Unit trusts and portfolio selection on the Johannesburg Stock Exchange

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 S anda d-Nu zungsbedingungen: Die Dokumen e au EconS o dü en zu eigenen wissenscha lichen Zwecken und zum P i a geb auch gespeiche und kopie we den. Sie dü en die Dokumen e nich ü ö en liche ode komme zielle Zwecke e iel äl igen, ö en lich auss ellen, ö en lich zugänglich machen, e eiben ode ande wei ig nu zen. So e n die Ve asse die Dokumen e un e Open-Con en -Lizenzen (insbesonde e CC-Lizenzen) zu Ve ügung ges ell haben soll en, gel en abweichend on diesen Nu zungsbedingungen die in de do genann en Lizenz gewäh en Nu zungs ech e. Te ms o use: Documen s in EconS o may be sa ed and copied o you pe sonal and schola ly pu poses. You a e no o copy documen s o public o comme cial pu poses, o exhibi he documen s publicly, o make hem publicly a ailable on he in e ne , o o dis ibu e o o he wise use he documen s in public. I he documen s ha e been made a ailable unde an Open Con en Licence (especially C ea i e Commons Licences), you may exe cise u he usage igh s as speci ied in he indica ed licence. h ps://c ea i ecommons.o g/licenses/by/4.0/ 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.