A thesis presented to the School of Economic and Business Sciences, Faculty of Commerce, Law and Management, University of Witwatersrand in fulfilment of the requirements for the degree of Master of Commerce (M.Com) in Business Finance, January 2017 / Diversification has remained a central tenet in investment theory over multiple decades due to its demonstrated value as a risk mitigation technique. Increasing the number assets in a portfolio, where the magnitude of correlation is relatively slim, increases the amount of diversification while also encountering increased costs in the form of transaction costs, taxes and the like. Thus, it is imperative to solve for the optimal point of diversification to ensure an investor does not encounter unnecessary costs. This study aims to solve for the point of optimal diversification in an equity portfolio, focusing on the South African environment. This is achieved by employing a framework using both the traditional simulation method as well as more advanced mathematical techniques, namely: genetic programming and particle swarm optimisation. Marked improvements are realised in this study with regards to the methodology and results through the application of advanced mathematical approaches in addition to removing the restriction of equal weightings being applied to each share in the portfolio. The results revealed that an optimal portfolio can be constructed using up to only 15 shares. Secondly, the genetic programming approach demonstrated increased strength compared to the traditional simulation and particle swarm optimisation approaches, obtaining a greater level of diversification with fewer shares. Finally, although the aim of the study is focused on modelling the relationship between the number of shares in a portfolio and the achievable diversification benefits, it is also established that the portfolios indicated as being optimally diversified achieved market beating returns. / XL2018

Thesis (M.Com. (Finance))--University of the Witwatersrand, Faculty of Commerce, Law and Management, School of Economic and Business Sciences, 2017 / This dissertation investigates the inclusion of volatility into the asset allocation decision, first as an asset class, and second as a tool for dynamic equity allocation. An examination on whether volatility exposure as an asset class has the necessary characteristics to form part of the broader investment universe is conducted. This is accomplished by comparing the risk-return characteristics of three naked option-selling strategies, a bull put spread strategy and a VIX futures strategy with the S&P 500 Index. Each volatility strategy is also included as part of a 30/30/40 volatility/equity/bond portfolio and compared to a traditional 60/40 equity/bond portfolio. Historically, the results indicate that all individual volatility strategies generated superior Sharpe ratios and exhibited less severe drawdowns than the S&P 500 Index, particularly during the 2008 Global Financial Crisis. Additionally, all volatility blended portfolios experienced better tail-risk profiles than the 60/40 equity/bond portfolio, with the naked option-selling strategies also generating similar returns as the 60/40 portfolio both over the full sample period as well during the period of recovery following the 2008 Global Financial Crisis. The results suggest that the returns associated with option-selling strategies are consistent, and have resulted in strong long-run risk-adjusted performance, qualifying short volatility exposure attained through option-selling strategies as an asset class. It however remains unclear whether the VIX futures strategy qualifies as an asset class given that it aims to exploit a market anomaly in the form of potentially non-priced volatility clustering in the S&P 500 Index. While the strategy generated considerable outperformance from 2004 to 2009, it underperformed from 2009 to 2016 suggesting that much of the non-priced volatility clustering has since been traded away. Drawing on the evidence of volatility clustering in equity markets, a managed volatility trading rule that regulates portfolio exposure between cash and equity based on how high the prevailing volatility level was relative to historical volatility levels is developed. Although transaction costs were not accounted for, the results indicated that the managed volatility trading rule has historically generated considerably superior Sharpe ratios than equity in developed and developing markets. In conclusion, volatility exposure attained through option-selling strategies has proven to be an attractive asset class, and historical evidence suggests that its inclusion into a traditional 60/40 equity/bond portfolio is likely to reduce the risk of future risk-adjusted underperformance relative to what had been achieved in the past. Additionally, the managed volatility trading rule remains an attractive alternative to investors who are precluded from investing in volatility as an asset class. / GR2018

The international linkages of stock markets have important implications for cost of capital and portfolio diversification. Recent trends in globalization, financial liberalization and financial innovation raises questions with regard to whether African stock markets are being integrated into world equity markets. This study examines the extent to which the South African (SA) equity market is integrated into the world equity markets using daily data for the period 1995-2007. The study is divided into three main parts, each looking at the different ways in which integration can be considered. The first investigates whether there is long run comovement between the SA and the major global equity markets. Both bivariate and multivariate Johansen (1988) and Johansen and Juselius (1990) cointegration approaches were utilised. Vector Error Correction Models (VECMs) are then estimated for portfolios which show evidence of cointegration. The second part analyses returns linkages using the Vector Autoregressive (VAR), block exogeneity, impulse response and variance decomposition. The third part examines the behaviour of volatility and volatility linkages among the stock markets. Firstly volatility is analysed using the GARCH, EGARCH and GJR GARCH. Simultaneously, the hypothesis that investors receive a premium for investing in more risky stock markets is explored using the GARCH-in mean. The long term trend of volatility is also examined. Volatility linkages are then analysed using the VAR, block exogeneity, impulse response and variance decomposition. The first part established that no bivariate cointegration exists between the SA and any of the stock markets being studied, implying that pairwise portfolio diversification is potentially worthwhile for SA portfolio managers. However, multivariate cointegration exists for some portfolios, with the US, UK, Germany and SA showing evidence of error correction for some of these portfolios. Findings on return linkages is that there are significant returns linkages among the markets, with the US and SA being the most exogenous and most endogenous respectively. Findings regarding volatility are that the volatility in all the markets is inherently asymmetric and that except for the US there is no risk premium in any of the markets. The long term trend of volatility in all the stock markets was found to be relatively stable. The final finding was that significant volatility linkages exist among the markets, with the US being the most exogenous and SA and China showing evidence of bidirectional linkages. Overall, except for volatility linkages, the integration of SA into the global equity markets is still quite low. Thus, both SA and international investors can capitalise on this portfolio diversification potential. On the other hand, policy makers should capitalise on this and make policies that will attract the much needed foreign investors.

Thesis (MComm (Business Management))--University of Stellenbosch, 2009. / Measuring the performance of any financial portfolio is only relevant if compared relative to another similar portfolio. Over the years the norm in the industry has been to use market capitalisation indices as benchmarks to measure performance. Market capitalisation indices, such as the FTSE/JSE ALSI, create a natural return drag because of the overweighting of overvalued stocks and the underweighting of undervalued stocks. It is this return drag that led to the creation of the Fundamental Indexing concept by Research Affiliates in 2005. Fundamental Indexing weights stocks based on their economic footprint in the market rather than their market capitalisation. The Fundamental Indexing approach uses four metrics, namely sales, book values, dividends and cash flows to calculate this economic footprint. The Fundamental Index is referred to as the RAFI (Research Affiliates Fundamental Index) Index The Fundamental Index concept delivered very good results when applied to the South African stock market. The South African RAFI Composite Index outperformed the FTSE/JSE All Share Index by 5.55% p.a. compounded annually during the period 1995 to 2006. This return was achieved with a similar risk profile as the FTSE/JSE All Share Index. This index also had similar turnover rates relative to the FTSE/JSE All Share Index. The South African RAFI Composite Index also outperformed the FTSE/JSE All Share Index by 5.48% p.a. compounded during the measurement period when investment income is included. The Fundamental Index outperformance clearly disproves the efficient market hypothesis. According to modern portfolio theory it is impossible to earn abnormal profits in excess of a market capitalisation index. The success of Fundamental Indices proves that market capitalisation indices are not optimal and deliver sub-optimal returns. Specifically, it can be seen that the South African market is inefficient and that the FTSE/JSE All Share Index is not the best tool for measuring the performance of the financial markets in South Africa.

Thesis (MComm)--Stellenbosch University, 2002. / ENGLISH ABSTRACT: This assignment sets out to address the concept of equity duration, where equity duration is viewed as a measure of the interest rate sensitivity of common stock's market value. The traditional use of standard dividend discount models, results in extremely long duration estimates for equities - in the order of 10 years for income stocks to 25 years and more for growth companies whose cash flows are not expected to materialize until some future period. Leibowitz (1986) identified an alternative approach for assessing equity duration empirically. These empirical estimates of actual stock price sensitivity to underlying changes in interest rates imply that equities behave as if they are much shorter duration instruments. Various attempts have been made to reconcile the difference between theoretical predictions of equity duration and empirical findings. The differences in duration of assets in place and growth opportunities are given as a possible reason for the above mentioned differences. It is argued that investment opportunities are similar to options a company has. These option-like characteristics of growth opportunities may alter the basic relationship between equity valuation and interest rate changes. The option framework suggests that the duration of growth companies may be shorter (not longer) than those of assets in place. The results from option theory can however not be applied directly to growth options, since some of the assumptions may not be valid in the case of growth options. The presence of these growth options makes it virtually impossible to calculate equity duration theoretically. This study empirically tests the relationship between growth opportunities and equity duration by focussing the attention on the interest rate sensitivity of South African growth companies. The following hypotheses regarding equity duration and growth companies are postulated: • There is a significant difference in interest rate sensitivity between growth companies and low-growth companies. • There is a significant difference between duration of growth companies measured using nominal interest rates and duration of growth companies using real interest rates. All non-mining companies on the Johannesburg Securities Exchange SA, for the period 1980 to 2000, were analysed. These companies were sorted into different portfolios that reflected their growth opportunities. Market capitalisation, book-to-market and price-earnings ratios were used as proxies to rank companies according to growth opportunities. The results from univariate regressions suggest positive duration for common equities. The negative relationship between equity returns and changes in nominal interest rates are independent of size, book-to-market or price-earnings ratios of the sampled companies. Including the market factor as an independent variable results in markedly different equity duration. The duration is correlated with size, as both coefficients and t-statistics increase when moving from small companies to larger companies. In addition, the small companies have negative not positive duration, as was the case for simple univariate regressions. There is also some evidence that high growth portfolios, as measured by low book-to-market and high price-earnings ratios, are less sensitive to interest rate changes than low growth portfolios. Employing all three Fama and French's factors, there is no longer a cross-sectional dependence on company size, with the mean duration being close to zero and statistically insignificant in virtually all cases. Also, when dividing changes in the nominal interest rate into changes in real rates and changes in inflation, it does not significantly affect the estimates of equity duration. The author found no evidence to support the stated hypotheses, when employing the Fama and French's three factor model. This may mean that the relationships are subsumed in the Fama and French risk factors. / AFRIKAANSE OPSOMMING: Hierdie werkstuk bestudeer die konsep van die duur van gewone aandele (equity duration), waar die duur van 'n gewone aandeel gedefinieer word as 'n maatstaf van die rentekoerssensitiwiteit van die markwaarde van die aandeel. Die tradisionele gebruik van standaard dividend verdiskonterings modelle, lei tot uiters lang duur beramings vir gewone aandele - in die orde van 10 jaar vir inkomste aandele tot 25 jaar en meer vir groei ondernemings wie se kontantvloei nie verwag word om te materialiseer voor 'n sekere toekomstige datum nie. Leibowitz (1986) identifiseer 'n alternatiewe empiriese benadering vir die beraming van gewone aandeel duur. Hierdie empiriese bepaling van die sensitiwiteit van die werklike aandeelprys tot onderliggende veranderings in rentekoerse, impliseer dat gewone aandele reageer asof hulle baie korter duur instrumente is. Verskeie pogings is aangewend om die verskille tussen teoretiese voorspellings van gewone aandeel-duur en empiriese bevindings te rekonsilieer. Die verskille tussen duur van bates in plek en groei-geleenthede word aangevoer as 'n moontlike rede vir bogenoemde verskille. Dit word geargumenteer dat investeringsgeleenthede soortgelyk is aan die opsies wat 'n onderneming het. Hierdie opsie-soortgelyke eienskappe van groei-geleenthede kan die basiese verhouding tussen gewone aandeel waardasie en rentekoers verandering wysig. Die opsie raamwerk dui daarop dat die duur van groei-ondernemings korter kan wees (en nie langer nie) as die van bates in plek. Die resultate van opsie teorie kan egter nie direk toegepas word op groei-opsies nie, aangesien sekere van die aannames nie geldig mag wees in die geval van groei-opsies nie. Die teenwoordigheid van hierdie groei-opsies het tot gevolg dat dit feitlik onmoontlik is om gewone aandeel-duur teoreties te bereken. Die studie toets empiries die verhouding tussen groei-geleenthede en gewone aandeel-duur deur te fokus op die rentekoers sensitiwiteit van Suid Afrikaanse groei-ondernemings. Die volgende hipoteses met betrekking tot die gewone aandele duur en groei-ondernemings word gestel: • Daar is 'n betekenisvolle verskil in rentekoers sensitiwiteit tussen groei-ondernemings en lae groei-ondernemings. • Daar is 'n betekenisvolle verskil tussen duur van groei-ondernemings gemeet deur gebruik te maak van nominale rentekoerse en duur van groei-ondernemings deur gebruik te maak van reële rentekoerse. Alle nie-myn ondernemings op die Johannesburg Sekuriteite Beurs SA, vir die periode 1980 tot 2000, is ontleed. Hierdie ondernemings is gesorteer in verskillende portefeuljes wat hulle groei geleenthede reflekteer. Markkapitalisasie, boek-tot-markwaarde en prysverdienste verhoudings is gebruik as maatstawwe om ondernemings te rangskik volgens groeigeleenthede. Die resultate van enkel veranderlike regressies dui positiewe duur aan vir gewone aandele. Die negatiewe verhouding tussen aandeelopbrengs en verandering in nominale rentekoerse is onafhanklik van grootte, boek-tot-markwaarde of prysverdienste verhoudings vir die getoetste ondernemings. Indien die markfaktor ingesluit word, as 'n onafhanklike veranderlike, lei dit tot opvallend verskillende gewone aandeel-duur. Die duur is gekorreleer met grootte, met beide koëffisiënte en t-statistieke wat styg wanneer beweeg word van klein ondernemings tot groter ondernemings. Addisioneel, die klein ondernemings het negatiewe, nie positiewe duur, anders as in die geval van eenvoudige enkel veranderlike regressies. Daar is ook bewyse dat hoë groei portefeuljes, soos gemeet deur lae boek-tot-markwaarde en hoë prysverdienste verhoudings, minder sensitief is vir rentekoers veranderings as lae groei portefeuljes. Met die aanwending van al drie Fama en French se faktore is daar nie meer kruis-selektiewe afhanklikheid (cross-selectional dependence) op ondernemingsgrootte aanwesig nie, met die gemiddelde duur wat naby nul is en statisties onbedeidend in feitlik all gevalle is. Wanneer die verandering in die nominale rentekoers verdeel word in veranderings in reële koerse en veranderings in inflasie, beïnvloed dit ook nie betekenisvol die bepaalde gewone aandeel duur nie. Die outeur het met die gebruik van die Fama & French drie faktor model geen bewyse gevind wat die vermelde hipoteses staaf nie. Dit mag beteken dat die rente-risiko verwantskappe in die Fama en French risiko faktore vervat is.

Thesis (MComm)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: Investment styles and more particularly the relative outperformance of certain styles under differing market conditions have been widely researched. Furthermore, investment professionals are constantly on the lookout for factors that could possibly be indicative of the subsequent outperformance of certain investment styles. With the value-growth phenomenon at the centre of this debate, there is an attempt in this study to shed some light on this anomaly from a purely South African perspective. Using monthly data for the period 1991 to 2011, and calculating price-to-book value (P/B) ratios for all the stocks included in the FTSE/JSE All-Share Index, the methodology employed by The Brandes Institute (2009A), based on work of Lakonishok, Shleifer and Vishny (1994), will be utilised in this study in order to determine whether the relative outperformance of value stocks over growth stocks can be anticipated in advance. Stocks were ranked monthly on the basis of their relative P/B ratios and subsequently four new portfolios were created each month, with the growth portfolio consisting of the highest 25% P/B ratio stocks and the value portfolio capturing the lowest 25% P/B ratio stocks. After portfolio creation, quartile-by-quartile performance was tracked over the following five years. The relative performance of the value versus growth portfolio was compared to the valuation difference multiple, calculated as the median P/B ratio of the growth portfolio divided by the median P/B ratio of the value portfolio, to determine if a relationship existed between valuation disparities and the subsequent relative performance of value and growth stocks. The all-cap (FTSE/JSE All-Share Index) segment was further divided into large-cap (FTSE/JSE Top-40 Index), mid-cap (FTSE/JSE Mid-cap Index) and small-cap (FTSE/JSE Small-cap Index) segments in order to determine if a consistent relationship could be identified within different market capitalisation sectors of the market. A significant relationship was found between the valuation difference multiple and subsequent performance of value and growth stocks in all segments of the JSE Mainboard. Historically, the higher the valuation difference multiple, the higher the subsequent outperformance of value stocks over the subsequent five-year period, as compared to growth stocks. This was found to be significant within the FTSE/JSE All-Share Index, the FTS/JSE Top-40 Index, the FTSE/JSE Mid-Cap Index and the FTSE/JSE Small-Cap Index. An exception to the above findings was the post-2002 period within the FTSE/JSE Top-40 Index. During this period it was not possible to identify a relationship between the valuation difference multiple and subsequent value stock outperformance. / AFRIKAANSE OPSOMMING: Verskillende beleggingstyle en meer spesifiek, die relatiewe uitprestering van sekere style onder verskillende mark omstandighede, is wyd nagevors oor die afgelope paar dekades. Professionele beleggers is ook gedurig op die uitkyk vir moontlike faktore wat die uitprestering van sekere beleggingstyle vooraf kan aandui. Met die waarde-groei verskynsel sentraal in hierdie debat, is die doelwit in hierdie studie om die waarde-groei verskynsel te ondersoek vanuit 'n eg Suid-Afrikaanse mark perspektief. Deur maandelikse data vir die periode 1991 tot 2011 te gebruik en daaropvolgende prys-tot-boekwaarde (P/B) verhoudings te bereken vir al die aandele wat deel was van die FTSE/JSE Alle-Aandele Indeks, sal daar in hierdie studie die metodologie van 'The Brandes Institute' (2009A) in die Verenigde State van Amerika, gebaseer op die werk van Lakonsihok, Shleifer en Vishny (1994), toegepas word om te probeer bepaal of die relatiewe uitprestering van waarde aandele oor groei aandele vooraf voorspel kan word. Aandele is maandeliks ingedeel op die basis van hul onderskeie P/B verhoudings. Deur hierdie proses is daar maandeliks vier nuwe portefeuljes geskep, met die groei portefeulje wat die hoogste 25% van P/B verhouding aandele bevat het en die waarde portefeulje wat die laagste 25% van P/B verhouding aandele verteenwoordig. Prestasie beoordeling van die nuut geskepde portefeuljes was die volgende stap in die navorsingsproses waar kwartiel-tot-kwartiel prestasie beoordeling oor die daaropvolgende vyf-jaar periode na portefeulje ontstaan, plaasgevind het. Die relatiewe prestasie van die waarde en groei portefeuljes is vergelyk met die waardasie pariteit maatstaf, wat bereken is as die mediaan P/B verhouding van die groei portefeulje gedeel deur die mediaan P/B verhouding van die waarde portefeulje. Hierdie vergelyking is gebruik om te bepaal of 'n verhouding tussen die onderskeie waardasies van groei en waarde aandele en daaropvolgende prestasie bestaan. Die alle aandele segment is verder ook opgedeel in drie onderskeie indekse om te bepaal of 'n verwantskap binne al die verskillende markkapitalisasie sektore bestaan. Die grootste markkapitalisasie aandele is verteenwording deur die FTSE/JSE Top-40 Indeks; die medium markkapitalisasie aandele deur die FTSE/JSE Mid-Cap Indeks; en die kleinste markkapitalisasie aandele wat deel vorm van die FTSE/JSE Alle-Aandele Indeks is verteenwoording deur die FTSE/JSE Small-Cap Indeks. 'n Beduidende verwantskap is gevind tussen die waardasie pariteit maatstaf en daaropvolgende vyf-jaar prestasie van waarde en groei aandele. Histories hoe hoër die waardasie pariteit maatstaf, hoe groter die relatiewe uitprestering van waarde aandele oor die daaropvolgende vyf-jaar periode. Hierdie verskynsel is beduidend gevind vanuit 'n FTSE/JSE All-Share Indeks, FTSE/JSE Top-40 Indeks, FTSE/JSE Mid-Cap Indeks en FTSE/JSE Small-Cap Indeks perspektief. 'n Uitsondering was die FTSE/JSE Top-40 Indeks vir die periode na 2002, waar dit nie moontlik was om 'n beduidende verwantskap te identifiseer nie.

Thesis (MComm)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: This study examines the role of cross-sectional return dispersion in portfolio management by examining two topics. To begin with, the study considers why return dispersion changes over time. Given the influence of return dispersion on active portfolio return opportunity, it is important for managers to understand why return dispersion changes over time. For a sample of South African listed shares over the period June 1996 to December 2011, univariate time-series analysis reveals significant serial correlation in return dispersion which may be modelled using ARMA (1, 1) and GARCH (1, 1) processes. Further analysis within a rational economic framework reveals that return dispersion is countercyclical to aggregate economic activity and related to both local and foreign economic uncertainty. The study then considers the relationship between return dispersion and the return to investment strategies. If substantial association between return dispersion and any investment strategy exists, then it is possible for managers and fund sponsors to augment an understanding of when active return opportunity is high with strategies for exploiting return opportunities. Continuing within the rational economic framework, the study uses Spearman‟s rank correlation coefficients to show a significant positive relationship between return dispersion and the value premium. In aggregate, these findings suggest that it is possible for South African investors to understand why return dispersion changes over time, as well as how to take advantage of changes in return dispersion. / AFRIKAANSE OPSOMMING: Hierdie studie ondersoek die rol van opbrengsverspreiding oor die kruissnit van „n mark in portefeuljebestuur deur twee onderwerpe te bestudeer. Eerstens bestudeer die studie hoekom opbrengsverspreiding oor tyd verander. Gegewe die invloed van opbrengsverspreiding op aktiewe beleggingsgeleentheid is dit belangrik vir bestuurders om te verstaan hoekom opbrengsverspreiding oor tyd verander. Vir „n steekproef van Suid Afrikaanse aandele oor die periode Julie 1996 tot Desember 2011 dui enkelvoudige tydreeks analise aan dat opbrengsverspreiding beduidende outokorrelasie het, waar die outokorrelasie beskryf word deur ARMA (1, 1) en GARCH (1, 1) prosesse. Verdere analise binne „n rasionele ekonomiese raamwerk dui daarop dat opbrengsverspreiding kontra-siklies aan makro-ekonomiese aktiwiteit is en verwant is aan beide plaaslike en buitelandse ekonomiese onsekerheid. Die studies ondersoek daarna die verhouding tussen opbrengsverspreiding en die opbrengs van beleggings strategieë. Indien daar „n noemenswaardige verhouding is tussen opbrengsverspreiding en enige beleggings strategie, dan kan bestuurders beter oordeel watter strategieë hoë opbrengste lewer wanneer beleggingsgeleenthede hoog is. Die studie hou binne „n rasionele ekonomiese raamwerk en gebruik Spearman se rang-orde korrelasie koeffisiënte om „n beduidende positiewe verwantskap tussen opbrengsverspreiding en die opbrengs van die waardepremie aan te dui. As „n geheel dui hierdie bevindinge daarop aan dat dit moontlik is vir Suid-Afrikaanse beleggers om te verstaan hoekom opbrengsverspreiding oor tyd verander asook hoe om voordeel uit die verwantskappe te trek.

Thesis (MBA)--Stellenbosch University, 2006. / ENGLISH ABSTRACT: The Omega function is a relatively newly developed performance measure, falling within the class of downside risk measures. This measure does not make any assumptions regarding the return distributions evaluated, but incorporates the actual return distribution in its calculation. The sensitivity of this measure to simulated changes within the class of stable distributions was tested, within the range of parameters that was evident in the South African investment environment. The Omega and Sharpe ratios that were calculated for these distributions were ranked and compared. Even though the rankings were similar, discrepancies did occur. On investigation it was found that these discrepancies were caused by the inability of the Sharpe measure to differentiate between increased volatility caused by higher probability weighted gains (or positive skewness) and losses, as the Sharpe ratio penalises funds for volatility. The simulated tests were extended to various distributions, which have different risk profiles and distribution shapes, and ranked. A higher incidence of ranking differences occurred due to the inability of the Sharpe ratio to differentiate between gains and losses, correctly account for the risk of positively skewed distributions and lastly due to negative Sharpe ratios, caused by the average realised returns being exceeded by the threshold (target) rate, resulting in incorrect rankings. Comparison of rankings based on the Sharpe and Omega measures was performed on the class of general equity unit trusts over a five-year period, which resulted in statistically similar rankings. In extending the evaluation over shorter periods, the ran kings were still statistically similar, even though some differences were noteworthy. As the returns became more variable, the Omega measure captured this variation and risk whilst the Sharpe ratio was unable to, as its formulation is limited to two statistics, thus losing all this additional information. Normally performance evaluation is not initiated with a detailed analysis of the return distributions in order to determine which performance measure is more appropriate. The Omega measure incorporates the distribution into the calculation, which is not the case with the Sharpe measure. Therefore, even if the distributions are normal, the Omega measure gives exacty the same result as the Sharpe measure. However, where return distributions diverge from normality, we can be certain that the Omega measure will correctly incorporate the divergence, whilst it has been shown that in certain instances the Sharpe measure does not. The Omega measure adds another dimension to risk-adjusted performance evaluation and should be incorporated in the evaluation process. / AFRIKAANSE OPSOMMING: Die Omega-funksie, wat as 'n afwaartse risikomaatstaf geklassifiseer word, is 'n relatiewe nuut-ontwikkelde prestasiemaatstaf. Hierdie maatstaf maak nie enige aannames ten opsigte van die opbrengsverdelings wat ge-evalueer word nie, maar inkorporeer die werklike opbrengsverdeling in die berekening. Die sensitiwiteit van hierdie maatstaf tot gesimuleerde veranderinge in die klas van stabiele verdelings is getoets, binne die parameters van toepassing in die Suid Afrikaanse beleggingsomgewing. Die Omega- en Sharpe-maatstawe is bereken, georden en vergelyk. Alhoewel die rangordes meestal dieselfde was, het verskille in sommige gevalle voorgekom. Hierdie verskille is veroorsaak deur die onvermoe van die Sharpe-maatstaf om te onderskei tussen verhoogde volatiliteit veroorsaak deur 'n hoer waarskynlikheidsgeweegde wins, of positiewe skeefheid en verliese. Die Sharpe-maatstaf penaliseer alle volatiliteit. Die gesimuleerde toetse is uitgebrei na alternatiewe verdelings wat verskillende risikoprofiele het en is weereens georden. Weereens was die rangordes meestal dieselfde. Die verskille wat plaasgevind het, is veroorsaak deur die onvermoe van die Sharpe-maatstaf om tussen winste en verliese te onderskei, positiewe skeefheid korrek te verdiskonteer en laastens om negatiewe Sharpe-verhoudings in die korrekte rangorde te plaas. 'n Vergelyking van die rangordes van die Sharpe- en Omega-maatstawe is gedoen op die algemene effektetrusts oor 'n tydperk van vyf jaar. Die rangordes in geheel was statisties dieselfde. Hierdie toetse is vervolgens uitgebrei om korter tydperke in te sluit, wat weereens in geheel statisties dieselfde korrelasie getoon het, maar 'n paar individuele portefeuljes se rangordes het heelwat verskil. Soos die opbrengste gevarieer het, kon die Omega-maatstaf hierdie variasies en risiko verdiskonteer terwyl die Sharpe-maatstaf nie in staat was om hierdie risiko te verdiskonteer nie, aangesien sy formulering beperk is tot twee statistieke wat 'n verlies van inligting tot gevolg het. Normaalweg word prestasie-beoordeling nie begin met 'n gedetailleerde analise van die opbrengsverdelings om te bepaal watter prestasie-maatstaf meer toepaslik is nie. Die Omega-maatstaf inkorporeer die verdeling in die berekening, wat nie die geval is met die Sharpe-maatstaf nie. AI is die opbrengsverdelings normaal, gee die Omega-maatstaf dieselfde resultate as die Sharpe-maatstaf. Waar die verdelings egter afwyk van normaal, weet ons dat die Omega-maatstaf die afwykings korrek verdiskonteer, terwyl dit bewys is dat die Sharpe-maatstaf in sekere omstandighede nie die afwykings korrek verdiskonteer nie. Die Omega-maatstaf voeg 'n verdere dimensie by risiko-aangepaste prestasiemeting en behoort dus ingesluit te word in die evauleringsproses.

A research report submitted to the Faculty of Commerce, Law and Management in partial fulfilment of the requirements for the degree of Master of Commerce (Specialising in Taxation) / In this research report the South African taxation of carried interest in a private equity context is examined. The extent to which reform of that taxation should be considered is also presented in this report. The nature of carried interest in the South African private equity context is initially examined. Thereafter, a discussion of the relevant provisions of the Income Tax Act and related South African case law that would likely apply to the taxation of carried interest is set out. An analysis and determination of how appropriate and adequate the taxing provisions and relevant principles from case law are in the taxation of carried interest is provided. A recommendation for new legislation to deal with the taxation of carried interest has also been made. / MT2017

The volatility transmission in financial markets has important implications for investment decision making, portfolio diversification and overall macroeconomic stability. This paper analyses volatility transmission across four South African financial markets that is the stock, bond, money and foreign exchange markets, using daily data for the period 2000-2010. It also shows whether the volatilities in the SA financial markets present a different behaviour in bull and bear market phases. The effects of the international markets volatility to the local markets volatility was also looked at in this study. To obtain estimates of market volatility, the study experimented with various volatility models that include the GARCH, EGARCH and TARCH. To examine volatility interaction and the transmission of volatility shocks, a VAR model was estimated together with block exogeneity, impulse response and variance decomposition. The study found that there is limited volatility transmission across the SA financial markets. The study also found that the money market is the most exogenous of all markets since the other three financial markets volatility is insignificant to the money market (see impulse response results). For the bond market, volatility transmission was characterized with a decreasing trend. With regard to international markets volatility, it concluded that, the shocks in the international markets will eventually affect the movement in the local markets. The results also highlighted that, world and local markets are important in accelerating the volatility transmission in SA financial markets depending on whether they are in their bull or bear phases. In the case of South Africa, the study found that volatility transmission across markets is higher during bear market periods than bull market periods. Basing on the study results which show that the volatility transmission is limited across SA financial markets, the implication to local and international investors is that there is a greater potential for diversifying risk by investing in different South African financial markets.