Cameron Luke Wilson

The Relevance and Propriety of Chasing Alpha​: A Study into Active versus Passive Investing in South Africa Cameron L. Wilson A research paper submitted to the School of Economics at the University of Cape Town in partial fulfilment of the requirements for the Bachelor of Commerce Honours degree in Financial Analysis and Portfolio Management. Cape Town 2018 Approved by: Lucian Pitt © 2018 Cameron L. Wilson ALL RIGHTS RESERVED The Relevance and Propriety of Chasing Alpha​: A Study into Active versus Passive Investing in South Africa (Under the supervision of Lucian Pitt) Executive Summary Although literature exploring the performance disparity between active and passive investment strategies dates back decades, its relevance once again becomes apparent with the rise of exchange traded funds (ETFs) in South Africa. The research question explores the age-old question in a South African context and asks whether it is still appropriate and relevant for active asset managers to chase excess returns at the risk of their clients’ capital. The consulted literature largely tells the same story. It is evident that markets need to be somewhat inefficient for active managers to capture excess returns. Proponents of efficient capital markets hold the stance that active managers cannot generate excess returns consistently. However, proponents of “mostly” efficient markets hold the stance that superior managers with superior analysts and superb track records can generate excess returns consistently. What is widely acknowledged is that the average active manager, after fees and adjusted for risk, does not outperform their respective benchmark. The consulted literature derives its conclusions from research conducted on large, deep, and developed capital markets, primarily the United States’ capital market. A South African context was chosen with the belief that its relatively small capital market may provide opportunities for the average active manager to produce excess returns above the JSE Ltd All Share Index (JSE ALSI). The sample of active funds was drawn from the population of South African domiciled, Rand denominated, active equity funds. Monthly returns data over a period of eight years was considered as to include as many funds as possible whilst allowing enough time for returns data to establish any trends that may be present. A second sample of ​ex-post “​ superior” funds was selected from the original sample. Both samples of active funds were tested against the JSE ALSI, with respect to risk-adjusted return metrics, at the five percent level of significance using the right-tailed Student’s T-test. All statistical tests were made given three scenarios; zero fees, lower-bound fees, and higher-bound fees. 1 Before fees, the average active fund outperformed the passive JSE ALSI, as per consulted literature. However, when fees were accounted for, the average active fund underperformed the respective passive index. Again, this result fell in line with the consulted literature. Interestingly, the average ​ex-post s​ uperior active fund outperformed the respective passive fund when adjusted for risk and fees. If superior actively managed funds can be selected using historic risk-analyses and historic performance-metrics of funds and fund-managers, then alpha should be generated on a recurring basis. However, the capturing of recurring alpha returns relies on an active management of funds, that is, actively managing one’s portfolio of active funds, ignoring transaction costs and taxes. Given the apparent failure of the average actively managed fund compared to the JSE ALSI benchmark, it is not advisable to hold a passive instrument which tracks active funds, such as a fund tracker ETF or index-styled investment vehicles tracking active funds. Key Words​: Active vs Passive, Index Investing, Excess Returns, South Africa, JSE Ltd. 2 Acknowledgements My sincerest gratitude, first and foremost, goes to my supervisor, Lucian Pitt. Lucian has been actively involved in my academic career, providing invaluable insight, from my undergraduate years to my final postgraduate days at the University of Cape Town (UCT). His sincerity and passion for his students is truly remarkable, making him an invaluable asset to UCT’s academic body. Secondly, my parents’ unwavering emotional and financial support has made this journey possible. Without their backing, I would not have had the opportunity to study at this fine institution. I am unbelievably fortunate to have been granted the opportunities they have made possible. Finally, without the University of Cape Town’s resources, the research could not have been conducted. Gratitude goes to the individuals that make UCT the world-class institution it is today. 3 Table of Contents Executive Summary i Acknowledgements iii Table of Contents iv Table of Figures v List of Abbreviations vi Literature Review 1 Introduction 1 Efficient Markets and the Foundation of Passive Management 1 The Defence of Efficient Markets and the CAPM 2 ‘Mostly Efficient’ Markets and The Defence of Active Management 4 Is Active and Passive Management Mutually Exclusive? 5 Literature Evaluation and Working Hypothesis in a South African Context 6 Conclusion 6 Methodology 7 Introduction 7 Paradigm 7 Theoretical Framework 8 Research Approach/Research Design 9 Data Collection 10 Validity and Reliability 11 Data Analysis Strategy 11 Ethical Considerations 12 Conclusion 12 Results and Discussion 13 Introduction 13 Descriptive Statistics 13 Risk-Adjusted Performance before Fees 14 Risk-Adjusted Performance after Fees 16 Implications of Findings 18 Concluding Remarks 19 Limitations and Recommendations 19 References vii 4 Table of Figures Table 1​: Mean monthly measures of central tendency 13 Table 2​: Mean monthly risk-adjusted metrics before fees. 14 Table 3​: Right tailed Student’s T-test statistical inference summary, zero fees. Average active fund vs J203. 15 Table 4​: Right tailed Student’s T-test statistical inference summary, zero fees. Average superior (ex-post) active fund vs J203. 16 Table 5​: Right tailed Student’s T-test statistical inference summary, lower-bound Fees. Average active fund vs J203 16 Table 6​: Right tailed Student’s T-test statistical inference summary, lower-bound fees. Average superior (ex-post) active fund vs J203 17 Table 7​: Right tailed Student’s T-test statistical inference summary, higher-bound fees. Average active fund vs J203. 18 Table 8​: Right tailed Student’s T-test statistical inference summary, higher-bound fees. Average superior (ex-post) active fund vs J203. 5 18 List of Abbreviations CAPM Capital Asset Pricing Model ETF Exchange Traded Fund EMH Efficient Market Hypothesis HML High Minus Low JSE ALSI JSE Ltd All Share Index M​2 Modigliani-Modigliani MPT Modern Portfolio Theory MRP Market Risk Premium RAP Risk-Adjusted Performance SD Standard Deviation SMB Small Minus Big SSD Semi Standard Deviation UCT University of Cape Town 6 Literature Review Introduction Literature on active and passive investment strategies date back to the early fifties when Harry Markowitz introduced Modern Portfolio Theory (MPT) in his 1952 article, ​Portfolio Selection​, which featured in The Journal of Finance. It was not until the introduction of the Efficient Market Hypothesis (EMH), by Eugene Fama and Paul Samuelson in 1965, did the debate between active and passive management truly capture the attention of finance and economics audiences alike (Delcey, 2018). This literature review explores active and passive management through various concepts underlying both investment strategies. First, the theoretical foundations of active and passive investing strategies are laid down through the exploration of the EMH. The Capital Asset Pricing Model (CAPM) and pricing anomalies are discussed. The case for active management is considered with reference to; “mostly efficient markets”, the value added of active management, and acute market inefficiencies. Finally, allocation between, and the optimisation of, active and passive investment strategies will be evaluated. Efficient Markets and the Foundation of Passive Management A perfectly efficient market is one in which new publicly-available information is disseminated in a timely and costless manner to all market participants and is one in which trade-execution costs are zero (Vasicek & McQuown, 1972). The EMH does not hold up perfectly as theory suggests, but empirical evidence shows that the main conclusions of EMH, namely the weak-form and semi-strong form efficiency, hold up very well in real markets (Vasicek & McQuown, 1972). The EMH is said to follow three forms of efficiency: 1) weak-form efficiency: where historic information is priced into current stock prices, 2) semi-strong-form efficiency: where historic and current information is priced into current stock prices, and 3) strong-form efficiency: where historic, current, and insider information​1 is priced into current stock prices (Fama, 1969). 1 In strong-form market efficiency it is assumed that non-public, material information pertaining to company management and idiosyncratic factors is disseminated to all market participants timeously and at zero cost. 1 Given Markowitz’ and Fama’s contribution of MPT and the EMH respectively, Treynor (1962), Sharpe (1964), Lintner (1965), and Mossin (1966) independently developed the Capital Asset Pricing Model (CAPM). The CAPM describes the determination of asset prices, given a market in equilibrium, by considering an asset’s systematic risk relative to the market portfolio’s​2 risk (Eun, 1994). Together, MPT, the EMH, and the CAPM form the foundation upon which active versus passive investment strategies are debated. The logic of passive investing or “beta grazing” considers the fees to advisors, brokerage fees, bid-ask spreads, and marginal risks undertaken from chasing an active investment strategy for no guarantee of matching or outperforming the market portfolio (Keane, 1986) (Liebowitz, 2005). This logic is founded upon the assumption that markets are perfectly efficient and that CAPM holds, implied by perfectly efficient markets. Whereas active management relies on the assumption that assets can be mispriced through market inefficiencies. The Defence of Efficient Markets and the CAPM Since the inception of the CAPM many market-related pricing anomalies have been discovered with academics disputing the CAPM, thus, the legitimacy of the model has been undermined (Eun, 1994). The most well-known critique of the CAPM is from Roll (1976) in what is known today as ‘Roll’s Critique’ in finance classrooms. The CAPM is a single-factor model which only considers the “beta risk”​3 or systematic risk of an asset with respect to the systematic risk of the Market Portfolio to determine the price of said asset. Roll critiques the CAPM as only useful for testing the mean-variance efficiency of the Market Portfolio (Roll, 1976). That is, if the Market Portfolio is the optimal, mean-variance portfolio as per Markowitz’s MPT, then will assets only be correctly priced by the model (Roll, 1976). Roll says, “There is an ‘if and only if’ relation between return/beta linearity and market portfolio mean-variance efficiency” (1976: p.130). The fundamental flaw of the CAPM lies in the fact that it relies on an ‘unobservable market portfolio’ (Eun, 1994). Eun proposes that the CAPM has been incorrectly specified, saying that there is a part of the market portfolio that is certainly observable, be it a broad market 2 The market portfolio is a collection of every tradable asset weighted by its prominence in the asset universe and is assumed to be held by all rational, risk averse investors (Markowitz, 1952). 3 Beta risk is the measure of how sensitive an asset’s returns are relative to the Market Portfolio’s returns. It is the covariance of the asset’s returns and the Market Portfolio’s returns divided by the variance of the Market Portfolio’s returns (Sharpe, 1964). Where ​β=COV(Ri,Rm)VAR(Rm)​. Alternatively, is the slope coefficient when the single asset returns are regressed on the Market Portfolio’s returns. 2 index or a portfolio tracking a large array of assets​4​, and a part of the market portfolio that is unobservable (Eun, 1994). Eun deconstructed the CAPM’s β into the observable β and the unobservable or ‘latent β ’, reformulating the CAPM​5​, which he then used to tackle asset pricing anomalies (1994). Using this definition of the CAPM, Eun was able to solve the more prominent anomalies brought forward by Friend and Blume (1970), Banz (1981), and Reinganum (1981). Friend and Blume found that positive Jensen’s Alpha​6 returns are inversely related to an asset’s beta coefficient (Friend & Blume, 1970). Eun found that the Friend/Blume anomaly is perfectly consistent with the CAPM so long as the benchmark and latent portfolios are positively correlated to each other (Eun, 1994). Banz (1981) and Reinganum (1981) found that asset returns are inversely correlated to firm size in what is known as the ‘firm size effect’ or ‘small firm effect’. Smaller firms experienced higher returns even after adjusting for beta-specific risk (Banz, 1981) (Reinganum, 1981). Eun proposes that this market anomaly is explained by the relative sizes of the latent betas: that the small firm effect is consistent with the CAPM so long as the latent beta of the smaller firm is larger than the latent beta of the larger firm (1994). Eun has effectively solved some of the more prominent anomalies associated with the CAPM through his theoretical and mathematical approach to decomposing beta-risk. However, the practical value of this theory is limited as pricing unobservable components of risk becomes highly problematic. 4 This portfolio can be set up as a theoretical benchmark for academic purposes or developed for investment purposes. However, the cost of purchasing and rebalancing such a portfolio through full replication would offset any benefit gained through diversification. This implied cost relates to the costs of ‘over-diversification’ (Denis, Denis & Yost, 2002:-). 5 Treynor (1962), Sharpe (1964), Lintner (1965), and Mossin’s (1966) single factor CAPM estimates asset prices based on the risk-free rate and a proportion of the market-risk premium determined by the coefficient. Ri=Rf+i,m(Rm-Ri)​. Reformulated, Eun suggests a CAPM which accounts for the unobserved . Thus: Ri=Rf+Bi,B+Li,L​ where ​Bi,B​ is the observable benchmark beta and ​Li,L​ is the unobservable latent beta (Eun, 1994). 6 Jensen’s Alpha is a risk-adjusted measure for returns above or below the security market line found in the CAPM and can thus be positive or negative. 3 ‘Mostly Efficient’ Markets and The Defence of Active Management Active investment strategies involve strategic asset allocation and risk expenditure in accordance with prescribed investment mandates to match or beat a benchmark. “The objective of active management is to maximise the value added from residual return, where the objective awards a credit for the expected residual return and a debit for the residual risk” (Grinold & Kahn, 2000, p. 119). It is reasonable to assume that developed markets satisfy weak-form and semi-strong-form market efficiency: that current asset prices on developed exchanges reflect all historic and current data (Fama, 1970). By this argument, it is also reasonable to assume that there is no place for active management and that all rational investors will hold a passive portfolio that ticks along with the market. Contrary to the EMH, Grossman and Stiglitz argue that in a world of costly information, analysts must receive a premium for their work or else there would be no incentive for these analysts to collect and analyse data (1980). It is by this process of data analysis that markets are operationally efficient which results in efficient price discovery by market participants. Put simply, Jones and Wermers remark, “markets need to be ‘mostly but not completely efficient’ or else investors would not make the effort to assess whether prices are ‘fair’” (2011:31). It is thus reasonable to conclude that markets are weak-form and semi-strong-form efficient ​due to the market participation of active managers whom assure that price discovery is an efficient process. “By making markets more efficient, active management improves capital allocation – and thus economic efficiency and growth – resulting in greater aggregate wealth for society as a whole.” (Jones & Wermers, 2000:31). Liebowitz takes a different stance to market inefficiencies through discussing dubious behaviour demonstrated by market participants (2005:32). Such inefficient behaviour discussed by Liebowitz include: “Process vs. Outcome” where losses are more meticulously analysed as opposed to gains. The issue that arises due to the “Process vs. Outcome” irrationality is that managers who neglect to analyse gains thoroughly never truly know if the gains were generated through a sound investment process or due to other factors resulting in ‘dumb luck’ (2005:34). The “Convoy Behaviour” is described as the behavioural bias of mainstream participants who follow other institutional managers’ portfolios for fear of greater risk should they ‘sail solo’ (Liebowitz, 2005:35). Liebowitz states that in times of market ambiguity, people are naturally inclined to follow their peers’ behaviour (2005:35). 4 Liebowitz expands on other key behavioural biases of market participants, all which result in the same conclusion; that human behavioural biases create acute market inefficiencies which are exploitable by ‘Pure Alpha’ funds and have been exploited consistently over many decades (Liebowitz, 2005:32). Finally, Doukas, Kim, and Pantzalis put forth the idea that arbitrageurs play an important role in capital market efficiency (2010). This is no remarkable finding, but they go on to explain that arbitrage contains implicit risk due to idiosyncratic factors affecting stocks (Doukas et al. 2010). Due to arbitrage risk, mispriced securities with high levels of idiosyncratic risk may remain mispriced due to the failure of arbitrageurs to effectively manage the implied risk of making the arbitrage trade. This results in the persistence of market inefficiency (Doukas et al. 2010). Is Active and Passive Management Mutually Exclusive? There is a false dichotomy prevalent in the debate between ‘Actives’ versus ‘Passives’, where proponents of either strategy vehemently denounce the legitimacy of the other on the grounds of academic theory. It is safe to say, according to Markowitz’s MPT, that all rational and risk averse investors want to maximise return for a given level of risk or minimise risk for a given level of return: in other words, to invest in the optimal portfolio (1952). Ambachtsheer, Farrell and Farrell say that active management adds value to a portfolio through management’s ability to identify key requirements for generating alpha returns (1979). Value-added or residual expected returns are dependent on (i) management skill and their ability to make reasonable valuation judgements, (ii) the conversion of valuation judgements into unbiased residual return expectations, (iii) portfolio construction rules that consider transaction costs and risk controls, and (iv) the availability of software computation for data processing (Ambachtsheer, Farrell and Jr, 1979:45). Sorensen, Miller and Samak evaluate the value-added from active management on the grounds of manager skill, where skill is calculated on the historic stock-picking success of a manager measured as a percentage of their historical success versus failures (1998). It is concluded that mutual and pension funds who employ managers, who consistently experience index performance or worse, should replace them with managers who have a success rate of 56% or better (Sorensen et al, 1998). However, even if a fund can access superior managers, 5 optimisation of risk adjusted returns requires the use of passive instruments or quantitative index-enhancing products (Sorensen et al. 1998). Literature Evaluation and Working Hypothesis in a South African Context Literature on active and passive investment strategies rely on key assumptions regarding the degree to which markets are efficient. Proponents of passive strategies are so by default given their belief of the EMH. Although strong-form efficiency is a stretch of the imagination, proponents of the EMH find it reasonable to assume that developed markets satisfy weak-form and semi-strong-form efficiency. Although the EMH allows for mispricing and return anomalies to occur in the market, it states that these anomalies occur at random and cannot prevail. Thus, it is logical to conclude that proponents of the EMH disregard the value added from active managers. Most of the literature on the subject finds issues with the EMH and the simplifying assumptions behind pricing models, namely the CAPM. Attempts to support the EMH and the CAPM, although theoretically sound and offers insights into the mechanics of the theories, offer no practical value to industry practitioners. The literature finds that inefficiencies do persist due to biased behaviour of market participants or structural barriers which prevent the correct pricing of marketable assets, as discussed in Liebowitz’s (2005) and Doukas et al (2011) articles respectively. South Africa has an advanced financial sector coupled with a relatively small capital market. Just as practitioners have and continue to generate pure alpha returns globally, it is believed that industry practitioners have the means to exploit inefficiencies that potentially exist in South Africa’s capital markets through active management strategies. This hypothesis can be tested through comparing various active, passive, and hybrid fund performances situated in South Africa. Conclusion This literature review explores the debate between active and passive investing. First, the defence of efficient markets and thus passive investment strategies is considered with most of the literature agreeing that markets are operationally efficient and that passive strategies are greatly beneficial to investors. Second, the defence of active management considering market inefficiency is explored. Proponents of active management identify the importance of index funds and other quantitative index-enhancing products. However, active management relies 6 on the ability of superior managers to take advantage of acute market inefficiencies to generate pure alpha returns. Industry practitioners and financial academics note the existence of superior managers and largely agree that markets are mostly efficient allowing for active management to better allocate capital, thus resulting in a more efficient market. Finally, the false dichotomy of active versus passive investment is considered. It is noted that optimised portfolios rely on passive and quantitative index-enhanced products in conjunction with superior stock-selection skills of an active manager. Most of the literature reviewed agrees that markets are operationally efficient, but acute inefficiencies do arise allowing for the exploitation of such inefficiencies and thus the generation of excess returns. However, it is important for active management to balance excess returns with marginal risk. Methodology Introduction Given the literature reviewed, it was possible to design the research question and develop the data-analysis strategy with sound academic practises. The following chapter describes the research paradigm employed to analyse the observed data collected as well as the theoretical underpinnings for the analysis of the data, all of which was informed by the reviewed literature. The research design and data collection methods are discussed in depth, followed by the reliability and validity of the approaches employed. Finally, the data-analysis strategy and ethical considerations are discussed. Paradigm The research question considers whether it is relevant and appropriate for asset managers to chase alpha at the risk of their client’s capital. This question requires a quantitative analysis of returns data of various South African domiciled equity funds whilst adhering to widely-held academic beliefs about asset pricing. The Capital Asset Pricing Model (CAPM) is primarily considered for securities pricing in this paper. The CAPM suggests that individual securities are correctly priced given their beta risk or systematic risk in the long-run. Additionally, equity funds are comprised of individual equity securities, thus applying the CAPM to the analysis of these funds is deemed appropriate given the time-period under consideration. Due to the nature of the research methods required, it is fitting to use a post-positivist paradigm for the quantitative analysis of the returns data observed. The research question 7 looks to uncover new information which can be applied to South African equity funds given South African economic and market conditions. Additionally, Critical Realism will be employed due to the changing nature of pricing-model theories in financial academia. Examples of changing pricing models include; the adjustments made to the CAPM by Michael Jensen (1967) in explaining alpha returns, or the CAPM adjustments made by Eugene Fama and Kenneth French (1996) in their Three-Factor Model which explains excess returns by adding a size and value premium over and above the market risk premium considered in Treynor (1962), Sharpe (1964), Lintner (1965), and Mossin’s (1966) original CAPM. E (Ri ) = Rf + β (M RP ) Lintner, Mossin, Sharpe, and Treynor’s CAPM (1) E (Ri ) − Rf = αi + β (M RP ) ​Jensen’s Alpha (2) E (Ri ) = Rf + β 1 (M RP ) + β 2 (SM B) + β 3 (HM L) Fama-French 3FM (3) Where​: E (Ri ) = Expected return for asset i Rf = Risk Free Rate (Yields on respective government bonds or treasury bills) βi = Slope coefficient of asset returns regressed on respective benchmark returns αi = Jensen’s alpha return over and above benchmark (can be negative) M RP = Market Risk Premium SM B = Size Premium (Small minus big) HM L = Value Premium (High minus low) Final considerations made for the post-positivist paradigm employed include; the treatment of Finance as a social science with respects to how people play an integral role in price discovery, the objectivity of unchanging historical quantitative returns data, and the observational nature of secondary data collection methods used. Theoretical Framework The theoretical underpinnings of active vs passive investing rely on the assumptions made about market efficiency. The reviewed literature mostly concludes that markets are efficient 8 but that acute mispricing does occur due to several factors. Mispricing primarily occurs due to human behaviour, as discussed by Liebowitz (2005), and due to the failure of closing out arbitrage opportunities caused by implicit arbitrage risk and other financial implications, as discussed by Doukas, Kim, and Pantzalis (2010). These acute mispricings which occur at random, as per the EMH, provide the incentive necessary for active managers to pursue excess returns. As summarised by Grossman and Stiglitz, active management and security analysis must receive a premium in a world of costly information, otherwise there would be no incentive to collect and analyse data (1980). By looking at historical returns data over a long period of time and measuring the volatility of these returns can one most accurately forecast trends in the future. As per Figlewski, historical data bases assumptions on stability which are unlikely to hold over time (1994). However, historical risk data over long periods of time generally provide the most accurate forecasts for both long- and short-time horizons (Figlewski, 1994). Thus, the assumption of current risk continuing into future time periods, given historical risk data, can be made with little effect on the outcome of the research conducted. This assumption implies that superior funds on a risk-adjusted basis will continue to be superior going into the future. Additionally, superior funds can be identified ​ex ante b​ y considering past risk adjusted past performance, macro-economic past performance, manager characteristics, and analyses of fund holdings (Jones & Wermers, 2011). Research Approach/Research Design The research question was answered by comparing South African-domiciled equity funds risk-adjusted returns against an appropriate broad-market benchmark’s returns. The chosen benchmark was the JSE Ltd All Share Index (JSE ALSI) weighted by market capitalisation. The index designation is J203 on The Bloomberg Terminal. Returns data on a monthly-basis over an eight-year period formed the foundation upon which the research was conducted. Risk-adjusted metrics of the observed returns data was compared to the benchmark returns data. The risk-adjusted equity fund returns were primarily treated for average management fees whilst ignoring the effects of taxation, additional service fees, and transaction costs. The key assumption made when comparing actively managed equity funds against the passive equity fund is that the passive equity fund has zero tracking-error. That is, holders of 9 the passive equity fund essentially hold the J203. With the passive fund established, risk adjustments and fee adjustments were made to the J203 to effectively compare both strategies pari passu. Mean risk-adjusted metrics of actively managed equity funds were tested against the respective metric of the passive equity fund using the right tailed Student’s T-Test at the five percent level of significance. The p-value approach was employed. Three groups of tests were conducted on mean risk-adjusted metrics: 1) zero fees 2) lower-bound fees 3) upper-bound fees. Data Collection The data collected was first sourced on a Thomson Reuters DataStream global financial and macroeconomic data platform. The search was narrowed down to South African-domiciled, Rand denominated equity funds. The funds’ price data was pulled from The Bloomberg Terminal using a Bloomberg Excel plug-in. Funds that passed the criteria of eight-years’ worth of monthly price data were used for the study. The time period chosen was arbitrary as to allow as many funds as possible to be included in the study whilst allowing enough monthly data points to be considered, given the central limit theorem, to ensure statistical significance. The sample consisted of 43 equity funds with eight-years’ worth of monthly price data. The sample was tested against the J203 over the same period. The price data was converted to returns data using natural logarithms, assuming that returns are compounded continuously, and that trading occurs continuously. Continuous trading was assumed given the continuous passage of time. The sample was drawn from the universe of South African-domiciled, Rand denominated equity funds with an unknown population variance. Thus, a right-tailed Student’s T-Test was employed at the five percent level of significance with 42 degrees of freedom. Additionally, a sub-sample of 29 equity funds was tested against the passive J203 fund using a right-tailed Student’s T-test with 28 degrees of freedom. This sample contains “superior” equity funds with mean returns greater than or equal to the mean return of the J203. The theoretical reasoning for the selection of this sample relies on Figlewski’s (1994) and Jones and Wermers’ (2011) findings that 1) past historic risk data is a good measure for risk trends in the future and, 2) that superior fund performance can be identified ​ex ante given past fund 10 and macroeconomic performance, respectively. The idea was to see how “superior” actively managed equity funds stacked up to the J203 passive fund over the given time period on a risk adjusted basis. 11 Validity and Reliability The data was sourced from financial information services used as global industry staples. Both Thomson Reuters DataStream and The Bloomberg Terminal are industry leading financial information software-as-a-service providers. The data sources were utilised on the University of Cape Town’s (UCT) campuses through UCT’s subscription of the services. The statistical method employed for comparing sample means was appropriate. The Student’s T-Test was used due to the unknown variance of the population from which the samples were drawn. The data treatment was in line with industry and academic standards of comparing and ranking fund or security returns. The funds were compared on a risk-adjusted performance basis through calculating widely used risk-adjusted metrics (Estrada, 2011:99-122): - Sharpe Ratio - Treynor Ratio - Information Ratio - Modigliani-Modigliani (M​2​) Risk-Adjusted Performance (RAP) - Semi-Standard Deviations (SSD) The above metrics were adjusted for respective management fees. Data Analysis Strategy The returns data obtained through the method described in ‘Data Collection’ was used to calculate an array of statistics used to determine the risk adjusted performance of each equity fund compared to the J203 benchmark. The metrics calculated were: - Tracking error of the equity fund against the J203 - Beta coefficient of the respective equity fund’s returns regressed on the J203’s returns - Mean monthly returns of the equity funds and the J203, whilst ignoring geometric mean returns as the study focuses on period-for-period performance and not the evolution of investments over the period considered - Standard deviation of the equity funds’ and the J203’s returns 12 - Semi-standard deviations of equity fund returns, or downside risk. That is, the standard deviation of fund returns below the mean return of the J203 - Risk free rate, calculated as the mean yield on the R186 South African Sovereign domestic currency 10-year bond over the period under review - CAPM expected return for each fund using the theoretical underpinning of the CAPM theory and calculated with the risk-free rate, beta coefficient and the market risk premium The above statistics were used in the calculation of the risk-adjusted metrics discussed in ‘Validity and Reliability’ above. Finally, the risk adjusted metrics were treated for three fee scenarios; 0%, 1.75%, and 2.5% for the actively managed equity funds whilst the J203 passively managed fund was also adjusted for three fee scenarios; 0%, 0.03%, and 0.04%. The fees applied to the risk-adjusted metrics of the equity funds were informed by the average active management fees in South Africa (Sygnia, 2016). The fees paid on the passive J203 was informed by management fees paid for Satrix’s JSE ALSI ETF (Satrix, 2018). Ethical Considerations Under no circumstances were the resources provided by UCT used for individual financial gain by the researcher nor will the resources provided by UCT be used for individual financial gain by the researcher. The findings of the research paper are academic in nature and are intended to inform readers on the topic at hand and are in no way meant to act as trading or investing advice. Conclusion The methods used in conducting the analysis of data was discussed in depth. The methodology employed has allowed a statistical analysis of the observed data to be performed with some degree of statistical significance. The next chapter reviews the results of the data-analysis and further discusses the outcome of the data-analysis performed. 13 Results and Discussion Introduction The previous chapter laid down the methods used to acquire the results needed to make statistical inferences. The results acquired were used to test whether actively managed equity funds outperformed passively managed equity funds on a risk adjusted basis at the five percent level of significance using a right-tailed Student’s T-test. This chapter presents the results obtained through the methodology discussed above. First, the descriptive statistics are presented and discussed, followed by statistical inferences comparing both management strategies which is then discussed. Finally, concluding remarks on the results are presented. Descriptive Statistics The descriptive statistics presented in ​table 1 compare the three component measures of central tendency required for the risk adjusted metrics discussed in “​Validity and Reliability​” in the ​Methodology section above. The measures of central tendency used are: the sample mean, the sample standard deviation, and the sample semi-standard deviation. Where semi-standard deviations measure downside risk below a given benchmark. The benchmark considered in this study was the JSE ALSI Index (J203). Additionally, the descriptive statistics compares the sample of actively managed equity funds, the sub-sample of superior actively managed equity funds, and the passive J203 equity fund, all before fee adjustments. Table 1 ​describes mean monthly measures of central tendency. Metric Mean Mean-Returns Mean Standard Deviation Mean Semi-Standard Deviation Equity Funds 0.7719% 2.8684% 1.9097% Superior Equity Funds (ex-post) 0.8880% 3.1199% 1.9072% J-% 2.9301% 2.9301% Table 1​: Mean monthly measures of central tendency On average, the sample of actively managed equity funds offer greater returns and less variability and less downside variability than the J203 before fees. This result falls in line with Jones & Wermers’ results where it is noted that the average active manager performs slightly worse than the market index by an amount just less than their fees (2011). This suggests that the average active fund creates alpha returns before fees and expenses (Jones & Wermers, 2011). The average ​ex-post ​superior fund offers an even greater return over the J203 but with marginally more variability in the returns. However, downside variability of the average superior fund returns is substantially lower than the downside variability of the 14 J203. The lower downside variability of the average superior fund compared to the J203 is not surprising given the performance disparity between the average superior fund and the J203. Risk-Adjusted Performance before Fees Ranking the performance of various securities by returns alone gives no helpful insight as to how effectively the securities in question meet investment objectives. Risk needs to be spent adequately to meet investment goals and is extremely important when making investment decisions. Knowing the variability of historic returns can adequately shed light on the future variability of returns (Figlewski, 1996). ​Table 3 c​ ompares various mean risk-adjusted measures between the average active equity fund, the average superior fund, and the passive J203. ​ etric M Mean Sharpe Ratio Mean Treynor Ratio Mean Information Ratio Mean M2 Mean M2 (SSD) Equity Funds-% 0.7180% Superior Equity Funds (ex-post-% 1.0301% ​Table 2​: Mean monthly risk-adjusted metrics before fees. J-% 0.7117% The first interesting result is the greater Sharpe ratio of the J203 over the average equity fund’s Sharpe ratio. ​Table 1 ​shows that the average active equity fund offers a greater return for less variability. However, ​table 2 shows that the passive J203 is a more efficient portfolio than the average active equity fund. The mean Sharpe ratio value in ​table 2 is the average of all Sharpe ratios across the sample of actively managed equity funds. The conflicting results between ​table 1 and ​table 2 are attributable to many active funds exhibiting lower Sharpe ratios than the J203’s Sharpe ratio, or negative Sharpe ratios. A negative Sharpe ratio occurs when the expected CAPM return of the security is less than the risk-free rate. The average information ratio of active equity funds is positive. This suggests that the average actively managed equity fund is creating alpha returns above the respective J203 benchmark before fees. This finding falls in line with both Jones and Wermers’ (2011) and Grossman and Stiglitz’s (1980) arguments; where it is postulated that the average fund manager produces alpha returns before fees, and that in a world of costly information, analysts must receive a premium for their work or else there would be no incentive for these analysts to collect and analyse data, respectively. 15 Table 3 ​below summarises the statistical inferences made on various metrics of the average active fund compared to the J203, given zero fees. The null hypothesis states that the average active fund metric is equal to the respective J203 metric. The alternative hypothesis states that the average active fund metric is greater than the respective J203 metric. Statistical inferences were made at the five percent level of significance using the right-tailed Student’s T-test given the unknown population variation in returns of South African domiciled, Rand denominated, actively managed equity funds. The t-tests were conducted with 43 observations and 42 degrees of freedom. Zero Fees One Tailed: CV = 1.682 Metric Sharpe Ratio Treynor Ratio Information Ratio RAP (SD) RAP (SSD) Test Statistic -7.4843 - - P-Value- Decision Do Not Reject Null Hypothesis Do Not Reject Null Hypothesis Reject​ Null Hypothesis Do Not Reject Null Hypothesis Reject​ Null Hypothesis Table 3​: Right tailed Student’s T-test statistical inference summary, zero fees. Average active fund vs J203. The average equity fund’s Sharpe ratio, Treynor ratio, and M​2 risk adjusted performance (RAP), using standard deviations, is not greater than the J203’s respective ratios. This is largely attributable to many active funds exhibiting low or negative Sharpe and Treynor ratios which leads to a low M​2 RAP. Low or negative Sharpe and Treynor ratios occur when the CAPM expected return of an active fund is close to or less than the expected return on the J203, respectively. The M​2 ​RAP is largely dependent on a security’s Sharpe ratio. However, the average active fund exhibits a positive information ratio, where the market portfolio would theoretically have an information ratio of zero. Finally, given zero fees, the M​2 RAP using downside risk or semi-standard deviations is greater the ​ M​2 RAP of the J203. The J203’s semi-standard deviation (SSD) is equal to its standard deviation because the J203 is the benchmark; where SSD measure variation of returns below the average benchmark return. The rejection of the null hypothesis with respects to the average active fund’s information ratio and M​2 RAP, using SSD, suggests that the average active fund does produce excess returns before fees, as per Grossman & Stiglitz (1980) and Wermers & Jones (2011). Table 4 ​below summarises the statistical inferences made on various metrics of the average superior active fund compared to the J203, given zero fees. The null and alternative hypotheses remain the same as above and are also conducted at the five percent level of 16 significance using the right tailed Student’s T-test. The t-tests were conducted with 29 observations and 28 degrees of freedom. Metric Sharpe Ratio Treynor Ratio Information Ratio RAP (SD) RAP (SSD) Zero Fees One Tailed: CV = 1.701 Test Statistic P-Value- Decision Reject​ Null Hypothesis Reject​ Null Hypothesis Reject​ Null Hypothesis Reject​ Null Hypothesis Reject​ Null Hypothesis Table 4​: Right tailed Student’s T-test statistical inference summary, zero fees. Average superior (ex-post) active fund vs J203. The average superior fund has greater risk adjusted performance metrics, on all considered fronts, than the J203, before fees. If superior funds can be identified ​ex-ante a​ s per Figlewski’s (1996) long term risk-analysis and Jones & Wermers’ (2011) analysis of historic fund performance, then allocation of capital to superior funds could offer excess returns over the J203 with lower downside variability in returns before fees. Risk-Adjusted Performance after Fees The fee structures employed for actively managed funds were informed by Sygnia’s (2016) article, “​Are You Getting Value for Your Investment Fees?”​, featured on Moneyweb.co.za. The fees employed for the J203 were informed by Satrix’s JSE ALSI (J203) exchange traded fund fact sheet. The average active fund and the average superior active fund was tested against the J203 on three fee-scenarios; zero fees (see above), lower-bound fees, and upper-bound fees. ​Table 5 ​and ​Table 6 ​below summarise the statistical inferences made on comparing various risk-adjusted metrics between active funds and the passive J203 fund after lower-bound fees. The null and alternative hypotheses remain the same from above. Metric Sharpe Ratio Treynor Ratio Information Ratio RAP (SD) RAP (SSD) Lower-Bound Fees One Tailed: CV = 1.682 Test Statistic P-Value Decision - Do Not Reject Null Hypothesis - Do Not Reject Null Hypothesis - Do Not Reject Null Hypothesis - Do Not Reject Null Hypothesis - Do Not Reject Null Hypothesis Table 5​: Right tailed Student’s T-test statistical inference summary, lower-bound Fees. Average active fund vs J203 17 Metric Sharpe Ratio Treynor Ratio Information Ratio RAP (SD) RAP (SSD) Lower-Bound Fees One Tailed: CV = 1.701 Test Statistic P-Value Decision- Reject​ Null Hypothesis- Reject​ Null Hypothesis Do Not Reject Null- Hypothesis- Reject​ Null Hypothesis- Reject​ Null Hypothesis Table 6​: Right tailed Student’s T-test statistical inference summary, lower-bound fees. Average superior (ex-post) active fund vs J203 After lower-bound fees, it is apparent that the average actively managed fund falls short of the market-index on all considered risk-adjusted fronts. This finding falls in line with most of the literature on the subject. Keane’s (1986) and Liebowitz’s (2005) findings considers fees from chasing an active management approach and conclude that passive strategies make more sense given no guarantee of outperforming the market. Additionally, Jones & Wermers’ (2011) find that the average active equity fund underperforms the broad-market index after fees. However, it is implied that the average passive fund also underperforms the index after fees; that is, if passive funds are meant to have zero-tracking error, any application of fees will reduce returns (Jones & Wermers, 2011). Jones & Wermers state, “​In fact, virtually 100 percent of passive funds underperform their relevant indices, net of fees”​ (2011:31). Average ​ex-post ​superior active funds tell a more promising story after lower-bound fees as they outperform the J203 on all considered risk-adjusted metrics barring the information ratio. The failure to reject the null hypothesis at the five percent level of significance when considering the information ratio of the superior active fund compared to the J203 can be attributed to the variation of returns of the average ​ex-post s​ uperior fund, as seen above in the Descriptive Statistics s​ ection. The information ratio’s denominator is the standard deviation of the differences between a security’s returns and its respective benchmark. The higher variation in returns of the average superior fund compared to the variation in returns of the J203 could imply a larger standard deviation of the differences in returns, thus inflating the denominator of the information ratio, and thus lowering the ratio. Table 7 ​and ​table 8 b​ elow summarise the statistical inferences made on comparing various risk-adjusted metrics between active funds and the passive J203 fund after higher-bound fees. The null and alternative hypotheses remain the same from above. 18 Metric Sharpe Ratio Treynor Ratio Information Ratio RAP (SD) RAP (SSD) Higher-Bound Fees One Tailed: CV = 1.682 Test Statistic P-Value Decision Do Not Reject Null - Hypothesis Do Not Reject Null - Hypothesis Do Not Reject Null - Hypothesis Do Not Reject Null - Hypothesis Do Not Reject Null - Hypothesis Table 7​: Right tailed Student’s T-test statistical inference summary, higher-bound fees. Average active fund vs J203. Metric Sharpe Ratio Treynor Ratio Information Ratio RAP (SD) RAP (SSD) High Fees One Tailed: CV = 1.701 Test Statistic P-Value Decision Do Not Reject Null- Hypothesis Do Not Reject Null- Hypothesis Do Not Reject Null - Hypothesis Do Not Reject Null- Hypothesis- Reject​ Null Hypothesis Table 8​: Right tailed Student’s T-test statistical inference summary, higher-bound fees. Average superior (ex-post) active fund vs J203. The average actively managed equity fund fails to reject the null hypothesis on all risk-adjusted fronts given higher-bound fees. This is no surprise given that the average actively managed equity fund failed to reject the null hypothesis on all risk-adjusted fronts for lower-bound fees. The average ​ex-post s​ uperior actively managed fund fails to reject the null hypothesis on all risk-adjusted fronts barring the M​2 RAP metric adjusted for downside variations in returns. It was found that downside variations in returns of the superior fund was lower than that of the J203 which explains the greater adjusted RAP of the superior fund over the J203. Implications of Findings Not surprisingly, given the level of development of South Africa’s financial sector, the findings closely match what has been uncovered in developed financial markets, as discussed by the consulted literature. However, the study does not disregard active management completely. Valuable information regarding the method of selecting superior active funds has 19 surfaced when considering Figlewski’s (1996) analysis of historic return variations and Jones & Wermers’ (2011) methods for identifying superior active managers. If superior actively managed funds can be selected using historic risk-analyses and historic performance metrics of funds and fund managers, then alpha should be generated on a recurring basis. However, the capturing of recurring alpha returns relies on an active management of funds, that is, actively managing one’s portfolio of active funds, ignoring transaction costs and taxes. Given the apparent failure of the average actively managed fund compared to the J203 benchmark, it is not advisable to hold a passive instrument which tracks active funds, such as a fund tracker ETF or index-styled investment vehicles tracking active funds. Concluding Remarks The research question explores the propriety and relevance of chasing excess returns in South African context. A South African context was considered given how small South Africa’s capital market is relative to other large developed capital markets abroad. The literature largely agreed that markets are efficient at disseminating information quickly and at almost no cost. However, the efficient market hypothesis does not explain acute mispricings in capital markets, which opens discussions as to how effectively can active managers exploit inefficiencies at the risk of their clients’ capital. The methodology employed tested mean monthly risk-adjusted metrics against their respective benchmark (J203) risk-adjusted metrics at the five percent level of significance using the right-tailed Student’s T-test. The average active fund outperformed the J203 before fees but failed when risk-adjusted metrics were adjusted for fees. However, the average superior active fund outperformed the J203 before and after fees on risk-adjusted performance. These findings suggest that excess returns can be generated consistently given the appropriate due diligence required to identify superior funds ​ex-ante​. The research further suggests that financial instruments which track active funds will not outperform its respective benchmark and that an active management approach to managing a pool of active funds is required to generate excess returns, ignoring taxes and transaction costs. 20 Limitations and Recommendations The primary research limitation is the failure of avoiding survivorship bias effectively. Many funds ceased to exist for the entire period under review. Survivorship bias was deemed acceptable to ignore as it was of the view that the impact of the exclusion of funds would not detract from the general message of the research conducted. Additionally, many new funds opened within the period under review. Unfortunately, fund closures and openings were excluded from the sample selected. The best way to counter this issue is to test the performance of each fund for the period in which it was open against its respective benchmark over the same period. The unavoidable problem faced is the amount investors lost on the Rand when funds were liquidated. Without this knowledge, it is futile to make any statistical inference on the performance of these funds under the period reviewed. Another limitation worth disclosing is the assumptions upon which asset pricing models are made. It was assumed that markets are ‘mostly’ efficient, given the literature reviewed, and that the CAPM does hold on average over the long-run. However, though it is a theory widely used in industry, its shortcomings do pose questions as to whether expected returns based on the CAPM are appropriate to use when conducting risk-adjusted returns calculations. It is recommended that future researchers decide upon which assumptions are appropriate when considering which pricing models to use when calculating risk-adjusted metrics. The CAPM has many adjustments, as discussed in the literature review and in the methodology. 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