A Collar Weighted Approach to Indexing in the South African Equities Market

Transcription

1 A COLLAR WEIGHTED APPROACH TO INDEXING IN THE SOUTH AFRICAN EQUITIES MARKET A Thesis presented to The Graduate School of Business University of Cape Town in partial fulfilment of the requirements for the Masters of Business Administration Degree by Brandon Taylor December 2009 Supervisor: Heidi Raubenheimer UCT Graduate School of Business - Research Report 2009 Page 1 of 148

2 . ACKNOWLEDGEMENTS A Collar Weighted Approach to Indexing in the South African Equities Market I would like to thank my fellow Investment Research Group colleagues Elvira Grobler and Greg Henshall for their assistance in obtaining data. I would like to thank my research supervisor, Heidi Raubenheimer for her support and direction throughout this research thesis. Finally, and most importantly, I would like to thank my wife and son for their patience, love and support during the last two years. UCT Graduate School of Business - Research Report 2009 Page 2 of 148

3 DECLARATION This thesis is not confidential. It may be used freely by the Graduate School of Business. A recognised convention for citation and referencing has been used. Each significant contribution and quotation from the works of other people has been attributed, cited and referenced. It is certified that this submission contains works only undertaken by the author, unless otherwise stated. Signed: Brandon Taylor UCT Graduate School of Business - Research Report 2009 Page 3 of 148

4 A COLLAR WEIGHTED APPROACH TO INDEXING IN THE SOUTH AFRICAN EQUITIES MARKET ABSTRACT Indices have two main purposes, viz., as a passive investment vehicle and as benchmark for portfolio managers. The market capitalization weighted method, has been the main method use to create an index until recently. A recent change has been the introduction of fundamental indexation. Fundamental indexation uses various fundamental data to weight the constituents of an index. Many studies have been performed detailing the superior performance of fundamental indexation over market capitalization indexation. However, these studies also noted periods of under-performance using a fundamentally weighted index. Arya & Kaplan (2006) proposed using a hybrid form of indexing to achieve an equitable return to that achieved by fundamental indexation but with lower risk and turnover. This study uses the collar weighted approach of Arya & Kaplan (2006) to determine if the hybrid form of indexing can achieve a return similar to that achieved by fundamental indexation, with a lower risk, lower turnover, lower concentration and a more stable sector composition. The results indicate that it is possible, using a collar weighted approach to indexing, to achieve returns that are equitable to those obtained by fundamental indexation and greater than that of the market capitalization method with similar risks and concentrations. However, the major finding of the Arya & Kaplan (2006) study was the lower turnover of the collar weighted approach whereas this study concluded that the turnover using a collar weighted approach was greater than other methods. KEYWORDS: Market capitalization, fundamental indexation, price-indifference, collar weight, indexing, portfolio construction, value premium, alternative weighting UCT Graduate School of Business - Research Report 2009 Page 4 of 148

5 CONTENTS A Collar Weighted Approach to Indexing in the South African Equities Market LIST OF TABLES INTRODUCTION RESEARCH AREA AND PROBLEM RESEARCH QUESTIONS AND SCOPE RESEARCH ASSUMPTIONS RESEARCH ETHICS LITERATURE REVIEW DISCUSSION CONCLUSION RESEARCH METHODOLOGY RESEARCH APPROACH AND STRATEGY RESEARCH DESIGN, DATA COLLECTION METHODS AND RESEARCH INSTRUMENTS SAMPLING RESEARCH CRITERIA Copyright 3.5 DATA PREPARATION... UCT CAPITAL INDEX (CI) CREATION TOTAL RETURN INDEX (TRI) CREATION DATA ANALYSIS METHODS CRITERIA MEASUREMENT RESEARCH FINDINGS, ANALYSIS AND DISCUSSION RESEARCH FINDINGS EFFECT OF COLLARING RETURNS TOTAL RETURN INDEX RISK RISK-ADJUSTED RETURN TURNOVER CONCENTRATION SECTOR COMPOSITION RESEARCH ANALYSIS AND DISCUSSION RETURNS RISK TURNOVER CONCENTRATION SECTOR COMPOSITION RESEARCH LIMITATIONS UCT Graduate School of Business - Research Report 2009 Page 5 of 148

6 5 RESEARCH CONCLUSIONS FUTURE RESEARCH DIRECTIONS REFERENCES AND BIBLIOGRAPHY APPENDICES LIST OF FIGURES Figure 1: 2 Year Comparison-FTSE/JSE Top 40 vs. FTSE/JSE RAFI 40 (at 17 June 2009)...10 Figure 2: Collar-Weighted Method of Indexing...11 Figure 3: Monthly Capital Index 31 January 2002 to 31 January Figure 4: Total Return Index 31 January 2002 to 31 January Figure 5: Effective Number of Shares at Rebasing...46 Figure 6: Sector Composition Market Cap Index...48 Figure 7: Sector Composition RAFI...49 Figure 8: Sector Composition Collar Weighted (Original) Index...50 Figure 9: Sector Composition Collar Weighted (Adjusted) Index...50 Copyright LIST OF TABLES UCT Table 1: Effect of Collaring...38 Table 2: Excess and Compounded Returns Capital Index...40 Table 3: Excess and Compounded Returns Total Return Index...42 Table 4: Standard Deviations Capital Index...43 Table 5: Standard Deviations Capital Index...43 Table 6: Sharpe Ratio Capital Index...44 Table 7: Sharpe Ratio Total Return Index...44 Table 8: Annual Turnover...45 Table 9: Effective Number of Shares and Resources Weighting...46 Table 10: Concentration in a Number of Constituents...47 Table 11: Differences in Sector Composition...48 Table 12: Paired t-test between the Collar Weighted Indices and the Market Cap Index...52 Table 13: Paired t-test between the Collar Weighted Indices and the RAFI...53 Table 14: F-Test between Collar Weighted Indices and the Market Cap Index...54 Table 15: F-Test between Collar Weighted Indices and the RAFI...54 UCT Graduate School of Business - Research Report 2009 Page 6 of 148

7 Table 16: Wilcoxon Signed Rank Sum Test for the Collar Weighted (Original) and Market Cap Indices - Turnover...56 Table 17: Wilcoxon Signed Rank Sum Test for the Collar Weighted (Adjusted) and Market Cap Indices - Turnover...56 Table 18: Wilcoxon Signed Rank Sum Test for the Collar Weighted (Original) Index and the RAFI - Turnover...57 Table 19: Wilcoxon Signed Rank Sum Test for the Collar Weighted (Adjusted) Index and the RAFI - Turnover...58 Table 20: Wilcoxon Signed Rank Sum Test for the Collar Weighted (Original) and Market Cap Indices Concentration...59 Table 21: Wilcoxon Signed Rank Sum Test for the Collar Weighted (Adjusted) and Market Cap Indices Concentration...59 Table 22: Wilcoxon Signed Rank Sum Test for the Collar Weighted (Original) Index and the RAFI Concentration...61 Table 23: Wilcoxon Signed Rank Sum Test for the Collar Weighted (Adjusted) and the RAFI Concentration...61 Table 24: Average Weight Change of Sector Weightings...62 UCT Graduate School of Business - Research Report 2009 Page 7 of 148

8 1 INTRODUCTION 1.1 Research Area and Problem A Collar Weighted Approach to Indexing in the South African Equities Market The use of indices has had a long and varied position in the investment industry. Indices are used for measuring the performance of portfolio managers and as a passive investment vehicle for both institutional and individual investors (Ferreira, 2009). Indices measure a variety of equity portfolios, i.e., the complete market, the largest equities (by market capitalization), the smallest equities (by market capitalization), a combination of sectors or a sector itself as well as specific user-derived indices. In the South African equity market, until 24 June 2002, the Johannesburg Stock Exchange (JSE) Actuaries Index Series was used. This was replaced by the FTSE/JSE Africa Index Series which is a joint venture between the FTSE group and the JSE. To ensure consistency of data, a rebasing of data prior to 24 June 2002 was done (on daily values) up to June 1995 (Immelman, 2002). The FTSE/JSE Africa Index Series consists of five headline indices, six tradable indices, ten economic group indices, thirty-six sector indices, six sub-sector indices (in the mining sector), two secondary market indices, six specialist indices (of which the RAFI is one) for South Africa. Until recently most indices on the various world bourses were calculated using a capitalization weighted method. In a capitalization weighted method the percentage of each equity held in the index is in proportion to the market capitalization of that equity as a percentage of the total market capitalization of the index. The use of the capitalization weighted method for constructing an index stems from the work of Harry Markowitz (in 1952) who developed Modern Portfolio Theory (MPT) and later the work of William Sharpe (in 1964) who developed the Capital Asset Pricing Model (CAPM). A common assertion of Modern Portfolio Theory is that as the number of companies you hold in a portfolio increases, the portfolio risk decreases provided the returns are not perfectly correlated (Markowitz, 1999). This law of average covariance results in a greater riskadjusted return by holding a diversified (i.e. uncorrelated) portfolio (Markowitz, 1999). Fama & French (2004) state that as a result of MPT and CAPM all investors hold the same portfolio T of risky assets each risky asset's weight in the tangency portfolio, which we now call M (for the "market"), must be the total market value of all outstanding units of the asset divided by the total market value of all risky assets (Fama & French, 2004, p.28). UCT Graduate School of Business - Research Report 2009 Page 8 of 148

9 However, CAPM and MPT have always attracted a level of attention as not all of the investment community has fully agreed that the theory presented by these two models always holds true in the real investment world. Hsu (2004) showed, using a two stock portfolio, that capitalization weighting leads to lower returns (even after transaction costs are introduced) than weighting by fundamentals and that the effect is exacerbated when noise is introduced. However, it was not until the empirical study of Arnott, Hsu & Moore (2005) that the concept of using fundamentals to weight an index gained support within the investment community. In their study of the US equities market over the period , Arnott et al., (2005) showed that an index constructed of six fundamental metrics (book value, trailing five-year average cash flow, trailing five-year average revenue, trailing five-year average gross sales, trailing five-year average gross dividends and total employment) delivered a 1.97% p.a. excess return compared to the S&P 500 (a capitalization weighted index) and a 2.15% p.a. excess return Reference portfolio (a capitalization weighted index, constructed by the authors, of the top 1000 equities). This was achieved with a lower volatility than either the Reference portfolio or the S&P 500. Although there were specific periods when the S&P 500 and Reference portfolio outperformed the fundamental index, in general, Arnott et al., concluded that Main Street indexing outperforms Wall Street indexing (Arnott et al., 2005, p.97). In a South African context, indices based on fundamental indexation have only been part of investment opportunities available since 1 October Since this date, investors could invest in a fundamentally weighted Top 40 exchange traded fund, via the JSE, as they would in market capitalization weighted Top 40 via the SATRIX 40. Ferreira (2009) has established that during the period , a Composite Fundamental Index outperformed the JSE All-Share Index (capitalization-weighted index) by 5.55% p.a. However there were periods, notably and 2002, where the JSE All-Share Index delivered a better return than the Composite Fundamental Index (Ferreira, 2009). The detractors of fundamental indexation argue that, albeit that back-testing by Arnott et al., (2005) proved that over the long run ( ) that fundamental indexation outperforms capitalization weighted indexing by 2 percentage points, equities with a strong growth bias performed very poorly during the period which could have affected the results due to the end-point bias (Dutta, 2009). In the current bear market in the United States, capitalization UCT Graduate School of Business - Research Report 2009 Page 9 of 148

10 weighted indices are outperforming fundamental indices further supporting the work of Perold (2007) and Kaplan (2008). They argued that fundamental indexing suffers from the same errors as capitalization weighted indexing in that it also suffers during periods of extreme panic and benefits during periods of over-exuberance because the market as a whole (independent of the type of indexing technique) will be affected (Dutta, 2009). The same phenomenon can be seen in the South African market during 2008 where the FTSE/JSE Top 40 Index outperformed the FTSE/JSE RAFI 40 Index (Figure 1). Figure 1: 2 Year Comparison-FTSE/JSE Top 40 vs. FTSE/JSE RAFI 40 (at 17 June 2009) JSE (2009) If neither indexing method delivers consistent excess returns against the other indexing method, is there a method which can capture the benefits of both and deliver superior returns? Arya & Kaplan (2006) proposed using a new hybrid form of indexing using a collar weighted approach (see Figure 2) whereby the fundamental weight (multiplied by a collar multiplier) of the individual equity would form the upper and lower bounds of the index weight assigned to that individual equity. Only if the market capitalization weight of that individual equity was greater or less than the fundamental bounds would that individual equity be assigned the fundamental bound. This research will investigate the application of a collar weighted approach to indexing in the South African equity market. UCT Graduate School of Business - Research Report 2009 Page 10 of 148

11 Figure 2: Collar Weighted Method of Indexing Portfolio Weight (%) Upper Collar Lower Collar 1.2 Research Questions and Scope Fundamental Weight (%) Arya and Kaplan (2006) Copyright This research focuses on the risk and return of the JSE All-Share Index UCT over the period using three different methodologies to weight the index, namely, capitalization weighted indexation, fundamental indexation and collar-weighted indexation. Although the study (Ferreira, 2009) has been performed to compare the results of capitalization weighted indexation versus fundamental indexation in the South African equity market, this study will provide a third option for portfolio managers to construct exchange traded funds by analysing the following hypotheses: Research Hypothesis 1 A collar weighted index (of the JSE) exhibits a higher return than a capitalization weighted index and a return comparable to a fundamentally weighted index (of the JSE), over the period Research Hypothesis 2 A collar weighted index (of the JSE) exhibits risk that is comparable to either a fundamentally weighted or capitalization weighted index (of the JSE) over the period UCT Graduate School of Business - Research Report 2009 Page 11 of 148

12 Research Hypothesis 3 A collar weighted index (of the JSE) exhibits an average annual turnover comparable to either a fundamentally weighted or capitalization weighted index (of the JSE) over the period Research Hypothesis 4 A collar weighted index (of the JSE) exhibits a lower concentration than a capitalization weighted index and comparable to a fundamentally weighted index (of the JSE) for the period Research Hypothesis 5 A collar weighted index (of the JSE) exhibits a different sector composition to either a fundamentally weighted or capitalization weighted index (of the JSE) for the period Research Assumptions The effect of taxation is not considered in this study. It is assumed that with any of the three portfolios constructed the market will be able to clear with sufficient shares available of each individual equity for the portfolio to be constructed. There is no effect on the underlying price of the equity. No transaction costs are incurred for trades in individual equities. 1.4 Research Ethics Diener & Crandall (in Bryman & Bell, 2007) determined the following four principles should be adhered to when conducting research: 1. No deception takes place as a result of the research 2. The privacy of participants is protected 3. The participants consent to partaking in the research 4. The participants are not harmed in any way as a result of the research. There is no harm to any participant, no consent is required nor is the privacy of any individual affected by this research as no interaction with individuals will take place as part of this research. All the data obtained will be processed and analysed so as to present the accurate results and will not be altered to influence the results in a certain direction. UCT Graduate School of Business - Research Report 2009 Page 12 of 148

13 2 LITERATURE REVIEW A Collar Weighted Approach to Indexing in the South African Equities Market 2.1 Discussion Indices are portfolios weighted by a certain characteristic. The manner in which portfolios are constructed has long been shaped by Modern Portfolio Theory (MPT), developed by Harry Markowitz in 1959, and the Capital Asset Pricing Model (CAPM), based on the work of William Sharpe in Some risk is correlated and as a result holding a diversified portfolio can eliminate some risk (Perold, 2004). Fama & French (1992) argue that the basis of the CAPM and MPT is that a portfolio constructed of the whole market is mean-variance efficient. This implies that the portfolio minimizes risk for a given return and maximizes the return for a given risk (Fama & French, 2004). Cubbin, Eidne, Firer & Gilbert (2006) state that the best return an investor can expect is the return of the market unless they have privileged information. Malkiel (2003) believes that over the short run there may be times when active strategies can work but over the long run, the best an investor can do is a buy-and-hold capitalization weighted portfolio. But CAPM and MPT are not without detractors. Arnott et al. (2005) argue that CAPM is fundamentally flawed as it leads to the belief that an individual investor can never beat the market even though CAPM is based on inaccurate assumptions. Arnott (2005) extends this theory further by asking (as it was proven that a capitalization-weighted market clearing portfolio is not mean-variance efficient, based on empirical evidence and theory) are the underlying theories of the Efficient Market Hypothesis (EMH) and CAPM still true? As a result of some skepticism with the real world workings of MPT, CAPM and EMH, investment academics have set out to prove whether the theories perform as they are expected to. One of the first studies into the efficiency of the market was that of Basu (1975). Based on his study, performed on US equities over the period , Basu (1975) concluded that there was market inefficiency as investors could earn abnormal returns by purchasing low P/E ratio equities but once tax and transaction costs were taken into account, this effect was made non-exploitable. In a study of the Japanese equities market, over the period , Chan, Hamao & Lakonishok (1993) found that employing a strategy, which they state is a value strategy, using fundamentals (book-to-market ratio, earnings yield, size, cash flow yield) they could achieve better results than the market. Malkiel (2003) established that in the US equities market during the period, , on average, capitalization weighted index funds consistently outperformed actively managed funds no matter what the timeline. He concluded that the market is and will always be efficient but UCT Graduate School of Business - Research Report 2009 Page 13 of 148

14 there will be times of anomalies and the anomalies do not lead to inefficiency because they are not exploitable time and time again. Probably the most cited work is by Fama & French (1992) where they established that size and value could explain a cross section of average stock returns (Fama & French, 1992, p.464). Although Fama & French (1992) argue the importance of size and value, Arnott (2005c) argued that the size and value phenomenon have been placed together too often when in fact the evidence (of a study of the effects in the US equity market over the period ) showed that size has very little influence on excess returns whereas the value effect can have quite a large impact. This is important because of the bias seen in capitalization weighted indices and fundamentally-weighted indices towards growth and value equities respectively. Fundamental indexation is seen a value strategy (Asness, 2006) and capitalization-weighted indexation is seen as a growth strategy (Arnott et al., 2005). Asness (2006) contends that the proponents of fundamental indexation are putting forward a semi-passive value strategy rather than a true, new revolutionary indexing method as the method of creating the fundamental index which is as follows: Weight of i = Market Capitalization Weight Copyright i *(Fundamental Measure UCT i /Fundamental Measure market ) creates an over-weighting of value equities and an under-weighting of growth equities. However, Arnott et al. (2005) argue that, because of the mathematical construction of a capitalizationweighted index, a similar argument holds true. Their argument is that because of the index construction, capitalization-weighted indices over-weight equities that trade above their true fair value (i.e. growth equities) and under-weight equities that trade below their true fair value (i.e. value equities). Hence, it is important to understand the differences between value-biased portfolios and growth-biased portfolios. Empirically, there have been studies trying to prove or disprove the concept that value-biased portfolios exhibit higher returns than growth-biased portfolios. Kwag & Lee (2006) performed a study of the US equity market over the period and ascertained that value-biased portfolios outperform growth-biased portfolios throughout the business cycle. Arnott (2005b) challenged that because of the efficiency of the market and symmetry of market returns the returns from growth equities will always be below the returns from value equities. In this world, value beats growth, on average, over time (Arnott, 2005b, p.12). UCT Graduate School of Business - Research Report 2009 Page 14 of 148

15 However, most studies conclude that although, in general, value outperforms growth there are periods when growth outperforms value. Over the period , Chan, Karceski & Lakonishok (2000) determined that whilst value and small cap equities generally outperformed growth equities, towards the end of the period growth equities outperformed value and small cap equities by significant amounts although their operating performance was worse than in previous years leading to the conclusion that the reason for the stellar performance of growth equities was based more on investor exuberance rather than the underlying performance of the company itself. In the findings of Malkiel (2004b), investors can observe that over the period , value outperformed growth but that, at points, growth outperformed value leading to the conclusion that not one strategy is perfect in exploiting returns and that the results are dependent on the period of the study. Black & McMillan (2005), in a study of the US equity market over the period , determined that although overall a value-biased portfolio outperforms a growth-biased portfolio, it can mostly be attributed to the fact that value-biased portfolios tend to be more responsive to changes in macro-economic cycles (particularly the contraction phase) but the most successful strategy is one which switches between the two, based on point in the economic cycle, particularly towards the end of the study period. Schwob (2004) identified that value will exhibit higher returns when there is a rising interest rate cycle and during periods of economic recovery. The study of Au & Foley (2006), of US equities over the period , suggests that investors who follow a core strategy (i.e. style neutral strategy) will achieve better performance than those investors who follow either a value-only or growth-only based strategy. The literature points to the use of both a value and growth strategy, applied at the correct time, as the optimum strategy. If the CAPM, MPT and EMH do not fully explain the real world workings and value-biased portfolios generally outperform growth-biased portfolios, what is the optimum method of constructing an index? As mentioned previously, the only method utilised (until very recently) to create an index fund was the capitalization-weighted method. There have been many questions over the applicability of the capitalization weighted method but Malkiel (2004) shows that although some sophisticated models might have a slightly better return than a buy-and-hold capitalization weighted portfolio, the higher return is so negligible that it is not worth the risk and costs for an average investor. Hsu (2004), however, questioned whether capitalization weighted indices offered optimal returns to investors. Marotta (2004) argued that capitalization weighted indices were UCT Graduate School of Business - Research Report 2009 Page 15 of 148

16 flawed as a result of their construction (basing weightings on price), their blind spots (the index fails to take into account the cash and debt values of a company) and can only deliver optimal returns when the larger companies perform. Treynor (2005) proved (theoretically) the fact that the capitalization weighting causes a lack of symmetry which results in more funds invested in overpriced equities rather than under-priced equities. By linking the co-variances of portfolio weights with errors, true value per equity and price per equity, Treynor (2005) was able to prove that indexing that does not rely on capitalization-weighting, avoids this over-pricing and under-pricing. However, it was not until the empirical study of Arnott et al. (2005) that the concept of using a method other than capitalization weighting gained momentum. In their empirical study of US equities, over the period , they constructed six portfolios based on fundamentals (one each on book value, trailing five-year cash flow, trailing five-year average revenue, trailing fiveyear average gross sales, trailing five-year average gross dividends and total employment), a composite fundamental portfolio and compared the results to the S&P 500 and a reference portfolio (a capitalization-weighted portfolio of the 1000 largest equities) with a re-balancing taking place annually. Arnott et al. (2005) constructed the composite portfolio, an average of four of the individual fundamental portfolios (employment was excluded because of access to information and revenues because it is similar to sales), but for companies not issuing dividends, the composite portfolio was an average of the remaining three individual fundamental portfolios. The study demonstrated that over the period, the six individual fundamental portfolios and the composite fundamental portfolio achieved returns 1.66 percentage points per annum to 2.56 percentage points per annum in excess of the reference portfolio and returns 1.52 percentage points per annum to 2.38 percentage points per annum in excess of the S&P 500 with lower volatilities for the composite portfolio that either the reference portfolio or the S&P 500 (Arnott et al., 2005). Further, once a trading cost of 1% was introduced, the excess returns only fell by 0.10% to 0.14% (Arnott et al., 2005). Finally, the results of the study of Arnott et al. (2005) illustrated that through both a bear and bull market the fundamental based portfolios would outperform either the reference or the S&P 500 albeit that the excess return was only 0.55 percentage points per annum during bull markets. There were three periods during which the fundamental portfolios underperformed, viz., the Nifty Fifty Age of 1972 (Arnott et al., 2005, p.89), and the technology dominated bubbles of and (Arnott et al., 2005). UCT Graduate School of Business - Research Report 2009 Page 16 of 148

17 This was followed by similar studies using smaller data samples. Arnott & West (2006) determined that the excess returns of fundamental indexation over capitalization weighted indexation is greatly increased for small cap equities whilst excess returns based on sectors can vary by as much as 7.7% and as a little as 1.0% (over the study period of ). Research by Arnott, Little & Shepherd (2008) established that a fundamental index will offer superior returns and over the period of the study ( ), the optimization tool allocated 100% of the portfolio construction in fundamental indexes and 0% to the capitalization weighted indexes. Their study also concluded that the volatility of the fundamental index portfolio was lower than the capitalization-weighted portfolio. The standard deviation being 4.9% for the fundamental index portfolio versus of standard deviation of 7.5% for the capitalization-weighted index portfolio (Arnott et al, 2008). There have also been studies outside of the US equities market. Hsu & Campollo (2006), in their study of US and World equity markets over the period , argue that the only period in which a fundamental index is likely to be outperformed by a capitalization weighted index is during a bubble due to the momentum effect. Fundamental indices are not value indices in disguise because they hold both value and growth equities (just the weighting mechanism is different) whereas value indices hold only value equities which are still weighted by capitalization (Hsu & Campollo, 2006). Hemminki & Puttonen (2007) replicated the study of Arnott et al. (2005) in the European indices market by creating a fundamentals based DJ Euro Stoxx 50 index and comparing this to the capitalization-weighted DJ Euro Stoxx 50 index over the period (the shortened period was due to data availability). The findings of Hemmeinki & Puttonen (2007) were very similar to the findings of Arnott et al. (2005), with the fundamental DJ Euro Stoxx 50 index outperforming the capitalization-weighted DJ Euro Stoxx 50 index by 1.76 percentage points per annum. Estrada (2008) performed a study for the period 1973 to 2005 of sixteen countries (including South Africa) to determine the optimum method of weighting country benchmarks when an investor decides to construct a global portfolio. Estrada (2008) found that although the fundamental based index outperformed the capitalization-weighted index over the period, by employing a simple equal-weighting method (i.e. assigning an equal amount of money amongst the sixteen countries) and a simple value strategy (using weighting by dividend yields) he could achieve even better results than the fundamental index. Estrada (2008) concluded that although fundamental indexation can deliver better results than capitalization weighted indexation, there are UCT Graduate School of Business - Research Report 2009 Page 17 of 148

18 other methods that can deliver even better results than fundamental indexation and it is up to the individual investor to decide how passive or active they wished to be and then employ the best method for that type of strategy. In South Africa, Ferreira (2009) performed a study over the period to determine whether a fundamental based portfolio (a RAFI All-Share Index) could outperform a capitalizationweighted portfolio (the FTSE/JSE All-Share Index). The study of Ferreira (2009) concludes that the fundamental based portfolio outperforms the capitalization-weighted portfolio, over the period, by 5.48 % p.a. with a standard deviation of 32.15% (compared to the capitalization-weighted portfolio standard deviation of 25.43%) and a lower turnover (to the capitalization-weighted portfolio). The study (Ferreira, 2009) showed similar results to the study by Arnott et al. (2005) whereby there were periods in which the capitalization-weighted method outperformed the fundamental indexation method, in this study the periods and This new method of indexing by fundamentals has been questioned by academics and investment professionals. Savage & De Groot (2006) argued that a wholesale replacement of capitalization- weighted indices is premature because of the bias towards value-based equities in fundamental indexation. Perold (2007) found fault with the theory of fundamental indexation by constructing a two equity market and, using the tenet principle of noisy market hypothesis that investors are uninformed about the true value of the equity, shows that, provided there is randomness in the over/under valuation of the two equities, capitalization weighting and equal weighting produce the same returns. Perold (2007) concluded, and agreed with Asness (2006), Bogle & Malkiel (2006) that although fundamental indexation has resulted in higher returns than capitalization-weighted indexation it is really only due to there being a value bias in the make-up of that index which can only be as a result of risk or mispricing. Perold (2007) argued that if it is risk, then risk-adjusted returns of fundamental indexation will actually be less than capitalization-weighted indexation and if it is due to mispricing, the fundamental index is relying on a pattern continuing and not being picked up by other investors to fully exploit the value tilt. Kaplan (2008) continued the work of Perold (2007) in disproving the theoretical models upon which fundamental indexation is based by demonstrating that the mathematics and assumptions behind the theory are not logical and cannot be used as a basis to support the empirical evidence of fundamental indexation outperforming capitalization weighted indexation. Kaplan (2008) created a theoretical model which illustrated that UCT Graduate School of Business - Research Report 2009 Page 18 of 148

19 errors in valuation must be more variable than fair value multiples (the number which links the unobserved fair value of an equity with the observed measure of the equity s fundamental value) for fundamental indexation to outperform capitalization-weighted indexation. There have also been empirical studies performed to disprove the theory that fundamental indexation is a superior indexing technique. Most notably, Jun & Malkiel (2007) presented a case against the movement away from capitalization weighted indices to fundamental indices by proving that weighting using fundamentals favours under-valued and small-cap equities and this is the reason for the current success of fundamental indexation. They argued that fundamental indexation is not new but just a repackaging of ideas that have been in academic literature for years (Jun & Malkiel, 2007, p.120). Jun & Malkiel (2007) regressed the results of the RAFI, in the United States during the period , against the three Fama-French risk factors and established that these factors returned very high R 2 s (in the order of 0.93 to 0.97 dependant on the period) and that the α s (the measure of excess return over and above the return explained by risk) were zero. Based on these results, Jun & Malkiel (2007) concluded that the superior results were explained by the factors rather than fundamental indexation choosing the best equities. Jun & Malkiel (2007) further managed to outperform the RAFI over the period by composing a simple portfolio of Exchange Traded Funds containing the same factor tilts (i.e., funds favouring small-cap equities and value-based equities) further enhancing their theory that fundamental indexation is not a new revolution in finance theory but simply a re-working of old ideas. Blitz & Swinkels (2008) performed a similar analysis to Jun & Malkiel (2007) by regressing the RAFI 1000 Index against traditional capitalization weighted indices and, using the Fama-French three factor model, found that once the value premium is removed there is very little added benefit of fundamental indexation over traditional capitalization weighted indexation. Blitz & Swinkels (2008) concluded that fundamental indexation has a slight benefit over other value-based strategies but underperforms compared to more sophisticated quantitative strategies and that it is not a truly passive strategy because of the constant rebalancing required which makes it more of a managed fund than a true index. The debate has mainly been between the two opposing methodologies, capitalization weighted versus fundamental indexation. However, Arya & Kaplan (2006) sought out a compromise method which wanted to combine the best of both capitalization weighted indexation and UCT Graduate School of Business - Research Report 2009 Page 19 of 148

20 fundamental indexation known as the collar weighted approach. In the collar weighted approach, the fundamental weight (multiplied by a collar multiplier) of the individual equity would determine the upper and lower bounds of the index weight assigned to that individual equity and only if the market capitalization weight of that individual equity was greater or less than the fundamental bounds would that individual equity be assigned the fundamental bound (Arya & Kaplan, 2006). The study by Arya & Kaplan (2006), over the period of the Morningstar US Market Index (97% of the total market capitalization of the United States equity market), found that they could avoid the over-exuberance and later crash of the technology stock bubble during and the sector distribution was more even than using a straight capitalization weighted index. The total return of the collar-weighted index was 8.01% p.a. compared to the fundamental index return of 9.07% p.a. but then the results were much closer (7.19% p.a. for the collar-weighted index versus 7.81% p.a. for the fundamental index) when costs were included resulting in a better medium between fundamental and capitalization-weighted indexing by reducing the overall risk in the long run (Arya & Kaplan, 2006). This illustrated that there was a third option that could be employed that could harness the benefits of both the capitalization-weighted indexation and fundamental indexation methods. 2.2 Conclusion There is no study, theoretical or empirical, which can prove that fundamental indexation will always outperform capitalization-weighted indexation. In fact all of the empirical studies highlight the fact that there will be periods in which fundamental indexation underperforms against capitalization-weighted indexation. The literature demonstrates that although the capitalizationweighted method is not perfect in the way it weights equities, neither is the fundamental-weighted indexing method. Because of the nature of construction, capitalization-weighted indexing is seen as having a growth bias and fundamental indexing is seen as having a value bias. Savage & De Groot (2006) state that because the market moves in cycles, there will be a point where growth-based equities are favoured again and only investor specifically looking for value-based equities should purchase fundamental indexed funds. Finally, as both methodologies have periods of underperformance, there is a third methodology, a collar-weighted approach to indexing, which can be utilized to obtain results very similar to the results from fundamental indexation, avoiding any over-exuberance during stock market bubbles whilst achieving a more evenly distributed weighting. UCT Graduate School of Business - Research Report 2009 Page 20 of 148

21 3 RESEARCH METHODOLOGY 3.1 Research Approach and Strategy This research was quantitative and deductive in nature. No qualitative data or variables were needed to fulfil this research. This research investigated the various measures of success of the three different strategies, viz., performance (measured via return, risk and risk-adjusted return), turnover and concentration. 3.2 Research Design, Data Collection Methods and Research Instruments The research compared the results of three different types of portfolio constructions over a period of 7 years and can therefore be seen as comparative longitudinal research. To create the three types indices (market capitalization, fundamental and collar weighted) the following information was required: Monthly closing share price of each share in the index Month end number of shares in issue of each share in the index Month end free-float factor (degree to which issue shares can be traded) of each share in the index Month end value of dividends paid (and type) of each share in the index Book Value of each share in the index Annual Dividends paid of each share in the index Annual Sales of each share in the index Annual cash Flow of each share in the index Monthly closing share prices and value of monthly dividend payout were collected from I-Net Bridge. To ensure the effect on an index due to changing number of shares and free float factor is minimised, the number of shares in issue were only updated when the change exceeded 1% between quarters or 10% on a cumulative basis (Immelman, 2004). If a change took place, between quarters, which exceeded these values, it was automatically enforced and an Index Change Announcement (ICA) was issued. To ensure the capitalization weighted index replicated the FTSE/JSE All-Share Index as closely as possible, the month end number of shares in issue and month end free-float factor were collected from the Index Department of the Johannesburg JSE. These figures are published on a quarterly basis on the JSE website. All changes to the number of UCT Graduate School of Business - Research Report 2009 Page 21 of 148

22 shares in issue and free-float changes were updated in accordance with the published ICAs. The Book Value, Dividends paid, Sales and Cash Flow were collected from I-Net Bridge (from the published Annual Financial Statements). If the information was not available on I-Net or the I-Net data did not go back far enough at the point of a share entering the index, BFA-McGregors was used. Had a similar situation arisen with data from BFA-McGregors, the annual reports (on the company websites) were used. If the data was not available on either of these the three sources then that company was excluded from this study. The collar weights was a multiplication of the fundamental weight and the collar multiplier and, therefore, no further data collection was required to calculate a collar weighted index. Both listed and de-listed companies formed part of this research. All information was freely available. The construction of each of the indices is detailed in section 3.5. Ferreira (2009) uses the following definitions for Book Value, Dividends, Sales and Cash Flow: Book Value Ferreira (2009) defines Book Value as ordinary shareholder s capital plus non-distributable reserves plus distributable reserves. Dividends Arnott et al., (2005) define dividends as cash dividends paid out which is the same definition applied by Ferreira (2009) and will be utilised as the definition in this research. The dividends was the total dividends paid out over the 12 month period. As per Immelman (2004) only interim and final dividends are included and extra-ordinary or special dividends do not form part of the annual dividends paid for the year. Sales Ferreira (2009) defined sales as interest earned on deposits for banks, real estate investment trusts, investment trusts and investment trusts and premiums earned as the measure of sales for insurance companies. For all other companies sales were defined as turnover. Cash Flow Ferreira (2009) defined cash flow as profit before depreciation plus taxation plus extraordinary profits. These are the same as defined by FTSE (2008) with the exception of sales, which is not prescriptively defined for financial institutions. It is important to note that in keeping with the exact UCT Graduate School of Business - Research Report 2009 Page 22 of 148

23 FTSE/JSE methodology, if a company had a secondary line (e.g. Grindrod and Grindrod-N) which also formed part of the index, the above fundamental data was split in relation to market capitalization (FTSE, 2008). 3.3 Sampling No sampling was required as the whole population of eligible companies that were a constituent of the JSE All-Share Index during the period January 2002 to January 2009 were utilised for the purpose of this research. The starting point of January 2002 was chosen as the free-float factor data was only freely available from January 2002 and the cost to obtain the retrospective data (from 31 July 1995) was outside the scope of this study. Pawley (2006, p. 21) defines survivorship bias as...the tendency to exclude failed companies from performance studies simply because they no longer exist. To ensure survivorship bias did not affect this research all de-listed companies were included as part of the data set. If a company was deleted (or added in the case of the marketcapitalization index only), the divisor (d) was altered to ensure the index value remained unaltered. 3.4 Research Criteria There are four indicators that were used to determine the stated hypotheses, viz., return, volatility turnover and concentration. Return was measured according to the methods of other researchers in the investments field. Volatility was measured using a normal standard deviation approach. Turnover is a measure of the percentage of equities that are replaced at any given re-balancing point. Concentration is the percentage weighting of a number of shares or of a sector. This type of measurement has been used in previous studies, most notably Ferreira (2009) and Arnott et al 2005). Finally, the determination of the collars was measured using the same methods employed by previous researchers in the area of collar weighted indexing. 3.5 Data Preparation FTSE/JSE (2009) defines the All-Share Index (JSE Code J203) as the top 99% of all entities on the Main JSE Board by total market capitalization (i.e., before a free-float factor is applied). FTSE/JSE (2009) states that these then make up the Large Capitalization Index (JSE Code - J200 and also know as the JSE Top 40), the Middle Capitalization Index (JSE Code - J201) and the Small Capitalization Index (JSE Code - J202). Any equity that formed part of these indices during UCT Graduate School of Business - Research Report 2009 Page 23 of 148

24 the period of this study was included. When they were excluded from these indices they were excluded from the indices of this study. The following steps were used to prepare the data: 1. Download the constituents for the period by assessing which constituents on the Main Board of the JSE formed part of J Download the number of shares in issue of each of the constituents at the beginning of the period. 3. Download the free float factor of each of the constituents at the beginning of the period 4. Download the following from the most recent annual financial statements for that period: Average book value of the last 5 years or the average book value of the preceding number of years if less than 5 years is available Average dividends of the last 5 years or the average dividends of the preceding number of years if less than 5 years is available Average sales of the last 5 years or the average sales of the preceding number of years if less than 5 years is available Average cash flow of the last 5 years or the average cash flow of the preceding number of years if less than 5 years is available 5. Calculate the weights for each of the indices. 6. Set the initial capital index value and total return index for that period. The actual J203 will be used initially for the capital index and a value of 1000 will be used for the total return index. Thereafter, it will be the closing value on 31 January of the following year, before the rebasing takes effect. 7. Calculate the divisor. 8. Repeat steps 1 and 2 for the rest of the months of the period. 9. Calculate the new capital index and total return index for each month. 10. Adjust the divisor if there are deletions or additions (for the market capitalization index only). 3.6 Capital Index (CI) Creation To calculate any of the measures it is necessary to calculate the market capitalization weights, fundamental weights, fundamental adjustment factor, collar weights, collar adjustment factor, UCT Graduate School of Business - Research Report 2009 Page 24 of 148

25 market capitalization weighted index, fundamental index and collar-weighted index. The calculations used are stated below. Market Capitalization Weight The market capitalization percentage (weight) of a stock i was calculated as follows (Immelman, 2004): Market Capitalization Weight i = (p i *e i )*s i *f i / n ((p i *e i )*s i *f i ) Where:n= Number of securities in the Index (this number will be determined by the qualification criteria set out in section 3.2) p= Price: The latest trade price of the component security (or the price at the close of the Index on the previous day). e= Exchange Rate: The exchange rate required to convert the security s home currency in to the index s base currency. s= Shares in issue: The number of shares in issue used by the FTSE/JSE for the security, as defined in the ground rules. f= Free float factor: The factor to be applied to each security to allow amendments to its weighting, expressed as a number between 0 and 1 where 1 represents 100% free float. The free float factor for each security is published by the FTSE/JSE. As not all shares in an equity are available for purchase because some shares are locked in (employee share options, family/trust control, etc.) a free float factor was used to reflect a more accurate availability of shares for purchase (FTSE, 2008b). Market Capitalization Index The standard market capitalization weight index calculation (Immelman, 2004, p. 22) was used to calculate the Index and market capitalization weights: Index = n ((p i *e i )*s i *f i )/d {for i = 1,2,3...n} Where:n= Number of securities in the Index (this number will be determined by the qualification criteria set out in section 3.2). UCT Graduate School of Business - Research Report 2009 Page 25 of 148

26 p= Price: The latest trade price of the component security (or the price at the close of the Index on the previous day). e= Exchange Rate: The exchange rate required to convert the security s home currency in to the index s base currency. s= Shares in issue: The number of shares in issue used by the FTSE/JSE for the security, as defined in the ground rules. f= Free float factor: The factor to be applied to each security to allow amendments to its weighting, expressed as a number between 0 and 1 where 1 represents 100% free float. The free float factor for each security is published by the FTSE/JSE. d= Divisor: A figure that represents the total issued share capital of the Index at the base date. The divisor can be adjusted to allow changes in the issued share capital of individual securities without changing the Index. The divisor was calculated at the beginning by setting the Index Value equal to a reference at the opening period and solving the above equation for the divisor. Once set the divisor does not change when calculating the Index Value at different periods, except for additions, deletions and changes to the adjustment factors. Although the study of Ferreira (2009) had an annual rebasing with no additions allowed during each period, this study allowed additions to the market capitalization index as the actual FTSE/JSE All-Share Index follows the same rules. Fundamental Value Before creating the Fundamental Index it is necessary to create a Fundamental Value (r i ) for each security. To calculate the Fundamental Value (r i ) for each security, the following methodology was used (FTSE, 2008c, p. 2): Step 1: Choose an index universe. In this research, all equities that meet the qualification criteria as set out in section 3.2 will form part of the index universe. Step 2: Calculate each security s percentage representation of the universe using only sales values (average of the previous 5 years or the available preceding years if less than 5 years of sales values is available). UCT Graduate School of Business - Research Report 2009 Page 26 of 148

27 Step 3: Calculate each security s percentage representation of the universe using only cash flow values (average of the previous 5 years or the available preceding years if less than 5 years of cash flow values is available). Step 4: Calculate each security s percentage representation of the universe using only book values (average of the previous 5 years or the available preceding years if less than 5 years of book values is available). Step 5: Calculate each security s percentage representation of the universe using only dividend values (average of the previous 5 years or the available preceding years if less than 5 years of dividends values is available). Step 6: A Company s Fundamental Value is defined as the average of the four percentage values (three in the case of companies not paying dividends) multiplied by In this study, was used instead to render the calculation more manageable. The value is a nominal value. Step 7: Rank the companies according to their Fundamental Values and place the cut-off at the relevant number of the index. In this research, no cut-off value is used as all the equities in the universe form part of data. Fundamental Weight The fundamental weight of a security i was calculated as follows (Ferreira, 2009): Fundamental Weight i = Fundamental Value i /( n Fundamental Value 1 to n ) Fundamental Adjustment Factor To create a Fundamental Index the following formula was used (FTSE, 2008, p ): Where r i c i = FTSE/RAFI adjustment factor (adjusted annually) = r i *f i /((p i *e i )*s i *f i ) = RAFI Fundamental Value Note that the fundamental adjustment factor was only altered annually on the rebasing date (the 31 st of January of the following period). Fundamental Index To create a Fundamental Index the following formula was used (FTSE, 2008, p ): Index = n ((p i *e i )*s i *f i *c i )/d for i = 1,2,3...n UCT Graduate School of Business - Research Report 2009 Page 27 of 148

28 Collar Weight To calculate the collar weight an upper and lower boundary are set (Arya & Kaplan, 2006). Arya & Kaplan (2006) used an upper and lower boundary as 0.5*Fundamental Weight and 2*Fundamental Weight. These values will also be utilised in this research. Van Rensburg & Roberston (2003) found that in 2002, the Top 5 shares (by market capitalization) account for 50% of the market capitalization of the JSE. Ferreira (2009) states that the South African equities market is very concentrated in comparison to other international markets finding that the Top 10 shares account for above 55% of the total JSE market capitalization over the period 2000 to The RAFI weights were very similar to the market capitalization weights (Ferreira, 2009). For this reason, it was decided to create two collar weighted indices, viz., one which used the collar weights as proposed by the Arya & Kaplan (2006) study (denoted Collar Weighted Original) and a second which used tighter collars of 1.5*Fundamental Weight for the upper boundary and 0.75*Fundamental Weight for the lower boundary (denoted Collar Weighted Adjusted), to avoid the collar weight being a replica of the market capitalization weights. The calculation to determine the weight of each security (Arya & Kaplan, 2006, pp ) was as follows: Copyright Let UCT N = number of stocks in the index (this number will be determined by the qualification criteria set out in section 3.2) x i = the market weight of the stock i, n x i = 1 w i = the fundamental weight of the stock i, n w i = 1 L = the lower bound of the ratio of a stock s collar weight to its fundamental weight U = the upper bound of the ratio of a stock s collar weight to its fundamental weight z i (L,U) = the collar weight for a stock i, for given values of L and U as defined in equation (1) below Z(L,U) = the sum of the collar weights given values of L and U We have z i (L,U) = Lw i if x i < Lw i x i if Lw i < x i < Uw i Uw i if x i > Uw i (1) UCT Graduate School of Business - Research Report 2009 Page 28 of 148

29 and Z (L,U) = n z i (L,U) (2) We need for Z(L,U) = 1 (3) Let L 0 U 0 = Proposed value of L = Proposed value of U We select a value of U 0 > 1 and set L 0 = 1/U o (4) If Z(L 0,U 0 )>1, we set U=U 0 and solve equation (3) for L. If Z(L 0,U 0 ) <1, we set L=L 0 and solve equation (3) for U. Arya & Kaplan (2006) do not state the methodology used in creating the collar weighted index, they only describe the results, i.e., average returns. It was proposed to follow the same methodology of creating a fundamental index as proposed by Ferreira (2009), to create a collar weighted index. Collar Weighted Value Before creating the Collar Weighted Index it was necessary to create a Collar Weighted Value (x i ) for each security. To calculate the Collar Weighted Value (x i ) for each security, a similar method to that of the methodology to create the fundamental value (Ferreira, 2009) was employed: Step 1: Choose an index universe. In this research, all equities that meet the qualification criteria as set out in section 3.2 will form part of the index universe. Step 2: A company s Collar Weighted Value is defined as the collar weight multiplied by Step 3: Rank the companies according to their Collar Weighted Values and place the cut-off at the relevant number of the index. In this research, no cut-off value is used as all the equities in the universe form part of data. UCT Graduate School of Business - Research Report 2009 Page 29 of 148

30 Collar Weighted Adjustment Factor To create the Collar-Weighted Adjustment factor a similar formula to FTSE (2008, p ) was utilised: Where z i = Collar-Weighted adjustment factor (adjusted annually) = x i *f i /((p i *e i )*s i *f i ) Where x i = Collar-Weighted Value Note that the collar-weighted adjustment factor is only altered annually on the rebasing date (the 31 st of January of the following period). Collar Weighted Index To create the Collar-Weighted Index a similar formula to FTSE (2008, p ) will be utilised: Index = n ((p i *e i )*s i *f i *z i )/d for i = 1,2,3...n There will be anomalies during each period if there are changes to the constituents. According to the methodology laid out in FTSE (2008) and FTSE/JSE (2009), changes to the constituent equities had the following impact: Additions The constituent was included at the next annual rebasing for the fundamental index and two collar weighted indices, however, to ensure the exact replication with the rules for market-capitalization indices used by the JSE, additions were allowed throughout the period for the market-capitalization index. Deletions The constituent was removed immediately from the index universe. The index value was held constant and the divisor (d) was recalculated to ensure the same index value before and after the deletion. Splits/Demergers The constituents were retained in the index universe with the same adjustment factor as the parent company. The adjustment factor was changed at the next annual rebasing. UCT Graduate School of Business - Research Report 2009 Page 30 of 148

31 Mergers /Take-overs between constituents (by issuing of shares only) The constituent being acquired was deleted and a new adjustment factor was calculated. The index value was held constant and the divisor (d) was recalculated to ensure the same index value before and after the merger/take-over. Mergers /Take-overs between constituents (by issuing of shares and cash) The constituent being acquired was deleted and a new adjustment factor (by taking out the cash component) was calculated. The index value was held constant and the divisor (d) was recalculated to ensure the same index value before and after the merger/take-over. Mergers /Take-overs between a constituent and non-constituent (issuing of shares or shares and cash) The new combined entity was included and a new adjustment factor was calculated only if the fundamental value was available for the non-constituent otherwise the constituent s adjustment factor was used until the next annual rebasing. The index value was held constant and the divisor (d) was recalculated to ensure the same index value before and after the merger/take-over. Mergers /Take-overs between a constituent and non-constituent (issuing of cash only) If cash was involved, both the constituent and non-constituent did not form part of the index universe. The index value was held constant and the divisor (d) was recalculated to ensure the same index value before and after the merger/take-over. 3.7 Total Return Index (TRI) Creation To ensure that a truer reflection is obtained about the actual performance, dividends were assumed to be re-invested and total return index were calculated. The Total Return Index was calculated as follows (Immelman, 2004, p. 10): TRI n+1 = TRI n * (CI n+1 /[CI n xd]) Where the ex-dividend adjustment (xd) is calculated as follows (Immelman, 2004, p. 9): xd = (Dividends per Share*Free Float*Number of Shares)/Divisor For the fundamental index and the two collar weighted indices, the xd adjustment for a share was adjusted by the ratio of the index weight for that share to the market capitalization weight of that share. This is in-line with the methodology presented by Ferreira (2009). UCT Graduate School of Business - Research Report 2009 Page 31 of 148

32 3.8 Data Analysis Methods A Collar Weighted Approach to Indexing in the South African Equities Market The following steps were utilised to create the initial capital index values: Creation of the Market Capitalization Index 1. Obtain the share price, number of shares, free float factor and past 5 years financial statements for each equity. 2. Calculate the market capitalization of each equity. 3. Set the initial value of the index. 4. Calculate the divisor (d) which will be used throughout the period (unless there are changes) by dividing the total market capitalization by the initial index value. Creation of the Fundamental Capital Index 1. Using the four "fundamentals" calculate the % constitution of each equity of the fundamental portfolio. 2. Calculate the Fundamental Value of each equity. 3. Calculate the Fundamental Adjustment Factor for each equity. Note that this value is changed only once per year. 4. Calculate the "RAFI Capitalization of each equity (p*s*f*c) and sum. 5. Set the initial value of the index the same as the Market Capitalization Index. 6. Calculate the divisor (d) which will be used throughout the period (unless there are changes) by dividing the total "RAFI Capitalization" by the initial index value. Creation of the Collar Weighted Capital Indices 1. Calculate the Upper Collar (U) and the Lower Collar (L). 2. Calculate percentage constituent of each equity. 3. Repeat sub-steps 1) and 2) to ensure that all constituent weights equal 100%. 4. Calculate the Collar-Weighted Value per equity. 5. Calculate the Collar Weighted Adjustment Factor per equity. 6. Calculate the "Collar Weighted Capitalization" of each equity (p*s*f*z) and sum. 7. Set the initial value of the index the same as the Market Capitalization Index. 8. Calculate the divisor (d) which will be used throughout the period (unless there are changes) by dividing the total "Collar Weighted Capitalization" by the initial index value. UCT Graduate School of Business - Research Report 2009 Page 32 of 148

33 The following steps were used to calculate the monthly capital index values: Market Capitalization Capital Index 1. Obtain the monthly closing share price, monthly free float factor and monthly closing number of shares in issue for each equity. 2. Calculate the market capitalization of each equity. 3. Calculate the Market Capitalization Index. 4. Repeat sub-steps 1) to 3) on a monthly basis. Fundamental Capital Index 1. Obtain the monthly closing share price, monthly free float factor and monthly closing number of shares in issue for each equity. 2. Calculate the "RAFI Capitalization" of each equity using the monthly closing share price, monthly free float factor, monthly closing number of shares in issue and the fundamental adjustment factor for that period (i.e. year) 3. Calculate the Fundamental Index. 4. Repeat sub-steps 1) to 3) on a monthly basis. Collar-Weighted Index 1. Obtain the monthly closing share price, monthly free float factor and monthly closing number of shares in issue for each equity. 2. Calculate the "Collar Weighted Capitalization" of each equity using the monthly closing share price, monthly free float factor, monthly closing number of shares in issue and collarweighted adjustment factor for that period (i.e. year). 3. Calculate the Collar-Weighted Index. 4. Repeat sub-steps 1) to 3) on a monthly basis. The following steps were required when rebasing the indices on an annual basis: Creation of the Market Capitalization Index 1. Obtain the share price, number of shares, free float factor and past 5 years financial statements for each equity. 2. Calculate the market capitalization of each equity. 3. Set the new value of the index. 4. Calculate the divisor (d) which will be used throughout the period (unless there are changes) by dividing the total market capitalization by the initial index value. UCT Graduate School of Business - Research Report 2009 Page 33 of 148

34 Creation of the Fundamental Index 1. Using the four "fundamentals" calculate the % constitution of each equity of the fundamental portfolio. 2. Calculate the Fundamental Value of each equity. 3. Calculate the Fundamental Adjustment Factor for each equity. Note that this value is changed only once per year. 4. Calculate the "RAFI Capitalization of each equity (p*s*f*c) and sum. 5. Set the new value of the index the same as the last value. 6. Calculate the divisor (d) which will be used throughout the period (unless there are changes) by dividing the total "RAFI Capitalization" by the initial index value. Creation of the Collar Weighted Index 1. Calculate the Upper Collar (U) and the Lower Collar (L). 2. Calculate percentage constituent of each equity. 3. Repeat sub-steps 1) and 2) to ensure that all constituent weights equal 100%. 4. Calculate the Collar Weighted Value per equity. 5. Calculate the Collar Weighted Adjustment Factor per equity. 6. Calculate the "Collar Weighted Capitalization" of each equity (p*s*f*z) and sum. 7. Set the new value of the index the same as the last value. 8. Calculate the divisor (d) which will be used throughout the period (unless there are changes) by dividing the total "Collar Weighted Capitalization" by the initial index value. A value of was used at the starting point, in this study, for the Capital Index of all four created indices as it was the actual J203 closing value for January The Total Return Index opening value for this study was set at 1000 for all four indices. The return, turnover and sector distribution were calculated for each period. 3.9 Criteria Measurement Return Return was calculated by determining the return for each period and the compounded annual return of the period for each of the four indices. Periods within the annual periods that are of significance were also highlighted. UCT Graduate School of Business - Research Report 2009 Page 34 of 148

35 Return was calculated as follows: A Collar Weighted Approach to Indexing in the South African Equities Market Return = [(Closing Index Value Opening Index Value)/Opening Index Value]*100% Geometric Return was determined as: Geometric Return = [ n (1 + i n )] 1/n 1 Where n = number of periods i = return for a period Risk Risk was measured by determining the annual standard deviation of returns of each of the three indices. Risk-Adjusted Return The Sharpe Ratio was used to determine the risk-adjusted return. The Sharpe Ratio is defined as (Sharpe in Ferreira, 2009, p. 63): SharpeRatio = (R p r f )/σ p Where R p r f σ p = the average portfolio returns = the risk free rate = the portfolio s standard deviation Based on Firer, Ross, Westerfield & Jordan s (2004) argument that the truest risk-free rate to use is the 90 day T-bill as it is more consistent with the intent of the CAPM, this research used the three month treasury bill rate as posted by the South African Reserve Bank. Turnover Banerjee (2009) states that, the lower of disposals and purchases divided by the average portfolio assets under management, during that period is defined as portfolio turnover. This was the methodology employed in this study. UCT Graduate School of Business - Research Report 2009 Page 35 of 148

36 Effective Number of Shares (N) Strongin, Petsch and Sharenow (2000) define the effective number of shares (N) as the number of shares that would have to be held by an equally weighted index to ensure it was as diversified as the portfolio being analysed. The larger the number, the more diversified the portfolio. It is calculated as follows (Strongin et al, 2000, p. 17): N = 1/w 2 Where w = weight of each individual share Concentration An effective but simple measure of concentration is to determine the percentage weight held by a certain number of shares. For this study, the categories of shares were the same as that of Ferreira (2009), viz., the Top 3, the Top 5 and the Top 10. Sector Distribution Resources have a large market capitalization on the JSE even though they contribute to less than 10% of South Africa s GDP (Kantor & Sessions, 2008). A study by Kantor & Sessions (2008) determined that although the output was low, the value of mining was still high leading to South Africa still being a commodity economy. It is therefore important to determine the sector composition and the degree to which the sector composition changes during changing market conditions. The distribution amongst the JSE sectors will be determined on an annual basis. The percentage that the index holds of each of the sectors was determined as follows: Sector Percentage = n (w i *Market Capitalization i )/Total Market Capitalization for i = {1,2,3,...n) Where: n= number of equities in that sector that form part of the index universe w = constituent weight based on the approach (i.e., market capitalization, fundamental or collar weighted) UCT Graduate School of Business - Research Report 2009 Page 36 of 148

37 4 RESEARCH FINDINGS, ANALYSIS AND DISCUSSION 4.1 Research Findings This section will detail the results obtained using the four different indices, viz., market capitalization weighted, fundamentally weighted and the two collar-weighted indices. The aim will be to demonstrate whether a collar weighted approach to indexing has better performance (i.e., higher returns), a lower risk profile with lower turnover and a more evenly spread concentration in a South African context. As detailed previously, this study contains all entities that were constituent of the JSE All-Share Index during the period January 2002 to January The total number of constituents during this period was 273. The fundamental index requires the fundamental data for at least the year preceding which it becomes part of the index. This was not possible for all the constituents as both I-Net and BFA-McGregors remove the pre-listing financial information upon listing. In these cases, those constituents were removed from the study to ensure consistency between indices. The companies (with their associated I-Net short codes in brackets) that were removed from the study are as follows: Copyright African Rainbow Minerals Gold Limited (AODX) UCT Diversified Property Fund Limited (DIVX) Emira Property Fund (EMI) Freestone Property Holdings Limited (FSPX) ifour Property Holdings Limited (IFRX) Makalani Investments Limited (MKL) Resilient Property Income Group (RES) SA Retail Properties Limited (SRLX) Vukile Property Fund Limited (VKE) Following the unbundling from Remgro (REM) and Reinet Investements (REI) of the British American Tobacco (BTA) shares, it was listed on 28 October 2008 (effective in November 2008 for the purposes of this study). However, on 12 November 2008, it was de-listed because it did not meet the listing requirements as it is classified as an inward foreign listing. As this study investigates the monthly changes in indices it was not included as it would have to be added and deleted in November 2008 creating a null effect on the monthly index. UCT Graduate School of Business - Research Report 2009 Page 37 of 148

38 As a result of the above, the total universe of constituents totalled 263 for the period of this study. Their weightings, in each of the four indices, at the beginning of each 7 year period (9 point of rebasing) can be seen in Appendices 1 to 8. The research findings will compare the four constructed indices in the different areas of performance, risk, turnover and concentration. A final section, sector composition, has been added to demonstrate the composition make-up of each of the indices in the 10 main economic group classifications of the JSE. Throughout this section a year period denotes 31 January of that year to 31 January of the following year (e.g., 2002 denotes 31 January 2002 to 31 January 2003) as this study begins with the closing values of January It was hoped that this study would replicate the results of Arya & Kaplan (2006) but during this study interesting nuances were picked up which could be attributed to the difference in markets between the studies. It was also an aim of this study to extend further the work of Ferreira (2009) which ended the study on 31 December 2006 to ascertain the effect of the severe downturn in the markets following the international credit crisis of Effect of Collaring Table 1 demonstrates that during the first years of the study, the amount of collaring was high using the original collars proposed by Arya & Kaplan (2006) and the adjusted collars discussed in section 3.6. As the period of the study progressed, the amount of collaring decreases with the exception of the adjusted collaring in 2008, where there is an increase. This is as expected as under normal market conditions, there is little need for collaring and only extreme market conditions (2002 and 2008 in the South Africa) would there be a need for collaring (Arya & Kaplan, 2006). Table 1: Effect of Collaring Large Cap Mid Cap Small Cap Overall Original 35.00% 40.00% 55.17% 44.30% Adjusted 80.00% 76.67% 70.69% 75.32% Original 27.50% 46.67% 59.68% 46.91% Adjusted 50.00% 70.00% 77.42% 67.90% Original 40.00% 41.67% 40.32% 40.74% Adjusted 65.00% 58.33% 67.74% 63.58% Original 32.50% 40.00% 40.00% 38.13% Adjusted 57.50% 55.00% 56.67% 56.25% Original 30.00% 28.33% 37.04% 31.82% Adjusted 70.00% 60.00% 57.41% 61.69% Original 20.00% 30.00% 44.83% 32.91% Adjusted 60.00% 55.00% 68.97% 61.39% Original 27.50% 33.33% 35.00% 32.50% Adjusted 67.50% 68.33% 70.00% 68.75% UCT Graduate School of Business - Research Report 2009 Page 38 of 148

39 4.1.2 Returns Capital Index The results of the performance can be seen in figure 3 which details the capital index values over the period of the study. All indices were started with the same index value of (which was the actual J203 index value on 31 January 2002). As can be seen in the figure below, the marketcapitalization weighted index (Market Cap) consistently returned the lowest values (with an ending value of ) and the fundamental index (RAFI) consistently returned the highest values (with an ending value of ). The outcome (i.e. the RAFI out-performing a Market Cap Index) is identical to that of Ferreira (2009), Estrada (2008), Hemminki & Puttonen (2007) and Arnott et al (2005) which all illustrated that a fundamental index outperforms a market-capitalization weighted index over time. The two collar weighted indices returned values in between the other indices, however the collar weighted index with the original collar values (Collar Weighted (Original)) returned values very similar to the Market Cap index. The Collar Weighted (Original) index ended with a value of and the Collar Weighted (Adjusted) index with a value of Figure 3: Monthly Capital Index 31 January 2002 to 31 January Index Value Jan-02 Apr-02 Jul-02 Oct-02 Jan-03 Apr-03 Jul-03 Oct-03 Jan-04 Apr-04 Jul-04 Oct-04 Jan-05 Apr-05 Jul-05 Oct-05 Jan-06 Apr-06 Jul-06 Oct-06 Jan-07 Apr-07 Jul-07 Oct-07 Jan-08 Apr-08 Jul-08 Oct-08 Jan-09 UCT Graduate School of Business - Research Report 2009 Page 39 of 148 Date Market Cap RAFI Collar Weighted (Original) Collar Weighted (Adjusted) J203

40 Table 2 gives a more detailed analysis as to the excess returns and compounded excess returns experienced by all four indices. As can be seen from the table, the RAFI index delivers the best annual returns in all the years (highlighted in green) and delivers the highest compounded return (highlighted in green). The compounded returns are not as significant as that of Ferreira (2009). However, this can be expected, given the different end-points of the two studies (one close to a market peak at the end of 2006 and one at the beginning of a market recovery following a serious downturn). The collar weighted returns deliver a return in between the Market Cap and RAFI indices however the Collar Weighted (Original) index delivers a return very similar to the Market Cap index (and even underperforms in 2004 and 2006) with only 0.58% excess return over the 7 year period. Table 2: Excess and Compounded Returns Capital Index Returns Total Return Index It is important to also ascertain what the effect of re-investing the dividends would be with regards to return. This gives a more comprehensive view of the return over the period of the study. Figure 4 illustrates that throughout the period, the RAFI index outperforms the other three indices. The results of the Total Return Index demonstrate an identical outcome to the Capital Index results with the RAFI index being the best performing index followed by the Collar Weighted (Adjusted) index, then the Collar Weighted (Original) index and finally, the Market Cap index. UCT Graduate School of Business - Research Report 2009 Page 40 of 148

41 The results were entirely expected and are identical to the study of Arya & Kaplan (2006) where the RAFI index had superior performance to the collar weighted and market capitalization approach. The study on Total Return Index was conducted over the same period but a starting point of 1000 was used as the Total Return Index is not a value that is disseminated by the JSE. Figure 4: Total Return Index 31 January 2002 to 31 January TRI Jan-02 Apr-02 Jul-02 Oct-02 Jan-03 Apr-03 Jul-03 Oct-03 Jan-04 Apr-04 Jul-04 Oct-04 Jan-05 Apr-05 Jul-05 Date Market Cap RAFI Collar Weighted (Original) Collar Weighted (Adjusted) Oct-05 Jan-06 Apr-06 Jul-06 Oct-06 Jan-07 Apr-07 Jul-07 Oct-07 Jan-08 Apr-08 Jul-08 Oct-08 Jan-09 Closer analysis (illustrated in Table 3) reveals that although the expectation is that throughout all of the 7-year periods the RAFI index should outperform the other three indices (based on the previous research mentioned in the section on capital index performance), the Collar Weighted (Adjusted) index does outperform the RAFI index (and the other two indices) in This is due to it achieving an excess return over the RAFI index (and the other two indices) for 7 of the 12 months of The Collar Weighted (Original) index also underperforms the Market Cap index on a total return basis in 2004 and In Table 3, the areas of highest yearly and compounded returns are, once again, highlighted in green and the areas of return below that of the Market Cap index are highlighted in red. UCT Graduate School of Business - Research Report 2009 Page 41 of 148

42 Table 3: Excess and Compounded Returns Total Return Index Risk One of the key research findings of Arya & Kaplan (2006) is that the standard deviation of the collar weighted approach is lower than that of a fundamentally weighted and market-capitalization weighted approach. This study demonstrates that in a South African context for the given period, the RAFI index has a lower standard deviation (based on annual returns) both on a capital and total returns basis. The standard deviations (based on monthly returns) of each of the 7 years during the period of this study reveal that no index offers a distinct advantage over the other indices. Table 4 and Table 5 reveal that through the periods 2002 to 2004 the RAFI index offers the lowest standard deviation (highlighted in green) after which the other indices also offer the lowest standard deviation. Further, there are years in which the Market Cap index has an advantage over the other indices with regards to lower risk, i.e., lower standard deviation (highlighted in red). UCT Graduate School of Business - Research Report 2009 Page 42 of 148

43 Table 4: Standard Deviations Capital Index Table 5: Standard Deviations Capital Index UCT Graduate School of Business - Research Report 2009 Page 43 of 148

44 4.1.5 Risk-Adjusted Return It is important to understand the returns generated for a level of risk. The Sharpe Ratio illustrates the amount of return generated above the risk free rate for a given level of risk. By doing so it indexes the risk portion so that portfolios with different levels of risk can be compared with a single factor (Opdyke, 2008). Table 6 and Table 7 demonstrate that the RAFI exhibits the highest Sharpe Ratios (both for the Capital Index and the Total Return Index). This is expected as the preceding sections detailed the RAFI exhibiting the highest returns and the lowest risk. Table 6: Sharpe Ratio Capital Index CAPITAL INDEX Average Return Risk Sharpe Ratio Market Cap Index 14.02% 28.46% 0.17 RAFI 16.45% 27.42% 0.27 Collar Weighted Index (Orginal) 14.56% 28.40% 0.19 Collar Weighted Index (Adjusted) 15.30% 27.97% 0.22 Table 7: Sharpe Ratio Total Return Index TOTAL RETURN INDEX Return Risk Sharpe Ratio Market Cap Index 17.52% 29.27% 0.29 RAFI 19.96% 28.10% 0.39 Collar Weighted Index (Org) 18.08% 29.19% 0.31 Collar Weighted Index (Adj) 18.83% 28.72% Turnover A key aspect of any portfolio is that turnover is low. The higher the turnover, the greater the costs involved in maintaining the correct weightings within the portfolio. Another disadvantage of a high turnover is that the portfolio requires a greater degree of active management. The reported benefits of indices are that, because they have low turnover, they are more passive and the cost in investing in them are lower (Ferreira, 2009). Even a market-capitalization index will require rebalancing as shares are added and deleted so it too does not have a zero turnover (Ferreira, 2009). Table 8 illustrates that, as expected, the Market Cap Index has the lowest average annual turnover (highlighted in green) and has the lowest turnover in 4 out of the 7 years (also highlighted in green). This is one of the benefits of a market-capitalization weighted index as it is self-rebalancing leading UCT Graduate School of Business - Research Report 2009 Page 44 of 148

45 to a low turnover (Arya & Kaplan, 2006). As can be seen in Table 8, the Collar Weighted indices have a higher turnover than the Market Cap index in all of the 7 years (highlighted in red), with the exception of the Collar Weighted (Adjusted) index which has a lower turnover than the Market Cap index in 2007 (incidentally the year in which it achieves the highest total return of the 4 indices). The study of Arya & Kaplan (2006) established that using a collar weighted approach, one could achieve a performance similar to a fundamental index but with a lower turnover. However, Table 8 demonstrates that in this study, the Collar Weighted indices do not have a lower turnover than the RAFI index during any period. Table 8: Annual Turnover Concentration The first measure of concentration is the effective number of shares (N). From Figure 5, it is demonstrated that in the years of negative market returns (2002 and 2008), the RAFI index has the highest number of effective shares (i.e., lower concentration) whereas in the interim years (2003 to 2007) the other indices have a higher effective number of shares. On average, the Collar Weighted indices have a higher effective number of shares (20 each) than the Market Cap and RAFI indices (both with 19). UCT Graduate School of Business - Research Report 2009 Page 45 of 148

46 Figure 5: Effective Number of Shares at Rebasing N Year of Rebasing Market Cap RAFI Collar Weighted (Original) Collar Weighted (Adjusted) Another finding that arose from this analysis is that the effective number of shares is lower when the percentage weighting of the index in Resources is higher. Table 9 shows that this phenomenon exists for all 4 of the indices. Table 9: Effective Number of Shares and Resources Weighting UCT Graduate School of Business - Research Report 2009 Page 46 of 148

47 The second measure of concentration is to determine the percentage weighting of the Top 3, Top 5 and Top 10 constituents of the indices. These percentages determine how much of an index is concentrated in the largest weighted constituents. The higher this percentage, the more the index is driven by these constituents and the more concentrated the index is. Table 10 illustrates that the average concentration for the Top 3 and Top 5 constituents is lowest in the Collar Weighted (Adjusted) index (highlighted in green) and for the Top 10 constituents it is lowest in the RAFI (highlighted in green). Table 10 also demonstrates that there is no particular index that has a dominant lowest concentration throughout the 7 year period nor in particular measure (Top 3, Top 5 or Top 10), although, in 2002 the RAFI has the lowest concentration amongst all the measures and in 2005 the Collar Weighted (Original) index has the lowest concentration amongst all the measures. Table 10: Concentration in a Number of Constituents Sector Composition In this study, there are three distinct periods, the first being the period 2002 to 2004 (the flat portion of the return graphs), 2005 to 2007 (the rising portion of the return graphs) and 2008 (the decreasing portion of the return graphs). Arya & Kaplan (2006) determined that the use of collars would provide a smoothing effect on sector composition during periods of extreme market conditions ( bubbles or downturns). The Resources sector is the largest sector of the JSE (by market capitalization) and the JSE index earnings being more representative of the commodities sector than GDP (Kantor & Sessions, 2008). Table 11 demonstrates that during the three periods, the difference in Resources allocation is least with the Collar Weighted (Adjusted) Index and most UCT Graduate School of Business - Research Report 2009 Page 47 of 148

48 with Market Cap Index between Period 1 and Period 2 and least with the RAFI and most with the Market Cap Index between Period 2 and Period 3. Table 11: Differences in Sector Composition Period 1 Period 2 Period 3 (Period 1 - Period 2) (Period 2 - Period 3) Market Cap 46.11% 42.12% 51.16% -3.99% 9.03% RAFI 39.14% 45.34% 44.69% 6.21% -0.66% Collar Weighted (Original) 44.48% 42.32% 50.57% -2.16% 8.25% Collar Weighted (Adjusted) 42.56% 43.43% 48.97% 0.87% 5.55% Period 1 = 2002 to 2004 Period 2 = 2005 to 2007 Period 3 = 2008 Figures 6, 7, 8 and 9 illustrate the monthly sector weighting in each of the ten economic groups of the JSE (see Appendix 9 for a full breakdown of the economic groups). At the start, the Market Cap Index has a very high Resources weighting but as the study progresses, the Resource weighting decreases as the Financials weighting increases but when market downturn of 2008 comes into effect, the weighting reverses towards Resources again. Copyright Figure 6: Sector Composition Market Cap Index UCT 100% 90% 80% 70% 60% (%) 50% 40% 30% 20% 10% 0% Jan-02 Apr-02 Jul-02 Oct-02 Jan-03 Apr-03 Jul-03 Oct-03 Jan-04 Apr-04 Jul-04 Oct-04 Jan-05 Apr-05 Jul-05 Oct-05 Jan-06 Apr-06 Jul-06 Oct-06 Jan-07 Apr-07 Jul-07 Oct-07 Jan-08 Apr-08 Jul-08 Oct-08 UCT Graduate School of Business - Research Report 2009 Page 48 of 148 Date Resources Basic Industries General Industries Cyclical Consumer Goods Non-Cyclical Consumer Goods Cyclical Services Non-Cyclical Services Financials Information Technology Utilities

49 The RAFI exhibits the opposite. At the start, the RAFI has a lower Resources weighting but as the study progresses it increases again decreases again during the market downturn of Figure 7: Sector Composition RAFI % 90.00% 80.00% 70.00% 60.00% (%) 50.00% 40.00% 30.00% 20.00% 10.00% 0.00% Copyright Date UCT Jan-02 Apr-02 Jul-02 Oct-02 Jan-03 Apr-03 Jul-03 Oct-03 Jan-04 Apr-04 Jul-04 Oct-04 Jan-05 Apr-05 Jul-05 Oct-05 Jan-06 Apr-06 Jul-06 Oct-06 Jan-07 Apr-07 Jul-07 Oct-07 Jan-08 Apr-08 Jul-08 Oct-08 Resources Basic Industries General Industries Cyclical Consumer Goods Non-Cyclical Consumer Goods Cyclical Services Non-Cyclical Services Financials Information Technology Utilities The two collar weighted indices exhibit a weighting in between the Market Cap Index and RAFI (as is expected) and display the smallest change between the distinctive market periods. UCT Graduate School of Business - Research Report 2009 Page 49 of 148

50 Figure 8: Sector Composition Collar Weighted (Original) Index 100% 90% 80% 70% 60% (%) 50% 40% 30% 20% 10% 0% Jan-02 Apr-02 Jul-02 Oct-02 Jan-03 Apr-03 Jul-03 Oct-03 Jan-04 Apr-04 Jul-04 Oct-04 Jan-05 Apr-05 Jul-05 Date Oct-05 Jan-06 Apr-06 Jul-06 Oct-06 Jan-07 Apr-07 Jul-07 Oct-07 Jan-08 Apr-08 Jul-08 Oct-08 Resources Basic Industries General Industries Cyclical Consumer Goods Non-Cyclical Consumer Goods Cyclical Services Non-Cyclical Services Financials Information Technology Utilities Figure 9: Sector Composition Collar Weighted (Adjusted) Index % 90.00% 80.00% 70.00% 60.00% (%) 50.00% 40.00% 30.00% 20.00% 10.00% 0.00% Jan-02 Apr-02 Jul-02 Oct-02 Jan-03 Apr-03 Jul-03 Oct-03 Jan-04 Apr-04 Jul-04 Oct-04 Jan-05 Apr-05 Jul-05 Date Oct-05 Jan-06 Apr-06 Jul-06 Oct-06 Jan-07 Apr-07 Jul-07 Oct-07 Jan-08 Apr-08 Jul-08 Oct-08 Resources Basic Industries General Industries Cyclical Consumer Goods Non-Cyclical Consumer Goods Cyclical Services Non-Cyclical Services Financials Information Technology Utilities UCT Graduate School of Business - Research Report 2009 Page 50 of 148

51 4.2 Research Analysis and Discussion This section will attempt to answer the 5 research hypotheses posed in Section 1 to determine if there is a difference between a collar weighted approach to indexing and a fundamental and market capitalization approach to indexing with respect to return, risk, turnover, concentration and sector composition and if there is a benefit to that difference Returns The first hypothesis aimed to determine if a collar weighted approach to indexing could deliver returns that are greater than a market capitalization approach and equal to a fundamental index approach. Table 2 and 3 illustrated that the highest returns were achieved by the RAFI with the Collar Weighted (Adjusted) Index achieving the second highest returns, then the Collar Weighted (Original) Index and finally the Market Cap Index.. A paired t-test was used to determine if the excess monthly return (over the Market Cap Index) of the two collar weighted indices was significant. In each case the hypothesis test is as follows: Copyright H 0 : The mean return of the Collar Weighted Index is not greater UCT than the mean return of the Market Cap Index H a : The mean return of the Collar Weighted Index is greater than the mean return of the Market Cap Index The equation for a paired t-test is as follows: t n 1 = x differences s differences n µ o Table 12 demonstrates that although the Collar Weighted (Original) Index has an excess return to the Market Cap Index it is not statistically significant as the t-statistic is with a p-value of and we accept the null hypothesis that the excess return is not significant.. However, the Collar Weighted (Adjusted) Index has an excess return to the Market Cap Index that is statistically UCT Graduate School of Business - Research Report 2009 Page 51 of 148

52 significant as the t-statistic is with a p-value of and we reject the null hypothesis that the excess return is not significant. Table 12: Paired t-test between the Collar Weighted Indices and the Market Cap Index Collar Weighted (Original) Market Cap Index Collar Weighted (Adjusted) Market Cap Index Mean Variance Observations Pearson Correlation Hypothesized Mean Difference 0 0 df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail A paired t-test was used to determine if the excess monthly return of the RAFI over the two collar weighted indices was significant. In each case the hypothesis test is as follows: H Copyright 0 : The mean return of the RAFI is not greater than the mean return of the Collar Weighted Index UCT H a : The mean return of the RAFI is greater than the mean return of the Collar Weighted Index The equation for a paired t-test is as follows: t n 1 = x differences s differences n µ o Table 13 demonstrates that the RAFI has an excess return to the Collar Weighed (Original) Index that is statistically significant as the t-statistic is with a p-value of and we reject the null hypothesis that the excess return is not significant. However, the RAFI has an excess return over the Collar Weighted (Adjusted) Index that is not statistically significant as the t-statistic is with a p-value of and we accept the null hypothesis that the excess return is not significant. UCT Graduate School of Business - Research Report 2009 Page 52 of 148

53 Table 13: Paired t-test between the Collar Weighted Indices and the RAFI RAFI Collar Weighted (Original) RAFI Collar Weighted (Adjusted) Mean Variance Observations Pearson Correlation Hypothesized Mean Difference 0 0 df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail This indicates that it is possible to achieve a return in excess of the market capitalization approach using a collar weighted approach to indexing. It further indicates that it is not possible to achieve a return greater than a fundamental index but that it is possible to achieve a return that is comparable to the fundamental index approach using a collar weighted approach to indexing Risk The second research hypothesis attempts to determine if the risk of the collar weighted indices is comparable to the risk of either a market-capitalization weighted index or a fundamentally- weighted index. An F-test was used to determine if the risk exhibited by either of the two Collar- Weighted indices was different than that of the Market Cap index. The hypothesis test in each case is as follows: H 0 : The variance of the Market Cap Index is the same as the variance of the Collar Weighted Index H a : The variance of the Market Cap Index is not the same as the variance of the Collar Weighted Index The equation for an F-test is as follows: F s 2 1 n 1 1, n 2 1 = 2 s2 Table 14 demonstrates that, although the variance of the two Collar Weighted indices is lower than the Market Cap index, the difference in standard deviation is not statistically significant (p-value UCT Graduate School of Business - Research Report 2009 Page 53 of 148

54 greater than 0.05 on a two-tailed test) and we accept the null hypothesis that the variance of the Market Cap Index is not greater than the variance of the Collar Weighted Index. Table 14: F-Test between Collar Weighted Indices and the Market Cap Index Market Cap Collar Weighted (Original) Market Cap Collar Weighted (Adjusted) Mean Variance Observations df F P(F<=f) one-tail F Critical one-tail P(F<=f) two-tail F Critical two-tail An F-test was used to determine if the risk exhibited by the RAFI was different than that of either of the two Collar-Weighted indices. The hypothesis test in each case is as follows: H 0 : The variance of the Collar Weighted Index is the same as the variance of the RAFI. H a : The variance of the Collar Weighted Index is not the same as the variance of the RAFI Copyright The equation for an F-test is as follows: UCT F s 2 1 n 1 1, n 2 1 = 2 s2 Table 15 demonstrates that, although the standard deviation of the two Collar Weighted indices is higher than the RAFI, the difference in standard deviation is not statistically significant (with a p- value greater than 0.05 on a two-tailed test) and we accept the null hypothesis that the variance of the Collar Weighted Index is not greater than the variance of the RAFI. Table 15: F-Test between Collar Weighted Indices and the RAFI Collar Weighted (Original) RAFI Collar Weighted (Adjusted) RAFI Mean Variance Observations df F P(F<=f) one-tail F Critical one-tail P(F<=f) two-tail F Critical two-tail UCT Graduate School of Business - Research Report 2009 Page 54 of 148

55 This indicates that, although the risk of the Collar Weighted indices is different to the Market Cap index and the RAFI, it is comparable as there is no statistical significance in the difference in variance Turnover The third research hypothesis attempts to determine if the turnover of the collar weighted indices is comparable to the risk of either a market-capitalization weighted index or a fundamentallyweighted index. Utts & Heckard (2007) state that where the number of observations is below 30 non-parametric testing techniques should be used to determine statistical validity. As there are only 7 observations for annual turnover, a Wilcoxon Signed Rank test was used to determine if the turnover of the Market Cap index was significantly different than that of the two Collar Weighted indices. In each case the hypothesis test is as follows: H 0 : The mean turnover of the Collar Weighted Index is the same as the mean turnover of the Market Cap Index H a : The mean turnover of the Collar Weighted Index is not the same as the mean turnover of the Market Cap Index The Wilcoxon Signed Rank test uses the following equation: positive ranks µ z = σ ( ) n n +1 where: µ = and σ = 4 n ( n +1 )( 2n + 1) 24 Table 16 demonstrates that the higher turnover of the Collar Weighted (Original) index compared to the Market Cap index is statistically significant with a t-statistic of and a p-value of and we reject the null hypothesis that the mean turnover of the Collar Weighted (Original) index is not greater than the mean turnover of the Market Cap index. UCT Graduate School of Business - Research Report 2009 Page 55 of 148

56 Table 16: Wilcoxon Signed Rank Sum Test for the Collar Weighted (Original) and Market Cap Indices - Turnover Wilcoxon Signed Rank Test Output Sample 7 Positive Ranks Sum 28 Negative Ranks Sum 0 Expected Value 14 Std Deviation z P-value (one tail) P-value (two tail) Table 17 demonstrates that the higher turnover of the Collar Weighted (Adjusted) index compared to the Market Cap index is statistically significant with a t-statistic of and a p-value of and we reject the null hypothesis that the mean turnover of the Collar Weighted (Original) index is not greater than the mean turnover of the Market Cap index. Copyright Table 17: Wilcoxon Signed Rank Sum Test for the Collar Weighted UCT (Adjusted) and Market Cap Indices - Turnover Wilcoxon Signed Rank Test Output Sample 7 Positive Ranks Sum 27 Negative Ranks Sum 1 Expected Value 14 Std Deviation z P-value (one tail) P-value (two tail) A Wilcoxon Signed Rank test was used to determine if the turnover of the RAFI was significantly different than that of the two Collar Weighted indices. In each case the hypothesis test is as follows: H 0 : The mean turnover of the Collar Weighted Index is the same as the mean turnover of the RAFI H a : The mean turnover of the Collar Weighted Index is not the same as the mean turnover of the RAFI UCT Graduate School of Business - Research Report 2009 Page 56 of 148

57 The Wilcoxon Signed Rank test uses the following equation: positive ranks µ z = σ ( ) n n +1 where: µ = and σ = 4 n ( n +1 )( 2n + 1) 24 Table 18 demonstrates that the higher turnover of the Collar Weighted (Original) index compared to the RAFI is statistically significant with a t-statistic of and a p-value of and we reject the null hypothesis that the mean turnover of the Collar Weighted (Original) index is not greater than the mean turnover of the RAFI. Table 18: Wilcoxon Signed Rank Sum Test for the Collar Weighted (Original) Index and the RAFI - Turnover Wilcoxon Signed Rank Test Output Sample 7 Positive Ranks Sum 28 Negative Ranks Sum 0 Copyright Expected Value 14 UCT Std Deviation z P-value (one tail) P-value (two tail) Table 19 demonstrates that the higher turnover of the Collar Weighted (Original) index compared to the RAFI is statistically significant with a t-statistic of and a p-value of and we reject the null hypothesis that the mean turnover of the Collar Weighted (Original) index is not greater than the mean turnover of the RAFI. UCT Graduate School of Business - Research Report 2009 Page 57 of 148

58 Table 19: Wilcoxon Signed Rank Sum Test for the Collar Weighted (Adjusted) Index and the RAFI - Turnover Wilcoxon Signed Rank Test Output Sample 7 Positive Ranks Sum 28 Negative Ranks Sum 0 Expected Value 14 Std Deviation z P-value (one tail) P-value (two tail) The analysis indicates that the Collar Weighted (Original) index has an annual turnover which is greater than a market capitalization index and fundamental index and the Collar Weighted (Adjusted) index has a turnover that is greater than a market capitalization index and a fundamental index Concentration The fourth research hypothesis attempts to determine whether the concentration of the Top 3, Top 5 and Top 10 shares within the collar weighted indices is lower than either market capitalization index or a fundamentally weighted index. As there are only 7 observations for concentration, a Wilcoxon Signed Rank test was used to determine if the concentration of the Market Cap index was significantly higher than that of the two Collar Weighted indices. In each case the hypothesis test is as follows: H 0 : The mean concentration of the Market Cap Index is not greater than the mean concentration of the Collar Weighted Index H a : The mean concentration of the Market Cap Index is greater than the mean concentration of the Collar Weighted Index The Wilcoxon Signed Rank test uses the following equation: positive ranks µ z = σ UCT Graduate School of Business - Research Report 2009 Page 58 of 148

59 where: ( n +1) n µ = and σ = 4 n ( n +1 )( 2n + 1) 24 Table 20 demonstrates that the higher concentration of the Market Cap index compared to the Collar Weighted (Original) index is statistically significant with p-values less than 0.05, for all three concentration bands, and we reject the null hypothesis that the mean concentration of the Market Cap index is not greater than the mean concentration of the Collar Weighted (Original) index. Table 20: Wilcoxon Signed Rank Sum Test for the Collar Weighted (Original) and Market Cap Indices Concentration TOP 3 TOP 5 TOP 10 Sample 8 Sample 8 Sample 8 Positive Ranks Sum 36 Positive Ranks Sum 36 Positive Ranks Sum 36 Negative Ranks Sum 0 Negative Ranks Sum 0 Negative Ranks Sum 0 Expected Value 18 Expected Value 18 Expected Value 18 Std Deviation Std Deviation Std Deviation z z z P-value (one tail) P-value (one tail) P-value (one tail) P-value (two tail) P-value (two tail) P-value (two tail) Table 21 demonstrates that the higher concentration of the Market Cap index compared to the Collar Weighted (Adjusted) index is statistically significant with p-values less than 0.05, for all three concentration bands, and we reject the null hypothesis that the mean concentration of the Market Cap index is not greater than the mean concentration of the Collar Weighted (Adjusted) index. Table 21: Wilcoxon Signed Rank Sum Test for the Collar Weighted (Adjusted) and Market Cap Indices Concentration TOP 3 TOP 5 TOP 10 Sample 8 Sample 8 Sample 8 Positive Ranks Sum 30 Positive Ranks Sum 35 Positive Ranks Sum 36 Negative Ranks Sum 6 Negative Ranks Sum 1 Negative Ranks Sum 0 Expected Value 18 Expected Value 18 Expected Value 18 Std Deviation Std Deviation Std Deviation z z z P-value (one tail) P-value (one tail) P-value (one tail) P-value (two tail) P-value (two tail) P-value (two tail) UCT Graduate School of Business - Research Report 2009 Page 59 of 148

60 A Wilcoxon Signed Rank test was used to determine if the concentration of the RAFI was significantly higher than that of the two Collar Weighted indices. In each case the hypothesis test is as follows: H 0 : The mean concentration of the RAFI is the same as the mean concentration of the Collar Weighted Index H a : The mean concentration of the RAFI is not the same as the mean concentration of the Collar Weighted Index The Wilcoxon Signed Rank test uses the following equation: positive ranks µ z = σ ( ) n n +1 where: µ = and σ = 4 n ( n +1 )( 2n + 1) 24 Copyright Table 22 demonstrates that the higher concentration of the RAFI UCT compared to the Collar Weighted (Original) index is not statistically significant with p-values greater than 0.05, for the Top 3 and Top 5 shares concentration bands, and we accept the null hypothesis that the mean concentration of the RAFI is not greater than the mean concentration of the Collar Weighted (Original) index. However, for the Top 10 shares concentration band, the RAFI has a lower concentration that is statistically significant with a t-statistic of and a p-value of and we reject the null hypothesis concluding that the mean concentration of the RAFI is lower than mean concentration of the Collar Weighted (Adjusted) index. The Market Cap index exhibited the lowest concentration in a bull market whereas the opposite was true in a bear market. The RAFI exhibited the lowest concentration in a bear market whereas the opposite was true for a bull market. As a result, we can also conclude that as the current market environment changes, the concentration of the Market Cap will decrease and the concentration of the RAFI will increase, with the Collar Weighted indices trying to moderate the concentration change. UCT Graduate School of Business - Research Report 2009 Page 60 of 148

61 Table 22: Wilcoxon Signed Rank Sum Test for the Collar Weighted (Original) Index and the RAFI Concentration TOP 3 TOP 5 TOP 10 Sample 8 Sample 8 Sample 8 Positive Ranks Sum 24 Positive Ranks Sum 19 Positive Ranks Sum 3 Negative Ranks Sum 12 Negative Ranks Sum 17 Negative Ranks Sum 33 Expected Value 18 Expected Value 18 Expected Value 18 Std Deviation Std Deviation Std Deviation z z z P-value (one tail) P-value (one tail) P-value (one tail) P-value (two tail) P-value (two tail) P-value (two tail) Table 23 demonstrates that the concentration of the RAFI compared to the Collar Weighted (Adjusted) index is not statistically significant with p-values greater than 0.05, for all three concentration bands, and we accept the null hypothesis that the mean concentration of the RAFI is not greater nor less than the mean concentration of the Collar Weighted (Adjusted) index. Table 23: Wilcoxon Signed Rank Sum Test for the Collar Weighted (Adjusted) and the RAFI Concentration TOP 3 TOP 5 TOP 10 Sample 8 Sample 8 Sample 8 Positive Ranks Sum 25 Positive Ranks Sum 24 Positive Ranks Sum 13 Negative Ranks Sum 11 Negative Ranks Sum 12 Negative Ranks Sum 23 Expected Value 18 Expected Value 18 Expected Value 18 Std Deviation Std Deviation Std Deviation z z z P-value (one tail) P-value (one tail) P-value (one tail) P-value (two tail) P-value (two tail) P-value (two tail) The results of the statistical testing indicate that using a collar weighted approach to indexing, it is feasible to achieve a lower concentration amongst the Top 3, Top 5 and Top 10 share concentration bands than by employing a market capitalization weighted approach. Although there is not statistical difference between the concentrations of the Collar Weighted (Original) index and the RAFI in the Top 3 and Top 5 share concentration bands, the RAFI has a lower statistically significant concentration than the Collar Weighted (Original) index in the Top 10 share concentration band. The analysis also illustrates that the Collar Weighted (Adjusted) index and the RAFI have no statistically significant difference in the relationship between their concentration levels in all three share concentration bands. UCT Graduate School of Business - Research Report 2009 Page 61 of 148

62 4.2.5 Sector Composition The final research hypothesis asks whether the weightings in the various sectors are more stable, over time with a collar weighted approach as opposed to a market capitalization weighted approach or a fundamentally weighted approach. Table 11 determined that between the defined period 1 and period 2 of the study, the average weighting change (for the Resources sector) was very low, for the Collar Weighted (Adjusted) index as opposed to the other three indices. The Collar Weighted (Adjusted) index also delivered the second lowest average weighting change (for the Resources sector) between the defined period 2 to period 3. Table 24 demonstrates the average weight changes of each index in the 10 different sectors over the period of the study. The lowest change in weighting is highlighted in green and the highest change in weighting is highlighted in red. In the four sectors that account for over 85% of the total weighting (for all four of the indices), viz. Resources, Financials, Non-Cyclical Consumer Goods and Cyclical Services, the Collar Weighted (Adjusted) Index had the lowest or second lowest change in weighting. Table 24: Average Weight Change of Sector Weightings Table 11 and Table 24 indicate that the Collar Weighted (Adjusted) index exhibits the lowest overall variance in the sectors that comprise the greatest weighting and can be seen as more stable over the period. The weighting changes of the Collar (Adjusted) index is likely to remain the most stable into the future as it experienced the lowest fluctuation in sector weightings across periods. UCT Graduate School of Business - Research Report 2009 Page 62 of 148