Persistence in the performance of South African unit trusts

Von Wielligh, J. F.C.; Smit, E. V.D.M. Article Persistence in the performance of South African unit trusts South African Journal of Business Management Provided in Cooperation with: University of Stellenbosch Business School (USB), Bellville, South Africa Suggested Citation: Von Wielligh, J. F.C.; Smit, E. V.D.M. (2000) : Persistence in the performance of South African unit trusts, South African Journal of Business Management, ISSN 2078-5976, African Online Scientific Information Systems (AOSIS), Cape Town, Vol. 31, Iss. 3, pp. 120-129, https://doi.org/10.4102/sajbm.v31i3.742 This Version is available at: https://hdl.handle.net/10419/218230 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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Box 610, Bellville, 7535 South Africa Received May 2000 The persistence of performance of the General Equity Unit Trusts and All Unit Trusts that traded in South Africa during the period January 1988 to December 1997 and January 1993 to December 1997, is analysed using three models of performance measurement, namely the Capital Asset Pricing Model, a two-factor Arbitrage Pricing Theory model and a three-factor Arbitrage Pricing Theory (APf) model developed in this study. The Capital Asset Pricing Model does not explain the relative returns of the different portfolios. Both APf models account for almost all of the cross-sectional variation in expected returns. It is shown that there is evidence of both short-term and long-term persistence in performance of South African unit trusts. It appears that the worst performing unit trust portfolio tends to stay the worst performer. The portfolio of unit trusts with an average monthly return may eventually become the top performing portfolio, while the top performer over time tends to becomes an average performing portfolio. Introduction The aim of this study is to detennine whether evidence of persistence in perfonnance exists amongst South African unit trusts. From the literature review in the second section it is clear that the periods of analyses and the yardstick used to detennine perfonnance, have an influence on all conclusions. Four data sets are discussed in the third section which allow analyses over a five-year and a ten-year period as well as for both General Equity Unit Trusts and All Unit Trusts. The fourth section deals with the three models of perfonnance measurement which are employed in the analyses to ensure more than one yardstick. These are the Capital Asset Pricing Model (CAPM), a two-factor Arbitrage Pricing Theory (APT) model and a three-factor APT model. Short-tenn persistence of performance as well as long-term persistence of performance of unit trusts are studied in the fifth section. The perfonnance of past-winners is also examined. The study is concluded with a summary of the central findings. Literature review Over the years different researchers have derived different conclusions about the persistence of perfonnance of unit trusts and specifically South African unit trusts. Knight & Firer (1989) present evidence that over the period 1977 to 1986, trusts have performed either consistently well or consistently poorly. Smith & Chapman (1994), Biger & Page {1994) and Oldfield & Page (1997), amongst others, conclude that there is little evidence of market timing ability amongst portfolio managers of South African unit trusts. They could not find any evidence of skills in selecting and switching securities within each asset class. Gavin concurs: 'Fund managers were not able to consistently outperfonn the market, neither did any manager consistently perfonn worse than the market. There is very little "persistence" in performance amongst fund managers. In other words, if a fund manager perfonned well in one period it does not imply that he will perform well in the subsequent period' (1995: 104). On the other hand Theron ( 1996) and De Lange ( 1996) argue that there is some evidence of persistence of performance of unit trusts in South Africa. They advise that it is important to invest in one of the better performers, which in the long run can make a significant difference in returns. If invested in the top quartile of best performers, one will consistently obtain positive returns. However, according to the Unit Trust Handbook ( 1997) only one in five of the funds in the top quartile of a five-year league table are likely to remain in the top quartile over the next five years. Meyer (1997) examines the persistence of South African unit trusts using the Jensen measure together with the security market line and the All Share Index over four-year, two-year and one-year intervals. Meyer (1997) concludes that the results are comparable to those obtained in much bigger markets and that some persistence in performance of unit trusts in the South African environment does ex'ist. The repeat winner phenomenon exists over two-year periods for total returns and the repeat loser phenomenon is present over one-year, two-year and four-year time periods at a much higher frequency. Meyer concludes that: 'Persistence in performance seems to exist and it appears to be a guide to beat the pack in the long run. The longer the evaluation period, the better the results' (1997: II). Most research done on mutual funds in the USA point towards positive persistence in performance. Grinblatt & Titman (1992), Hendricks, Patel & Zeckhauser (1993), Goetzmann & Ibbotson (1994), Brown & Goetzmann (1995), Elton, Gruber & Blake (1996) and Carhart (1997) all agree that there is some evidence of persistence in mutual fund performance. The conclusions reached in any one study, however, are model and benchmark dependent (see Page, 1993). Therefore, in order to add to the robustness of the current state of knowledge about persistence in performance in the South African market, due to the fact that most research is CAPM based, the APT framework is utilised in the current study. S.Afr.J.Bus.Manage.2000,31(3) The Capital Asset Pricing Model (CAPM) is the equation of the security market line showing the relationship between the expected return and beta. Arbitrage Pricing Theory (APT) is based on fewer and less restrictive assumptions than the CAPM and is also a more general model allowing for more than one risk factor to underlie share returns. The APT is based on the assumptions that markets are perfectly competitive and frictionless and that investors prefer more wealth to less wealth and are risk averse. In~ividuals sh~re the ~elief that for the set of assets being considered, the time series process underlying the generation of security returns can be represented by the following linear k-factor model: K R,, = E(R;,) + L Balk,+ E;, k = I (I) where: R;, realised returns earned by asset i in time period t, where i = 1,2 ... n and t = 1,2 ... T; E(R,J= the expected rate of return of asset i for period t at the beginning of period t; a coefficient that measures the sensitivity of R,, to movements in fk,; the kth risk factor that impacts on asset i's return, where k = 1,2 ... K. All risk factors represent unexpected movements in pervasive economic forces and have an expected value of zero; and a normally distributed random error t which measures the unexplained residual return of asset i in period t. Page (1985) concludes that in comparing the APT and the CAPM, the APT was found to be substantially better with regard to the explanation of variability in South African share returns and that the underlying macroeconomic variables detennining the return generation process can be divided into those that primarily influence the mining sector and those that affect the industrial sector to a greater extent. . Acc_ording to Ross ( 1976) arbitrage theory requires essentially identical expectations and agreement on the beta coefficien_ts i_f the identification of ex ante beliefs with ex post reahsat1ons is to provide empirically fruitful results. Page (1989) and Barr (1989) both conclude that a two-factor model is the best benchmark to use in measuring security price perfonnance in South Africa. Davidson (1993) concurs that the CAPM is not an appropriate model to use on the JSE, but at the same time argues that the APT is far from operational. Reese (1993) confirms that in terms of the JSE as a whole, two or three factors appear to be priced, although the research on a yardstick for unit trusts' performance by Biger & Page (1993) points towards an appropriate model containing three to five factors. , Va~ Rensburg & Slaney ( 1997) argue that a two index multi-market model' when employing the JSE All Gold and ~dustrial Indices as explanatory variables, aids the economic mterpretation of the results as well as introducing considerable efficiency in the ensuing cross-sectional estimation procedures. It also provides a model that is more easily applied by practitioners and bypasses the well-documented difficulties 121 associated with factor analysis. They conclude that the different so_urces of risk are rewarded with risk premia of different magnitudes and that the large majority of JSE shares are influenced by either the Mining or Industrial Indices but seldom by. ~oth_ to an equal degree. The two-factor APT model has ~ncmg implications not compatible with the CAPM employing the JSE All Share Index as the market proxy. Van Rensburg (1998) studies the effect of economic forces on the JSE a~d. concludes that the ritual 'poorly specified market portfolio appeal will always be the last untestable defense of the CAPM. However, his results indicate that the CA~M, as conventionally specified by South African academics and practitioners (i.e. using the JSE All Share Index ~s a market proxy), is seriously flawed. The relative superiority of the Slaney (1995) two-index APT model is demonstrated by using the Industrial and All Gold Indices as observable proxies. It is argued that not only does this procedure significantly improve the explanatory power of models using pre-specified macroeconomic variables, but also that its omission leads to upward bias in the variances of the coefficient estimators of these models. Data and sample selection Fo~r samples of data are used, namely all ten General Equity Unit Trusts that traded in South Africa over the period January 1988 to December 1997 (first sample), the General Equity Unit Trusts that traded in South Africa over the period January 1993 to December 1997 (second sample) and all Unit Trusts that traded in South Africa during these periods are used in the third and fourth samples (21 and 42) respectively. Trusts that were in existence over the entire fiveand ten-year periods are included in the four samples respectively. Monthly data was used. Selling prices were obtained from the Money Mate databank. Monthly rates of returns were calculated using the following equation: (2) where: R,, = the monthly rate ofreturn of unit trust i in period t; P 11 = the monthly selling price of unit trust i in period t; and P, 1•1 = the monthly selling price of unit trust i in period t-1. The yield on the three-month Treasury Bill is used to represent the risk-free rate of return. The data is obtained from 1Net for the period January 1988 to December 1997 on a monthly basis as a yearly rate ofretum. The monthly risk free rate of return over the ten-year period was recalculated on a monthly basis. The monthly excess rate of return for the four samples were calculated by subtracting the risk free rate from the monthly rate of return as determined by equation 2. Three models of performance measurement were employed: the Capital Asset Pricing Model as described in Ross, Westerfield & Jordan (1993), a two-factor Arbitrage Pricing Theory model (Van Rensburg & Slaney, 1997) and a threefactor Arbitrage Pricing Theory model developed in this study and suggested by Van Rensburg. 122 Capital Asset Pricing Model (CAPM) The first model of perfonnance measurement is the CAPM, specified as PORTF;, = a;y+ I};,,. ASHARE, +&;, t = I, 2 ... T ... (3) where: PORTF = the average monthly excess1 return for portfolio II i in period t; ASHAREt = the monthly rate ofretum of the All Share Index2 in period t; and = the stochastic error tenn of unit trust i in period t. Two-factor model The two-factor APT model has the following specification: PORTFit = aiT + JliT AGOLD1 + cIT INDUST1 + &it t = 1,2...T (4) where: A GOLD,= the monthly rate ofretum of the All Gold Index in period t; and INDUST,= the monthly rate of return of the Industrial Index in period t. Data on a monthly basis for the ten-year period is obtained for the All Share Index, the All Gold Index and the Industrial Index, from I-Net. The monthly returns are calculated using the same method as for the portfolios. This model is based on the findings of Van Rensburg & Slaney who claim that 'The empirical findings strongly suggest that a two index model, employing the JSE Industrial and All Gold Indices as "prescribed factors", is a more appropriate approach to adopt in asset pricing applications such as portfolio perfonnance evaluation and calculating South African companies' cost of equity capital' (1997: 20). S. Afr.J. Bus. Manage.2000,31(3) Three-factor model This model contains an additional factor intended to price risk explicity: PORTF; 1 = aiT + f3iT AGOLD 1 + ciT IND UST,+ d;T STDEV; 1 + &; 1 (S) t = 1,2 ... T where: STDEV = the standard deviation of the monthly rate ofre- " tum of portfolio i in period t. Summary statistics for the factor portfolios reported in Table I indicate that the two-factor model can explain considerable variation in returns for both the fiveand ten-year periods. First, note the relative high variance of the A GOLD and the INDUST and their low correlations with each other. This suggests that the two-factor model can explain sizeable time-series variation. Second, the low cross-correlations imply that multicollinearity does not substantially affect the estimated two-factor model loadings. Empirical results Persistence in the current year return sorted unit trust portfolios (base case) For all four data samples (All Unit Trusts and General Equity Unit Trusts over tenand five-year periods), three equally weighted portfolios of unit trusts have been formed based on the current year's excess return using a modified version of the methodology of Hendricks, Patel & Zeckhauser (1993). On the first of January of each year, three equally weighted portfolios of unit trusts, using reported yearly returns for the current year, are fonned. The top performers are included in portfolio I (PO RTF I), the average performers in portfolio 2 (PORTF2) and the worst performers in portfolio 3 (PORTF3). The portfolios are held for one year after which they are re· formed. From this, time series of monthly excess returns of each of the three portfolios are obtained from January 1989 to December 1997 for the two ten-year samples (All Unit Trusts and General Equity Unit Trusts) and January 1993 to Decem· ber 1997 for the two five-year samples (All Unit Trusts and General Equity Unit Trusts). Table 1 Performance measurement model summary statistics FIVEYEAR PERIOD (January 1993 -December 1997) Factor portfolio Average monthly Standard Cross-correlations return deviation 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 TENYEAR PERIOD (January 1988 -December 1997) Factor portfolio Average monthly Standard Cross-correlations return deviation 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.Afr.J.Bus.Manage.2000,31 (3) Multiple regression analyses are perfonned with the three portfolios' returns as the dependant variables. For each of the four samples three multiple regression analyses are run pertaining to each of the three models of perfonnance measurement. A total of 36 multiple regression analyses are reported on in Tables 2 and 3. The portfolios of both All Unit Trusts and General Equity Unit Trusts demonstrate strong variation in mean returns, as shown in these tables. The mean monthly excess returns of the three portfolios decline with portfolio rank for all four samples. Because the portfolios are fonned on the basis of the current year's performance this pattern is expected. The dispersions of the four samples indicate sizeable annualized spreads in returns of approximately 9% in the case of the General Equity Unit Trusts and 30% in the case of All Unit Trusts. Cross-sectional variation in return is considerably larger among the portfolios of All Unit Trusts than General Equity Unit Trusts and also larger among the portfolios in the ten-year samples than the five-year samples in three of the four samples. In all four samples the top portfolio (PO RTF I) exhibits positive excess returns, while the worst perfonners (PORTF3) show negative returns. 123 In the case of the General Equity Unit Trust portfolios, the CAPM betas for the three portfolios are almost identical and they consistently decrease from PORTFI to PORTF3, except for the five-year period. For the All Share Unit Trust portfolios, the CAPM betas consistently decrease from PO RTF I to PORTF3 indicating a higher risk for the portfolios with the higher excess returns. In all the samples the average portfolio (PORTF2) shows the best correlation with the All Share Index (ASHARE). During the five-year period, the General Equity Unit Trust portfolios correlate better with ASHARE than the All Share Unit Trust portfolios, while during the ten-year period the opposite is true. The results of two-factor model indicates that the General Equity Unit Trust portfolios are less sensitive to the All Gold Index (AGOLD) than the All Share Unit Trust portfolios. The opposite is true for the Industrial Index (INOusn. Note the small regression coefficients for the PORTF3's of the All Unit Trust portfolios. High adjusted R-square values indicate a good fit between the perfonnance of the portfolios and the two-factor model, especially in the case of the high and medium return portfolios. The three-factor model does not do substantially better than the two-factor model in tenns of the adjusted R-square values Table 2 Portfolios of general equity unit trusts formed on the current year returns FIVE-YEAR PERIOD TEN-YEAR PERIOD Portfolio PORTFI PORTF2 PORTF3 PORTFI PORTF2 PORTF3 (High) (Med) (Low) (High) (Med) (Low) Mean monthly excess return 0.723% 0.069% -0.004% 0.564% 0.061% -0.269% Std deviation 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% t-Stat -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-Stat 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-Stat 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% t-Stat 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-Factor I-Stat 3.884 5.497 3.922 5.305 6.621 3.499 Modtl IN DUST 0.663 0.690 0.664 0.687 0.687 0.616 t-Stat 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-Stat 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% t-Stat -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 t-Stat 4.261 5354 3.993 4.882 6.752 3.611 3-Factor IN DUST 0.656 0.703 0.664 0.678 0.698 0.626 Model I-Stat 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 t-Stat 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-Stat 2.279 124 S.Afr.J.Bus.Manage.2000,31(3) Table 3 Portfolios of All Unit Trusts formed on the current year returns FIVE-YEAR PERIOD TEN-YEAR PERIOD Portfolio PORTFI PORTF2 (High) (Med) Mean monthly excess return 1.039% 0.035% Std deviation 4.000% 3.337'% Alpha 0.069% -0.791% t-Stat 0.344 -5.481 CAPM A SHARE 0.823 0.702 t-Stat 18.857 22.464 Adj R-sq 0.857 0.895 OW-Stat 1.684 2.185 Alpha 0.369% -0.663% t-Stat 1.450 -4.412 A GOLD 0.188 0.077 2-F•ctor t-Stat 8.384 5.839 Model INDUST 0.561 0.662 t-Stat 9.454 18.900 Adj R·sq 0.769 0.884 OW-Stat 1.831 2.220 Alpha -0.474% -0.112% I-Stat -0.964 -0.223 A GOLD 0.173 0.073 t-Stat 7.423 5.207 J.F•ctor INDUST 0.559 0.661 Model I-Stat 9.673 18.912 STD EV 0.351 -0.380 t-Stat 1.985 -1.151 Adj R-sq 0.781 0.885 OW-Stat 1.796 2.184 which the STOEY variable is frequently insignificant and unstable in tenns of its sign. Persistence in one-year return-sorted unit trust portfolios The purpose of this section is to detennine whether shorttenn persistence exists in the perfonnance of South African unit trusts. Once again for all four data samples (All Unit Trusts and General Equity Unit Trusts over tenand five-year periods), three equally weighted portfolios of unit trusts have been fonned. For these analyses the portfolios have been fonned on the basis of lagged one-year returns, thus replicating the methodology of Hendricks et al. (1993). On the first of January of each year, three equal weighted portfolios of unit trusts are fonned, using reported yearly returns of the previous year. The top perfonners are included in portfolio I (PORTF l ), the average performers in portfolio 2 (PORTF2) and the worst performers in portfolio 3 (PORTF3). The portfolios are held for one year after which they are refonned. Once again a total of 36 multiple regression analyses have been run using the three models of performance measurement. Summaries of the results of the multiple regression 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 pertaining to the General Equity Unit Trusts and All Unit Trusts are shown in Tables 4 and 5 respectively. Once again variations in mean returns between the portfolios are demonstrated, although not as pronounced as in the base case. In the case of General Equity Unit Trusts, PORTFI shows the highest monthly excess returns and PORTF2 the lowest. In the case of All Unit Trusts, the monthly excess returns of the three portfolios increase with portfolio rank order. PORTFI has the lowest (negative) monthly excess returns of all portfolios. The four samples indicate annualised spreads of approximately 3% for the General Equity Unit Trusts and be· tween two and 14% for All Unit Trusts. Cross-sectional variation in returns is considerably larger among the portfolios of All Unit Trusts than General Equity Unit Trusts and also larger amongst the portfolios in the ten-year samples than the five-year samples. The CAPM does not explain the relative returns of these portfolios. There is no consistent relation between the CAPM betas and the returns on the three portfolios. The CAPM betas should be higher for higher returns indicating a higher risk for the portfolios with the higher excess returns. In all the sam· pies the average portfolio (PORTF2) shows the best correlation with the All Share Index (ASHARE), while during the s.Afr.J.Bus.Manage.2000,31 (3) 12S Table 4 Portfolios of General Equity Unit Trusts formed on lagg d e one year retu - ms FIVE-YEAR PERIOD TEN-YEAR PERIOD Portfolio PORTFI PORTF2 (High) (Med) Mean monthly excess return 0.310% 0.000% Std deviation 3.291% 3.540% Alpha -0.463% -0.883% t-Stat -2.392 -6.225 CAPM AS HARE 0.657 0.751 I-Stat 15.675 24.431 Adj R-sq 0.806 0.910 DW-Stal 2085 2.339 Alpha -0.353% -0.732% t-Stat -1. 761 -4.311 A GOLD 0.049 0.087 2-Factor t-Stat 2.751 5.778 Model IN DUST 0.645 0.691 t-Stal 13.820 17.453 Adj R-sq 0.789 0.869 OW-Stat 2.076 2.242 Alpha -0.988% -0.601% t-Stat -2.216 -1.307 A GOLD 0.047 0.087 t-Stat 2.700 5.732 J-Factor INDUST 0.649 0.693 Model t-Stat 14.072 17.025 STD EV 0.484 -0.1 IO t-Stat 1.590 -0.307 Adj R-sq 0.794 0.867 DW-Stat I 2.092 2.242 five-year period, the General Equity Unit Trust portfolios correlate better with the All Share Index (ASHA RE) than the All Share Unit Trust portfolios. During the ten-year period, the opposite holds. In Tables 4 and 5 the same phenomena are observed as in the base case. Using the two-factor model, it follows that the General Equity Unit Trust portfolios are less sensitive to the All Gold Index (AGOLD) than the All Share Unit Trust portfolios, while the opposite holds for the Industrial Index (INDUST). High adjusted R-square values indicate a good correlation between the perfonnance of the portfolios and the two-factor model in most cases. In all four samples the ~ORTF2's have the highest adjusted R-square values, which IDlplies that the perfonnance of the average portfolios can best be described by this model. The three-factor model does not do substantially better than the two-factor model, as the values of the standard deviation of the portfolios (STDEV) are not significant in a number of cases. In summary, the results show that short-term persistence does not exist for the All Share Unit Trust portfolios. In the case of the General Equity Unit Trust portfolios, however, 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 there is evidence of persistence. The top portfolio (PO RTF I) remains the portfolio with the highest average monthly excess return. PORTF2 and PORTF3 change positions but still retain positive excess returns. Most of the persistence can be explained by common-factor sensitivities. Performance on past-winner unit trusts (1 year lag) To further investigate the persistence of past-winners, the following method is used -for the ten-year periods (both for the All Unit Trusts and General Equity Unit Trusts), three equally weighted portfolios have been formed in each year based on the previous year's yearly excess returns. The top performers are included in portfolio I (PORTFI), the average performers in portfolio 2 (PORTF2) and the worst perfonners in portfolio 3 (PORTF3). The portfolios remain unchanged for the entire period and the average monthly excess returns are calculated for each portfolio for the formation year and in each of the next five years after formation. Figures 1 and 2 show the post-formation returns on the General Equity Unit Trust portfolios sorted on lagged one-year returns and the post-fonnation returns on 126 S .A fr.J .Bus.Manage.2000,3 l(l) Table 5 Portfolios of All Unit Trusts formed on lagged one-year returns FIVE-YEAR PERIOD TEN-YEAR PERIOD Portfolio PORTFI PORTF2 (High) (Med) Mean monthly excess return -0.913% 0.007% Std deviation 3.857% 3.373% Alpha -1.623% -0.821% t-Stat -4.401 -5.241 CAPM ASHARE 0.603 0.703 t-Stat 7.558 20.737 Adj R-sq 0.488 0.879 OW-Stat 1.626 1.916 Alpha -1.426% -0.707% t-Stat -3.932 -4.659 A GOLD 0.154 0.064 2-Factor t-Stat 4.810 4.805 Model INDUST 0.423 0.686 t-Stat 5.010 19.416 Adj R-sq 0.496 0.885 OW-Stat 1.668 2.184 Alpha -0.340% -0.624% t-Stat -1.032 -1.554 A GOLD 0.111 0.065 t-Stat 4.325 4.758 J-Factor IN DUST 0.533 0.689 Model I-Stat 7.880 18.249 STDEV -0.285 -0.057 I-Stat -6.279 -0.223 Adj R-sq 0.699 0.883 OW-Stat 1.859 2.188 the All Unit Trust portfolios sorted on lagged one-year returns respectively. From both figures it is clear that the relative higher returns of the top portfolios are short-lived. It can also be seen that u, 0.80% E ~ 0.80% ig 0.40% §Cl) 0.20% ~ t 0.00% ; -0.20% C) !!! -0.40% g? <( -0.60% A 1/.···~ .... ~ ,'/ v- .... _ ,,, . ~~ - ... , z ~ Cl) Cl) 0 ~ ~ j:: i > + > er "' ~ + I ---PORTF1 -PORTF2 -- /'\ '"'.:.:-\ •\ \ ~ ~ '~\ \ \ Cl) Cl) ~ I T • • • • • ·PORTF3 I Figure I Post-formation returns on the General Equity Unit Trust portfolios sorted on lagged one-year returns 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 the one-year performance persistence is mostly eliminated af· ter one to two years. For both the General Equity Unit Trusts and the All Unit Trusts a trend of persistent under-performance of the worst portfolio (PORT3) is notable. It appears that 0.80% tJ) E 0.60% i 0.40% sCI): 0.20% 0.00% >. i; -0.20% c ~ -0.40% t-0.60% g? -0.80% < -1.00% - ---...------ .,,.-- ... .. ,(\ /' v ·, .. ,, / ' ' ,,. __/ ' ':f-!-L--"" . \ /"' .. '(\\ ' '\ \ I + I + I- - -PORTF1 --PORTF2 • • • • • ·PORTFD Figure 2 Post-formation returns on All Unit Trust portfolios sorted on lagged one-year returns S.Afr.J.Bus.Manage.2000,31 (3) e 2.00% -r---,----,----,----,-----, ! 1~%+----c-~- .. ~.- .. -._--+----+----+----. ~ 100%+--_,..f>-..: ............ ,--~ ... -+----+----+----. = ' ... ~·. 9 050% -1----1--.>.,,,---,.--~---+----+------< G) ' .. ~ f 000% ~··..:.·..::·. I -050% .1----+----+----f>-..~~~,+.- .. -~ Ill .100% .l----l----+----+---__::1'=:,~--l e -1.50% -1--------------' ......... ---l f <( ·2.00% .L---.L.---'----'----'------' z a:: a:: a:: a:: Q < < < ;li Iw w w < >- >- >- >- N 7 ... ~ + + + a:: 0 u. - - - PORTF1 --PORTF2 • · · • • PORTFJ Figure J Post-formation returns on the General Equity Unit Trust portfolios sorted on lagged five-year returns the average portfolio (PORTF2) in the case of General Equity Unit Trusts generates the best average monthly excess returns in most post-formation years. Persistence in five-year return-sorted unit trust portfolios To determine whether evidence can be found for longer term 2.50% "' E 2.00% ~ 150% "' 1.00% ~ 050% CD 0.00% >, :j; -0.50% ~ ·100% -1.50% t -2.00% 1 -2.50% -3.00% !}... ; ... 127 ,...._ ·:~ -~ ·-~'- - '"\. _-,,<" ---...: '.' \;. '\ ~ ~ I + + + Figure 4 Post-formation returns on All Unit Trust portfolios sorted on lagged five-year returns persistence in performance, portfolios of All Unit Trusts and General Equity Unit Trusts are formed on lagged five-year yearly returns. This is done for the ten-year data samples only. Once again the methodology of Hendricks et al. (1993) is used. On the first of January of each year, three equally Table 6 Portfolios of General Equity Unit Trusts and All Unit Trusts formed on lagged five-year returns over a ten-year period GENERAL EQUITY UNIT TRUSTS ALL UNIT TRUSTS Portfolio PORTFI PORTF2 PORTF3 PORTFI PORTF2 PORTF3 (High) (Med) (Low) (High) (Med) (Low) Mean monthly excess return 0.032% 0.185% -0.011% 0.155% 0.199% -0.766% Std deviation 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-Stat -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 t-Stat 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-Stat 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-Stat -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-Factor t-Stat 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-Stat 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-Stat 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-Stat -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 t-Stat 5.613 5.115 3.944 5.656 6.903 11.419 J.Factor INDUST 0.670 0.674 0.687 0.651 0.560 0.457 Model t-Stat 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 t-~tat -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-Stat 2.356 2.338 2.166 2.236 2.021 1.705