Unit trusts and portfolio selection on the Johannesburg Stock Exchange

The application of the standard techniques of portfolio selection on the 34 sectors comprising the JSE All Share index is undertaken for the three equal non-overlapping five-year periods between February 1965 and January 1980. Efficient portfolios in each period which carry the same risk as the market index are seen to outperform the market substantiaily. Portfolios chosen at random to span the efficient frontier in each period reveal the consistent inefficiency of 10 sectors over the 15-year period. Three of these sectors, namely Mining Holding, Mining Houses and Industrial Holding are shown to be favoured in the Association of Unit Trusts portfolio relative to these sectors' proportion of the market. On the presumption that unit trust managers attempt to act efficiently, holding these sectors is only justified if the measure of risk used in the portfolio selection algorithm, namely standard deviation of expected return, is less appropriate than other measures of risk such as earnings volatility. If standard deviation of expected return is a more appropriate measure of risk in the selection of efficient portfolios, it must be concluded that the large sophisticated investors managing the unit trusts act inefficiently.

The Association of Unit Trusts was established in 1967 to represent the joint interests of its member trusts and their unit holders in dealing with the authorities, to promote the common interests of the industry, and to maintain communication with the media. 1 For the purposes of this paper, the Association of Unit Trusts portfolio <n. which is a combined ponfolio of the 12 underlying trusts, is significant in that it is the largest professionally managed portfolio, the constituents of which are public knowledge. In this paper, the structure of this portfolio at December 31, 1980 is analysed and discussed with respect to the selection of efficient portfolios on the Johannesburg Stock Exchange (JSE) over the past 15 years.

The JSE Actuaries index and the Association of Unit Trusts portfolio
Comparatively recently, a comprehensive set of share price indices has been produced for the JSE, 2 providing a monthly price history of the JSE from January 1960 to September 1978 and daily thereafter. Since these indices are weighted by marked capitalization, a useful guide to a portfolio's structure is provided by comparing the proportion of the portfolio invested in each sector with the proportion that sector represents of the JSE All Share index. Clearly a higher relative weighting of a sector in the portfolio to the market indicates a favourable expected outcome in future performance of that sector relative to the market. while a relative exposure of less than unity indicates expected future unde:-performance relative to the market. A relati,e exposure of unity indicates a neutral performan1:e expectation relative to the market. Table I shows the T portfolio represented in this way relative to the JSE All Shar1: index at December 31, 1980. It can be seen that two sectors, namely Fishing and Printing, were not present in the portfolio and therefore carried the lowest relative exposure at zero. The highest relative exposure was Stores at 5,09, followed by Tobacco, Beverages and Furniture, the former over four times, and the latter two more than three times the market proportion for these sectors. The gold sectors all carried a low relative weighting. The appropriateness ofthe weightings revealed in Table l will be discussed later in this paper.

Selection of effrclant portfolios
In 1952 Markowitz published a now famous paper on portfolio selection, 3 from which a whole theory of portfolio S.-Afr. Tydskr. Bedryfsl. 1982, l3 ( 4 ) selection has been derived. The basic notion is that only two factors need be considered in choosing a portfolio, namely the return an investor can expect to receive from holding the portfolio and the uncertainty associated with this return. For the purposes of this paper the generally accepted measures of these variables have been used and they are, respectively, the weighted average monthly return of the components of the portfolio, and the standard deviation of the monthly return on the portfolio (both expressed in per, cent per month). Any portfolio may thus be represented by · a point in a risk/return plane. In fact all feasible (i.e. attainable) portfolios will fill some region in this plane. fo par-tJcular, a set of portfolios, known as the efficient set, can -be.found which will dominate all other portfolios, because for these portfolios it is not possible to obtain either a greater . . expected return without incurring greater risk or .obtain stnaller risk without decreasing expected returns .. 4 Therefore investors will only wish to hold portfolios belongthg to the · efficient set and each investor is left to .choose the single . . oq_e portfolio (i.e. trade off the levels of risk and, return) for himself.
Standard techniques are available for choosing the effi-. cient set,5 and this has been done on the JSE. 6 • 7 For this paJ)er, three equal, non-overlapping time periods of monthly intervals were chosen for study, nam~ly: · February 1965 to January 197Q -. Period 1 · ·f~ruary 1970 to January 1975 -Period 2 · February 1975 to January 1980-'-Period 3. It must be stressed that these three time periods were not chosen because of any market or economic consider"1ion. They were chosen merely to divide the data set into three equal non-overlapping time periods.
The 34 sectors of the JSE Actuaries index (see Table 1) represented the universe of 'securities' for portfolio fonnation in each period. The efficient set chosen in each period is pictorially displayed in Figures 1, 2 and 3 for Periods 1, 2 and 3 respectively. Also marked as points in the risk/return plane are the JSE All Share index (M), the JSE All Mining index (A), the JSE Mining Financial index (F), the JSE Industrial and Financial index (I) and the Association of Unit Trusts portfolio (T).
It can be seen that the range and slope of the efficient set or frontier is markedly different in each period. Further, each of the indices plotted and the T portfolio have been consistently inefficient over time. The inefficiency of M particularly, suggests that efficient portfolios will contain set· tor weightings which differ greatly from the weightings ilP" . plying in the M index. This feature is examined in the ~xt · section.
It must be mentioned that this study is an ex post study whereas an investor wishing to utilize the Markowitz model must use estimates of the expected return and risk for each of the securities in the coming period (i.e. ex ante). Ne.ver· theless, ex post studies are useful in that they demonstrate the investment opportunities that actually were available in the period. An analysis of such results coold help invest~ to decide why their ex ante portfolios did not produce ·the desired results. In addition, investors whose portfolios lie far from the efficient frontier should realize that this is as a result of poor ex ante forecasts. Whether they could have s. Afr. J. Bus. Mgmt. 1982, 13(4) done better or not ex ante, is a question addressed by the efficient market hypothesis and beyond the scope of this paper.

Composition of efficient portfolios
On any given efficient frontier there are an infinite number of different portfolios. For the purpose of studying the composition of efficient portfolios several portfolios were I selected from each efficient frontier and are numbered in each of Figures 1, 2 and 3. They were chosen at random to embrace the full risk/return range of the efficient frontier, with the exception that the efficient portfolio which carried the same risk (i.e. standard deviation of return) as the M index was a required selection. Tables 2, 3 and 4 show the composition of these efficient portfolios by sector weighting for Periods 1, 2 and 3 respectively. Several points emerge from a study of these tables: At very high risk, limited diversification occurs because only a limited number of sectors in each period has a sufficiently high expected return to compensate the investor for the high risk.
As the risk decreases, diversification increases. In fact the increased diversification serves to reduce risk. Also lower-risk portfolios approach the area where M, by definition fully diversified, plots. Some sectors changed their risk character over the periods studied. For example, the gold sectors tend to occur in lower-risk portfolios in Period 1 and higherrisk portfolios in Period 2 while hardly at all in Period! 3. Undoubtedly the behaviour of the gold price in these  Table 1) and it is surprising that such a large por- "Portfolio with same risk as the market tion of the maret index has been so consistently inefficient. Arguments may possibly be lodged against this analysis because of its ex post nature, but the fact remains that over the past 15 years 10 of the 34 sectors examined did not appear in any ex post efficient portfolio. While it is possible that from an ex ante point of view some of these sectors may have appeared efficient to investors, the fact remains that ex post they were never efficient. This is true for each of the three periods examined and this should be the cause of some concern to investors who were heavily invested in these sectors.
The only reasonable conclusion one can draw is that these sectors appear to have been inefficient over the

Performance of efficient portfolios
To illustrate the performance of efficient portfolios relative to the M index, the efficient portfolios in each period carrying the same risk (i.e. standard deviation of return) as the M index were examined. These portfolios are designated in Tables 2, 3 and 4. In Table 5 the relative performance figures are shown. It can be seen that substantial superior performance is achieved by efficient portfolios thereby demonstrating that on the JSE it has been possible to outperform the market consistently without bearing additional risk to that borne by investing in the market index itself.

Efficiency of the Association of Unit Trust portfolio (T)
It has already been seen in Table l that the unit trust managers have collectively adopted a portfolio which has quite different sector weightings from those in the market index. Furthermore, it has been established that efficient portfolios also display this phenomenon with several sectors never appearing in efficient portfolios. One of the characteristics of the T portfolio is its low exposure to the gold sectors, representing only 6,360/o of T but 33,00/o of M. It has been shown 8 that the gold sectors on the JSE have produced similar mean monthly returns for a United States (US) and South African (SA) investor over the past 15 years. However, the US investor has borne very little undiversifiable risk in achieving this return, which has been almost four times the Standard and Poors 500 index mean monthly return, because the gold sectors' returns have virtually no covariance with the return on this index. To a SA investor, who is limited to the JSE for his equity investments, the covariance of the gold sector returns with the M index returns is high, which implies that undiversifiable or market risk is also high. Therefore the gold sectors as an asset group have more value to a US investor than a SA investor and should be preferred by the former and not the latter. The unit trust managers tend to act in a manner consistent with this hypothesis. It was shown that 10 sectors never appeared in any efficient portfolios. These sectors represent 53,60/o of the T portfolio compared with 33,80/o of the M index for a relative weighting of 1,59. At December 31, 1976, the earliest amalgamated T portfolio, the 10 inefficient sectors represented 55,40/o of the T portfolio compared with 33,2% of the M index for a relative weighting of 1,67. This means that, although historically very inefficient, these sectors have been and are currently favoured by unit trust managers to improve future performances. Even if the argument presented above concerning the gold sectors is accepted and these sectors are rebased in the M index at December 31, 1980 to reflect their relative exposure in T (i.e. 6,36% of M instead of 33,00/o), the IO inefficient sectors become 47 ,2% of the adjusted M index and the relative exposure in Tis still greater than unity at 1,14. Three of the IO sectors concerned, namely Mining Holding, Mining Houses and Industrial Holding, account for 36,20/o of the adjusted M or 25,9% of the unadjusted M. This represents 76,60/o of the total market capitalization of the 1 O inefficient sectors. It is worth noting that companies comprising these three sectors tend to have investments in quoted companies from other sectors of the JSE and/ or unquoted companies drawn from all parts of the economy. Therefore it is unlikely that these sectors will have low covariance with the market and, m~re importantly from the portfolio selection viewpoint, ~th other sectors. Furthermore, it is unlikely that companies invested largely in the M index will achieve returns significantly different from it. Hence it is theoretically 175 unl_ikely that these sectors will be selected in efficient portfolios, and this is evident in practice as well .
. Unit ~rust managers are presumed to attempt to act efficiently m the construction of their portfolios. How is it, ~heref~re, that they invest to such an extent in apparently meffic1ent sectors? The nature of the three sectors discussed above is such that the volatility of earnings performance is likely to be lower than that of other more specialized sectors on the market. For example, an industrial holding company is likely to have its earnings sourced from diverse parts of the economy, which means that if a particular economic sector suffers a downturn, the adverse effect is diluted by the other investments of the company. In other words, the risk, as measured by earnings volatility, is lower for a diversified company than for an individual industrial company in a specific sector. If an investor is prepared to pay a premium for lower risk earnings he may buy shares in such a diversified company in preference to a combination of its underlying holdings, assuming they are available for purchase. The fact that unit trust managers hold shares in the Mining Holding, Mining House and Industrial Holding sectors and the fact that these have proven to be inefficient in terms of the portfolio selection algorithm, produces an interesting conundrum. Either the standard deviation of return is a less correct measure of risk than earnings volatility and therefore the portfolio selection algorithm which has been used extensively in finance theory is wrongly specified, or if standard deviation of return is a more correct measure of risk, then the unit trust managers in South Africa are erroneously prepared to pay premiums for a diversification of risk which they can achieve themselves in the context of their portfolios at no cost.
If the former condition is true, finance theory, and in particular portfolio selection as applied on the JSE, will have to be revised. If the latter condition pertains, it implies that large and sophisticated investors on the JSE are operationally inefficient.