Persistence in the performance of South African unit trusts

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 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/ 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