
sec o s
o
he JSE Ac ua ies index (see Table
1)
ep esen ed he uni e se
o
'secu i ies' o po olio onna-
ion in each pe iod.
The
e icien se chosen in each
pe iod
is
pic o ially displayed in Figu es
1,
2 and 3 o Pe iods
1,
2 and 3 espec i ely. Also ma ked as poin s in he isk/ e u n
plane a e he JSE All Sha e index (M), he JSE
All
Mining
index (A), he JSE Mining Financial index (F), he JSE
In-
dus ial and Financial index (I) and he Associa ion
o
Uni
T us s po olio (T).
I can be seen ha he ange
and
slope
o
he e icien
se
o
on ie
is
ma kedly di e en in each pe iod. Fu he ,
each
o
he indices plo ed
and
he T po olio ha e
been
consis en ly ine icien o e ime. The ine iciency
o
M
pa -
icula ly, sugges s
ha
e icien po olios
will
con ain se ·
o weigh ings which di e g ea ly om he weigh ings
ilP"
.
plying in he M index. This ea u e
is
examined in he
~x
·
sec ion.
I mus be men ioned
ha
his s udy
is
an
ex
pos s udy
whe eas an in es o wishing o u ilize he Ma kowi z
model
mus use es ima es
o
he expec ed e u n and isk o
each
o
he secu i ies in he coming pe iod (i.e.
ex
an e).
Ne. e ·
heless,
ex
pos s udies a e use ul in
ha
hey demons a e
he in es men oppo uni ies
ha
ac ually we e a ailable
in
he pe iod.
An
analysis
o
such esul s coold help
in es ~
o
decide why hei ex an e po olios did
no
p oduce
· he
desi ed esul s. In addi ion, in es o s whose po olios
lie
a om he e icien on ie should ealize ha his
is
as
a esul
o
poo ex an e o ecas s. Whe he hey could
ha e
s.
A . J. Bus. Mgm .
1982,
13(4)
4,8
4,6
4,4
4,2
4,0
3,8
3,6
3,4
3,2
E 3,0
c
0
E 2,8
i;;
2,6
Q.
::.
2,4
C 2,2
:i
i 2,0
a:
"O
1,8
~
u
" 1,6
Q.
"
w 1,4
1,2
1,0
0,8
0,6
0.4
0,2
0,0
-0,20
6
Pe iod 1 - 02/65 -
01170
M = JSE All Sha e Index
F = JSE
Mining
Financial
Index
A = JSE All Minong Index
I = JSE Indus ial and Financial Index
T =
Associa ion
o Uni T us s Po olio
1 2 3 4 5 6 7 8 9 10
11
12 13 14 15 16 17 18
S anda d De ia ion
(%
pe mon h)
Flp e 1 E icien se chosen o Pe iod I
5,2
5,0
4.8
4,6
4.4
4.2
4,0
3.8
3,6
3,4
E 3.2
c 3,0
0
E
cii
2,8
Q. 2.6
{_
C 2.4
:i 2,2
i
a:
2.0
"O
Ill
u 1,8
Ill
Q.
1.6
"
w 1.4
1,2
1,0
0.8
0.6
0.4
0,2
0,0
-0.2
0
Pe iod 2 - 02/70 -01/75
M = JSE All Sha e Index
F = JSE
Mining
Financial Index
A = JSE All
Mining
Index
I = JSE
Indus ial
and
Financial
Index
T =
Associa ion
o
Uni
T us s
Po olio
7
123456
8 9 10
11
12
13
14 15 16 17 18
S anda d De ia ion
(%
pe mon h)
Figu e 2 E icien se chosen o Pe iod 2
E
c
0
E
iii
Q.
$.
C
:i
i
a:
"O
"
u
Ill
Q.
)(
w
5.0
4.8
4.6
4,4
4,2
4.0
3,8
3,6
3,4
3.2
3,0
2.8
2,6
2.4
2,2
2.0
1,8
1,6
1.4
1,2
1.0
0.8
0,6
0,4
0,2
0.0
5
e
,.
M
Pe iod 3 -
02175
-
01180
M =
JSE
All Sha e Index
F = JSE
Minon::i
Financial Index
A = JSE All Mining Index
171
I =
JSE
Indus ial and
F1nanc1al
Index
T = Associa ion o Uni T us s Po olio
-0.20
1 2 3 4 5 6 7 8 9 10
11
12
13 14 15 16 17 18
S anda d De ia ion
(%
pe mon h)
Figu e 3 E icien se chosen o Pe iod 3
done be e o no ex an e,
is
a ques ion add essed by he
e icien ma ke hypo hesis and beyond he scope
o
his
pape .
Composi ion
o
e icien
po olios
On any gi en e icien on ie he e a e an in ini e numbe
o
di e en po olios. Fo he pu pose
o
s udying he com-
posi ion
o
e icien po olios se e al po olios we e I
selec ed om each e icien on ie and a e numbe ed in
each
o
Figu es
1,
2 and 3. They we e chosen a andom
o
emb ace he ull isk/ e u n ange
o
he e icien on-
ie , wi h he excep ion ha he e icien po olio which ca -
ied he same isk (i.e. s anda d de ia ion
o
e u n) as he
M index was a equi ed selec ion. Tables 2, 3 and 4 show
he composi ion
o
hese e icien po olios by sec o
weigh ing o Pe iods
1,
2 and 3 espec i ely.
Se e al poin s eme ge om a s udy
o
hese ables:
A e y high isk, limi ed di e si ica ion occu s because
only a limi ed numbe
o
sec o s in each pe iod has a
su icien ly high expec ed e u n o compensa e he in-
es o o he high isk.
As he isk dec eases, di e si ica ion inc eases. In ac
he inc eased di e si ica ion se es o educe isk. Also
lowe - isk po olios app oach he a ea whe e M, by
de ini ion ully di e si ied, plo s.
Some sec o s changed hei isk cha ac e o e he
pe iods s udied.
Fo
example, he gold sec o s end
o
occu in lowe - isk po olios in Pe iod 1
and
highe -
isk po olios in Pe iod 2 while ha dly
a
all in Pe iod!
3.
Undoub edly he beha iou
o
he gold p ice in hese
172
Table 2 E icien po olios in Pe iod 1
Po olio no. 2
S anda d de ia ion 10,000
('lo pe mon h) 13,000
Expec ed e u n 3,193 3,028
('lo pe mon h)
I. Gold -Rand
2.
Gold -E ande
3.
Gold -Kle ksdo p
4. Gold -OFS
5.
Gold -
W.
Wi s
6. Coal
7. Diamonds
8.
Pla inum 0,0311 0,3560
9. Coppe , Tin, o he s
10.
Mining Holding
11.
Mining Houses
12.
In . T us s
13.
Insu ance 0,9689 0,6440
14.
P ope y
15.
Banks
16.
Ind. Holding
17.
Be e ages
18.
Building
19.
Chemicals
20.
Clo hing
21.
Elec ical
22.
Enginee ing
23.
Fishing
24.
Food
25.
Fu ni u e
26. Mo o s
27.
Pape . Packaging
28.
Pha maceu ical
29.
P in ing
30. S eel
31. S o es
32. Suga
33. Tobacco
34. T anspo
To al 1,0000 1,0000
"Pon olio wi h same isk as he ma ke
pe iods p o oundly a ec ed his si ua ion. O he sec-
o s like P in ing, Elec ical
and
Enginee ing only ap-
pea in lowe - isk po olios h oughou .
In each pe iod (Pla inum in Pe iod 1, Gold-Wes Wi s
in
Pe iod 2 and
Coal
and
Clo hing in Pe iod
3)
a sec-
o
appea ed in all e icien po olios conside ed. Since
each sec o is only a poin i sel in he isk/ e u n
plane, his can only occu
i
i displays no only a high
e u n bu also a low co a iance wi h o he cu en ly
e icien sec o s.
In
his way i will be selec ed o
he
high ma ginal e u n added o low ma ginal isk
bo ne.
I can
be
seen
ha
sec o s, once e icien , end
o
pe -
sis
in
e icien po olios o e qui e a ange in
he
e -
S.-A . Tydsk . Bed y sl.
1982,
13(4)
3 4• 5 6
7,500 5,020 3,400 2,500
2,784 2,312
1,331
0,184
0,0081
0,0612
0,0427 0,1002
0,0690
0,0584 0,2010
0,1468 0,0811
0,5519 0,3065 0,1503 0,0678
0,0887 0,2531 0,1615 0,0361
0,3124 0,0197
0,0100
0,0681
0,0331 0,0490
0,3111 0,2491
0,0047
0,0395 0,0712
0,1576 0,0932
0,0470 0,1163 0,0291 0,0045
1,0000 1,0000 1,0000 1,0000
icien on ie . This sugges s
ha
in each pe iod he
sec o s
end
o
o m in o a hie a chy
o
e iciency
dominance implying
ha
qui e a numbe
o
sec o s a e
oo
ine icien
o
be
held
in
e icien po olios.
Ce ain sec o s
do
no
appea
in
any
o
he e icien
po olios in
any
pe iod. They a e Mining
Hold~ng,
Mining Houses,
P ope y,
Banks, Indus ial Holding,
Building, Fu ni u e, Mo o s, Pha maceu ical and
S o es.
I
can
be
concluded
ha
i has always been
possible
o
eplace hese sec o s in a po olio wi h a
combina ion
o
o he
sec o s which has been mo e e ·
icien . Toge he hese
10
sec o s ep esen 33,8:o
o
he
ma ke capi aliza ion
o
he
JSE
All Sha e mdex
(see Table
1)
and
i is su p ising
ha
such a la ge po -

S.
A .
J.
Bus. Mgm . 1982,
13(4)
173
Table 3 E icien po olios
in
Pe iod 2
Po olio no. 2
S anda d de ia ion
(OJo
pe mon h) 17,000 14,000
Expec ed e u n
(OJo
pe mon h) 5,190 4,406
I. Gold -Rand 0,8601 0,5268
2.
Gold -E ande 0,1215 0,1129
3.
Gold -Kle ksdo p
4.
Gold -OFS
5.
Gold -
W.
Wi s 0,0185 0,3603
6.
Coal
7.
Diamonds
8. Pla inum
9.
Coppe , Tin, o he s
10.
Mining Holding
11.
Mining Houses
12.
In . T us s
13.
Insu ance
14.
P ope y
15.
Banks
16.
Ind. Holding
17.
Be e ages
18.
Building
19.
Chemicals
20. Clo hing
21. Elec ical
22. Enginee ing
23. Fishing
24. Food
25.
Fu ni u e
26. Mo o s
27. Pape , Packaging
28. Pha maceu ical
29. P in ing
30.
S eel
31. S o es
32. Suga
33. Tobacco
34. T anspo
To al 1,0000 1,0000
"Po olio wi h same isk as he ma ke
ion
o
he ma e index has been so consis en ly
ine icien .
A gumen s may possibly be lodged agains his analysis
because
o
i s
ex
pos na u e, bu he ac emains ha
o e he pas
15
yea s
10
o
he
34
sec o s examined
did no appea in any ex pos e icien po olio. While
i
is
possible ha om an ex an e poin
o
iew
some
o
hese sec o s may ha e appea ed e icien o in-
es o s, he ac emains ha ex pos hey we e ne e
e icien . This
is
ue o each
o
he h ee pe iods
ex-
amined and his should be he cause
o
some conce n
o in es o s who we e hea ily in es ed
in
hese sec o s.
The only easonable conclusion one can d aw
is
ha
hese sec o s appea
o
ha e been ine icien o e he
3
4•
5 6 7
11,000
7,861
6,000 5,000 4,500
3,500 2,392 1,606 1,064 0,637
0,2520 0,0497
0,1005 0,0658 0,0178
0,0363
0,5320 0,5329 0,4614 0,3398 0,1914
0,0601
0,1305 0,1839 0,2187
0,0585 0,0554 0,0536
0,0686
0,0070
0,2091
0,3596 0,4156
0,0520 0,0867 0,0484 0,0157
0,0635 0,1393 0,0702 0,0061
0,0261
0,0072 0,0414 0,0433
1,0000 1,0000 1,0000 1,0000 1,0000
ime pe iod s udied.
The composi ion
o
he e icien po olios changes
ma kedly om pe iod o pe iod. Fo example,
in
Pe iod
2,
he po olio wi h he same isk
as
he ma ke
has holdings which, wi h he excep ion
o
Coal, do no
appea
in
he co esponding po olio
o
Pe iod
3.
Clea ly he easibili y
o
a la ge in es o pe o ming
such a la ge shi
in
his po olio
is
an impo an ques-
ion,
as
is
he holding
o
a massi e p opo ion
o
a po -
olio
in
one sec o (e.g. 96,48%
in
Coal
in
po olio
l
o
Pe iod
3).
Al hough beyond he scope
o
his
pape , hese issues and ha
o
he ine iciency
o
he
M index and i s implica ions o mode n po olio
heo y applied o he JSE, ha e been add essed
174 S.-A . Tydsk . Bed y sl.
1982,
13(4)
Table
4 E icien po olios in Pe iod 3
Po olio no.
S anda d de ia ion
('lo pe mon h) 8,000
Expec ed e u n
('lo pe mon h) 3,644
I . Gold -Rand
2.
Gold -E ande
3.
Gold -Kle ksdo p
4. Gold -OFS
5.
Gold -W. Wi s
6. Coal 0,9648
7.
Diamonds
8.
Pla inum
9. Coppe , Tin, o he s
10.
Mining Holding
11.
Mining Houses
12.
In . T us s
13.
Insu ance
14.
P ope y
15.
Banks
16.
Ind. Holding
17.
Be e ages
18.
Building
19.
Chemicals
20.
Clo hing 0,0346
21. Elec ical
22.
Enginee ing
23.
Fishing
24.
Food
25.
Fu ni u e
26.
Mo o s
27.
Pape , Packaging
28.
Pha maceu ical
29.
P in ing
30.
S eel 0,0006
31. S o es
32.
Suga
33. Tobacco
34.
T anspo
To al 1,0000
"Po olio wi h same isk
as
he ma ke
elsewhe e. 7
Pe o mance
o
e icien
po olios
To
illus a e he pe o mance
o
e icien po olios ela i e
o
he M index, he e icien po olios in each pe iod ca -
ying he same isk (i.e. s anda d de ia ion
o
e u n) as he
M index we e examined. These po olios a e designa ed in
Tables
2,
3 and
4.
In Table 5 he ela i e pe o mance igu es
a e shown.
I can be seen ha subs an ial supe io pe o mance
is
achie ed by e icien po olios he eby demons a ing ha
on
he JSE i has been possible
o
ou pe o m he ma ke
consis en ly wi hou bea ing addi ional isk o ha bo ne
by in es ing in he ma ke index i sel .
2• 3 4 5
6,292 5,000 4,400 4,000
3,235 2,765 2,379 1,802
0,0044
0,7228 0,4523 0,2905 0,1442
0,0020
0,0376
0,0944 0,1031 0,0406
0,2726 0,3892 0,3283 0,1608
0,0867 0,1286
0,2338
0,0479
0,0558
0,0046
0,0134 0,0712 0,0759
0,0138
0,0325 0,0826 0,1104
1,0000 1,0000 1,0000 1,0000
E iciency
o
he
Associa ion
o
Uni
T us
po olio
(T)
I has al eady been seen in Table l ha he uni us
manage s ha e collec i ely adop ed a po olio which has
qui e di e en sec o weigh ings om hose in he ma ke
index. Fu he mo e, i has been es ablished ha e icien
po olios also display his phenomenon wi h se e al
sec-
o s ne e appea ing in e icien po olios. One
o
he
cha ac e is ics
o
he T po olio is i s low exposu e o he
gold sec o s, ep esen ing only
6,360/o
o
T
bu
33,00/o
o
M.
I has been shown8 ha he gold sec o s
on
he JSE ha e
p oduced simila mean mon hly e u ns o a Uni ed S a es
(US) and Sou h A ican (SA) in es o o e he pas
15
yea s.
Howe e , he US in es o has bo ne e y li le undi e -
si iable isk in achie ing his e u n, which has been almos
S.
A . J.
Bus.
Mgm . 1982, 13(4)
Table
5 Pe o mance o e icien po olios a same
isk
as
he ma ke
Pe iod I Pe iod 2 Pe iod 3
S anda d de ia ion
o
e u n
(% pe mon h) 5,020
7,861
6,292
Expec ed
e u n on po olio
(0/o
pe mon h) 2,312 2,392 3,235
Expec ed
e u n on he ma ke
(0/o
pe mon h) 0,804 0,749 1,482
Numbe s
o
imes po olio
ou pe o med he ma ke 2,876 3,194 2,183
ou imes he S anda d
and
Poo s
500 index mean mon h-
ly
e u n, because he gold sec o s' e u ns ha e i ually
no
co a iance wi h
he
e u n
on
his index.
To
a SA in-
es o , who
is
limi ed
o
he
JSE
o his equi y in es men s,
he co a iance
o
he gold sec o e u ns wi h he M index
e u ns
is
high, which implies
ha
undi e si iable
o
ma ke
isk
is
also high. The e o e he gold sec o s as
an
asse g oup
ha e
mo e alue
o
a US in es o
han
a SA in es o and
should be p e e ed by he o me
and
no he la e . The
uni
us manage s end
o
ac in a manne consis en wi h
his hypo hesis.
I
was
shown
ha
10
sec o s ne e appea ed in any e i-
cien
po olios. These sec o s ep esen
53,60/o
o
he T po -
olio
compa ed wi h
33,80/o
o
he
M index o a ela i e
weigh ing
o
1,59.
A
Decembe 31, 1976, he ea lies
amalgama ed T po olio,
he
10
ine icien sec o s
ep esen ed
55,40/o
o
he T po olio compa ed wi h 33,2%
o
he M index o a ela i e weigh ing
o
1,67. This means
ha , al hough his o ically e y ine icien , hese sec o s ha e
been
and a e cu en ly a ou ed
by
uni us manage s
o
imp o e u u e pe o mances. E en
i
he a gumen
p esen ed abo e conce ning he gold sec o s is accep ed
and
hese sec o s a e ebased in
he
M index
a
Decembe 31,
1980
o e lec hei ela i e exposu e in T (i.e. 6,36%
o
M ins ead
o
33,00/o),
he
IO
ine icien sec o s become
47
,2%
o
he adjus ed M index
and
he ela i e exposu e
in
Tis
s ill g ea e
han
uni y
a
1,14. Th ee
o
he
IO
sec-
o s conce ned, namely Mining Holding, Mining Houses and
Indus ial Holding, accoun o
36,20/o
o
he adjus ed M
o 25,9%
o
he unadjus ed M. This ep esen s
76,60/o
o
he o al ma ke capi aliza ion
o
he 1 O ine icien sec o s.
I
is
wo h no ing ha companies comp ising hese h ee
sec-
o s end o ha e in es men s in quo ed companies om
o he sec o s
o
he JSE
and/
o
unquo ed companies d awn
om all pa s
o
he economy. The e o e i is unlikely ha
hese sec o s will ha e low co a iance wi h he ma ke and,
m~ e impo an ly om he po olio selec ion iewpoin ,
~ h
o he sec o s. Fu he mo e, i
is
unlikely ha companies
in es ed la gely in
he
M index
will
achie e e u ns
signi ican ly di e en om i . Hence i
is
heo e ically
175
unl_ikely
ha hese sec o s
will
be selec ed in e icien po -
olios, and his
is
e iden
in
p ac ice as
well
.
. Uni
~ us
manage s a e p esumed o a emp o ac e i-
cien ly m he cons uc ion
o
hei po olios. How
is
i ,
~he e ~ e, ha hey in es o such an ex en in appa en ly
me ic1en sec o s? The na u e
o
he h ee sec o s discuss-
ed abo e
is
such ha he ola ili y
o
ea nings pe o mance
is
likely o be lowe han ha
o
o he mo e specialized sec-
o s on he ma ke . Fo example, an indus ial holding com-
pany
is
likely o ha e i s ea nings sou ced om di e se pa s
o
he economy, which means ha
i
a pa icula economic
sec o su e s a down u n, he ad e se e ec
is
dilu ed by
he o he in es men s
o
he company. In o he wo ds, he
isk, as measu ed by ea nings ola ili y,
is
lowe o a di e -
si ied company han o an indi idual indus ial company
in a speci ic sec o .
I
an in es o
is
p epa ed o pay a
p emium o lowe isk ea nings he may buy sha es
in
such
a di e si ied company in p e e ence o a combina ion
o
i s
unde lying holdings, assuming hey a e a ailable o pu -
chase. The ac ha uni us manage s hold sha es
in
he
Mining Holding, Mining House and Indus ial Holding
sec-
o s and he ac ha hese ha e p o en o be ine icien
in e ms
o
he po olio selec ion algo i hm, p oduces an
in e es ing conund um. Ei he he s anda d de ia ion
o
e u n
is
a
less
co ec measu e
o
isk han ea nings ola ili y
and he e o e he po olio selec ion algo i hm which has
been used ex ensi ely
in
inance heo y
is
w ongly speci ied,
o
i
s anda d de ia ion
o
e u n
is
a mo e co ec measu e
o
isk, hen he uni us manage s in Sou h A ica a e
e oneously p epa ed o pay p emiums o a di e si ica ion
o
isk which hey can achie e hemsel es in he con ex
o
hei po olios a no cos .
I
he o me condi ion
is
ue, inance heo y, and in pa -
icula po olio selec ion as applied on he JSE,
will
ha e
o be e ised.
I
he la e condi ion pe ains, i implies ha
la ge and sophis ica ed in es o s on he JSE a e ope a ional-
ly
ine icien .
Re e ences
I. The Associa ion
o
Uni T us s. Annual Re iew
1980.
Published
by
Associa ion
o
Uni T us s, Johannesbu g,
1981.
2.
The JSE Ac ua ies Index (3 d ed.). Published
by
he JSE Public
Rela ions Depa men , Johannesbu g, Ma ch
1982.
3.
Ma kowi z, H.M. Pon olio selec ion
J.
Finance,
1952,
7,
pp.77-91.
4.
Jensen, M.C.
Risk,
he p icing
o
capi al asse s and he e alua ion
o
in es men pon olios.
J.
Bus.,
1969,
42, pp.167-247.
5.
Sha pe, W.F. Po olio Theo y and Capi al Ma ke s. McG aw-
Hill, Inc.,
1970,
pp.45-
73.
6. A leck-G a es, J.F. Pon olio Selec ion on he Johannesbu g
S ock Exchange. Unpublished M.Sc Thesis, Cape Town,
1974.
7.
Ca e , K.J., A leck-G a es, J.F., Money, A.H. Ma kowi z
Pon-
olio Selec ion Applied o Sec o s on he Johannesbu g S ock Ex-
change. Technical Repon No. STM-7, Uni e si y
o
Cape Town,
1982.
8.
Cane , K.J., A leck-G a es, J.F., Money, A.H. A e Gold Sha es
Mo e A ac i e han Gold as a Di e si ica ion? Technical Repon
No. STM-8, Uni e si y
o
Cape Town,
1982.