Student Number : 9005994G - MSc research report - School of Construction Economics and Management - Faculty of Engineering and the Built Environment / The objectives of this research are to assess the returns, risks and correlation of a mixed-asset portfolio, establish the role of real estate in a mixed-asset portfolio and suggest an appropriate real estate allocation in the South African pension fund industry. The issue of low real estate allocation has been a subject of interest to practitioners and academics, both locally and internationally, despite the diversification benefit that real estate provides in a mixed-asset portfolio. A statistical approach was considered most the appropriate tool for analyzing returns. Solver optimizer in the excel spreadsheet package was used to generate efficient frontiers and the associated values of portfolios. Real estate provided a lower return of 1.25% and a lower standard deviation of 4.90% compared to equities with a return of 1.39% and the highest standard deviation of 6.23%, whilst bonds provided the best risk-return trade off, with a return of 1.42% and the lowest standard deviation of 2.64%. An equally -weighted portfolio consisting of bonds and stocks and a portfolio consisting bonds, stocks and real estate was simulated. The equally -weighted portfolio of bonds and stocks provides a return of 1.41% and a standard deviation of 3.76%. The minimum variance with bias to bonds provides a higher return of 1.42% at a lower level of risk of 2.62%. The equally -weighted portfolio consisting of bonds, stocks and real estate provides a return of 1.35%, with a lower risk of 3.49%. The minimum variance with bias to bonds provides almost the same return of 1.40% at a lower level of risk of 2.54% compared to the bond and share portfolio. The Chi-Square statistical tool was used to test the diversification benefit of real estate. It can be concluded that the standard deviation of the portfolio with property is close enough to the standard deviation without property of 3.76% and cannot statistically say that it is different given the 5% level of significance. The Sharpe ratio was used to test the favourable risk adjusted returns offered by real estate. It concluded that property provides favourable risk adjusted returns and diversification benefits, as illustrated with the increasing portfolio return from 7.44% to 8.66% on Sharpe ratio basis and standard deviation of the portfolio decreasing from 3.76% to 2.54%. The literature review generally supported the view that real estate has a role in a mixed-asset portfolio. Research topics such as securitized versus unsecuritized real estate, real estate allocation and diversification, returns and risk, inflation hedging, modern portfolio theory and the efficient -frontier were analysed and related to the research report. The empirical analysis supports the hypothesis that real estate provides diversification benefits. The property cycle is positive and it is supported by positive property fundamentals like (vacancies are at lowest levels, capitalisation rates are strengthening, the property cycle is turning positive and a stable interest rate environment). The positive property fundamentals will lead to earnings growth. An allocation of between 10% based on the lower end of the minimum variance and 15% based on the lower end of the risk/return ratio is recommended for a mixed-asset portfolio.

In an ever-changing global environment, the ability to adapt to the current economic climate is essential for a company to prosper and survive. Numerous previous re- search state that better risk management and low overall risks will lead to a higher firm value. The purpose of this study is to examine if portfolio theory, made for fi- nancial portfolios, can be used to compose product portfolios in order to minimize risk and optimize returns. The term contingent hedge is defined as an optimal portfolio that can be identified today, that in the future will yield a stable stream of returns at a low level of risk. For companies that might engage in costly hedging activities on the futures market, the benefits of creat- ing a contingent hedge are several. These include creating an optimized portfolio that minimizes risk and avoid trading contracts on futures markets that would incur hefty transaction costs and risks. Using quantitative financial models, product portfolio compositions are generated and compared with the returns and risks profile of individual commodities, as well as the actual product portfolio compositions of publicly traded mining companies. Us- ing Modern Portfolio Theory an efficient frontier is generated, yielding two inde- pendent portfolios, the minimum risk portfolio and the tangency portfolio. The Black-Litterman model is also used to generate yet another portfolio using a Bayesian approach. The portfolios are generated by historic time-series data and compared with the actual future development of commodities; the portfolios are then analyzed and compared. The results indicate that the minimum risk portfolio provides a signif- icantly lower risk than the compositions of all mining companies in the study, as well as the risks of individual commodities. This in turn will lead to several benefits for company management and the firm’s shareholders that are discussed throughout the study. However, as for a return-optimizing portfolio, no significant results can be found. Furthermore, the analysis suggests a series of improvements that could potentially yield an even greater result. The recommendation is that mining companies can use the methods discussed throughout this study as a way to generate a costless contin- gent hedge, rather than engage in hedging activities on futures markets.

Syfte: Studera sju portföljer och notera den bästa typen av portfölj med högst avkastning till lägst risk. Metod: Sekundärdata är grunden för uträkning av samtliga portföljers avkastningar, risker och korrelation. Studien är deduktiv med kvantitativa inslag av kända teorier av nobelpristagare i ekonomisk vetenskap.  Slutsats: Studien visar att stora bolag i olika branscher är ett vinnande portföljinnehåll för denna studie. Stora bolags aktier har visat högre avkastning till lägre risk jämfört med små bolag under studiens tid då ekonomiska kriser drabbade marknaden. Den mest presterande portföljen var därför storbolagsportföljen. Vidare forskning: Längre tidsperspektiv och nya teorier som Jensens alfa samt Treynorkvot är av intresse för vidare forskning för att styrka vår slutsats. / Intention: To study seven portfolios and note the best type of portfolio with the maximum return at a minimum risk. Method: Secondary data is the basis for calculation of the total portfolio returns, risk and correlation. This study is deductive based using a quantitative method of world-known theories of Nobel laureates in economic sciences. Conclusion: The study shows that the best efficient portfolio contains large companies in different lines of business. Large companies' shares have higher returns at lower risk compared to small companies in circumstances to difficult economic situations globally. The best performed portfolio was the portfolio with large companies.                                       Further Research: Longer period of time study and a study of new theories such as Jensens Alfa and Tretnor ratio would be interesting for further research.

Syfte: Syftet med studien är att undersöka hur aktivt förvaltade fonder presterar jämfört med indexfonder, när avkastningen har justerats för förvaltningsavgiften. Indexfonden representeras av ett jämförelseindex och studien omfattar en tioårsperiod, 2000-2009. Det faktum att en apa vann aktie SM 1993, framför professionella placerare, visar att aktiekurser är slumpmässiga. Varför ska en investerare då lita på att en förvaltare är bättre på att utvärdera marknaden och dess placeringsmöjligheter än andra? Metod: En kvantitativ metod har använts i uppsatsen, där data har erhållits från Morningstar och SIX Telekurs. Det insamlade materialet har bearbetats i Microsoft Excel för att beräkna fondernas avkastning och prestationsmått. Resultatet har redovisats i tabeller och diagram i empirikapitlet, för att sedan analyseras och jämföras med den teoretiska referensramen. Resultat & slutsats: Endast en av tio aktivt förvaltade fonder överträffar index, därmed dras slutsatsen att indexfonder är ett bättre investeringsalternativ än aktivt förvaltade fonder. Resultatet visar därmed att den högre förvaltningsavgiften som fondbolagen kräver från sina kunder inte är berättigat. Förslag till fortsatt forskning: Baserat på de resultat som kommit fram i uppsatsen, voredet intressant att genomföra en kvalitativ studie där fondförvaltarens åsikter är i fokus. Hur motiveras den höga förvaltningsavgiften, när de inte överträffar index? / Aim: The fact that a monkey won the Swedish Championship in stocks in 1993, ahead of professional investors, shows that stock prices are random. Why should an investor trust that a professional manager is better on evaluating the market and its investment opportunities than others? The purpose with this thesis is to investigate how active managed funds perform compared to index funds, after subtraction of the management fee. The index fund is represented by a “comparison index” and the research covers a period of ten years, between 2000 and 2009. Method: A quantitative method has been used in this study, where the information has been received from Morningstar and SIX Telekurs. Microsoft Excel has been used to process the collected data in order to calculate the expected return and the risk measures. The result is presented in diagrams and charts in order to analyse and compare it with the theory. Result & Conclusions: Only one out of ten active managed funds outperform index,therefore draws the conclusion that index funds is a better investment option than active managed funds. The result shows that the higher management fee that stock exchange companies claims is not appropriate. Suggestions for future research: Based on the results in this thesis, it would be interesting to do a qualitative research where the focus is on the fund managers’ opinions. How can they motivate the high management fee, when they don’t outperform index?

The combination of two or more portfolio rules is theoretically convex in return-risk space, which provides for a new class of portfolio rules that gives purpose to the Mean-Variance framework out-of-sample. The author investigates the performance loss from estimation risk between the unconstrained Mean-Variance portfolio and the out-of-sample Global Minimum Variance portfolio. A new two-fund rule is developed in a specific class of combined rules, between the equally weighted portfolio and a mean-variance portfolio with the covariance matrix being estimated by linear shrinkage. The study shows that this rule performs well out-of-sample when covariance estimation error and bias are balanced. The rule is performing at least as good as its peer group in this class of combined rules.

The modelling of volatility has long been seminal to finance and risk management in general, as it provides information on the spread of portfolio returns. In order to reduce the overall volatility of a stock portfolio, modern portfolio theory (MPT), within an efficient market hypothesis (EMH) framework, dictates that a well-diversified portfolio should have a market beta of one (thereafter adjusted for risk preference), and thus move in sync with a benchmark market portfolio. Such a stock portfolio is highly correlated with the market, and considered to be entirely hedged against unsystematic risk. However, the risks within and between stocks present in a portfolio still impact on each other. In particular, risk present in a particular stock may spill over and affect the risk profile of another stock included within a portfolio - a phenomenon known as volatility spill-over effects. In developing economies such as South Africa, portfolio managers are limited in their choices of stocks. This increases the difficulty of fully diversifying a stock portfolio given the volatility spill-over effects that may be present between stocks listed on the same exchange. In addition, stock portfolios are not static, and therefore require constant rebalancing according to the mandate of the managing fund. The process of constant rebalancing of a stock portfolio (for instance, to follow the market) becomes more complex and difficult during times of financial distress. Considering all these conditions, portfolio managers need all the relevant information (more than MPT would provide) available to them in order to select and rebalance a portfolio of stocks that are as mean-variance efficient as possible. This study provides an additional measure to market beta in order to construct a more efficient portfolio. The additional measure analyse the volatility spill-over effects between stocks within the same portfolio. Using intraday stock returns and a residual based test (aggregate shock [AS] model), volatility spill-over effects are estimated between stocks. It is shown that when a particular stock attracts fewer spill-over effects from the other stocks in the portfolio, the overall portfolio volatility would decrease as well. In most cases market beta showcased similar results; this change is however not linear in the case of market beta. Therefore, in order to construct a more efficient portfolio, one requires both a portfolio that has a unit correlation with the market, but also includes stocks with the least amount of volatility spill-over effects among each other. / MCom (Risk Management), North-West University, Potchefstroom Campus, 2013

The modelling of volatility has long been seminal to finance and risk management in general, as it provides information on the spread of portfolio returns. In order to reduce the overall volatility of a stock portfolio, modern portfolio theory (MPT), within an efficient market hypothesis (EMH) framework, dictates that a well-diversified portfolio should have a market beta of one (thereafter adjusted for risk preference), and thus move in sync with a benchmark market portfolio. Such a stock portfolio is highly correlated with the market, and considered to be entirely hedged against unsystematic risk. However, the risks within and between stocks present in a portfolio still impact on each other. In particular, risk present in a particular stock may spill over and affect the risk profile of another stock included within a portfolio - a phenomenon known as volatility spill-over effects. In developing economies such as South Africa, portfolio managers are limited in their choices of stocks. This increases the difficulty of fully diversifying a stock portfolio given the volatility spill-over effects that may be present between stocks listed on the same exchange. In addition, stock portfolios are not static, and therefore require constant rebalancing according to the mandate of the managing fund. The process of constant rebalancing of a stock portfolio (for instance, to follow the market) becomes more complex and difficult during times of financial distress. Considering all these conditions, portfolio managers need all the relevant information (more than MPT would provide) available to them in order to select and rebalance a portfolio of stocks that are as mean-variance efficient as possible. This study provides an additional measure to market beta in order to construct a more efficient portfolio. The additional measure analyse the volatility spill-over effects between stocks within the same portfolio. Using intraday stock returns and a residual based test (aggregate shock [AS] model), volatility spill-over effects are estimated between stocks. It is shown that when a particular stock attracts fewer spill-over effects from the other stocks in the portfolio, the overall portfolio volatility would decrease as well. In most cases market beta showcased similar results; this change is however not linear in the case of market beta. Therefore, in order to construct a more efficient portfolio, one requires both a portfolio that has a unit correlation with the market, but also includes stocks with the least amount of volatility spill-over effects among each other. / MCom (Risk Management), North-West University, Potchefstroom Campus, 2013

Submitted by glenda rossetti (glenda.rossetti@hotmail.com) on 2017-02-14T21:47:23Z No. of bitstreams: 1 Dissertação_GR_VF.docx: 838594 bytes, checksum: 74fa4382a60e547afda6b97112754b86 (MD5) / Rejected by Renata de Souza Nascimento (renata.souza@fgv.br), reason: Glenda, boa noite Para que possamos aceitar seu trabalho, por gentileza, deixe o seu nome em letras maiúsculas. Em seguida, submeter novamente. O trabalho deve estar em PDF. Att on 2017-02-14T22:36:30Z (GMT) / Submitted by glenda rossetti (glenda.rossetti@hotmail.com) on 2017-02-14T22:42:30Z No. of bitstreams: 1 Dissertação_GR_VF.docx: 838594 bytes, checksum: 74fa4382a60e547afda6b97112754b86 (MD5) / Rejected by Renata de Souza Nascimento (renata.souza@fgv.br), reason: Glenda, Por gentileza, na capa, contra capa seu nome deve estar em letras maiúsculas. Salvar o arquivo em PDF para submete-lo novamente. Att on 2017-02-14T23:00:11Z (GMT) / Submitted by glenda rossetti (glenda.rossetti@hotmail.com) on 2017-02-14T23:06:00Z No. of bitstreams: 1 Tese.pdf: 1154738 bytes, checksum: 1f5b61ad6de4e5cc8e13490446a2f782 (MD5) / Approved for entry into archive by Renata de Souza Nascimento (renata.souza@fgv.br) on 2017-02-14T23:12:23Z (GMT) No. of bitstreams: 1 Tese.pdf: 1154738 bytes, checksum: 1f5b61ad6de4e5cc8e13490446a2f782 (MD5) / Made available in DSpace on 2017-02-15T15:09:04Z (GMT). No. of bitstreams: 1 Tese.pdf: 1154738 bytes, checksum: 1f5b61ad6de4e5cc8e13490446a2f782 (MD5) Previous issue date: 2017-01-19 / This paper has two objectives: verify whether systematic risk is different across countries by comparing risk return ratio of market portfolios and equally weighted portfolios (1/N) to verify their efficiency and the levels of diversification across countries by showing risk behavior increasing diversification. Monthly dollars returns were selected from the forty (40) largest shares of fourteen (14) capital markets indexes of the major developed and emerging economies during the period from June 30, 2011 to May 31, 2016 to construct equally weighted portfolios (1/N) and compare them to market portfolios. Based on the assuming of Modern Portfolio Theory (MPT), the empirical tests have shown evidence that systemic risks are different between the capital markets of the main developed and emerging economies, that market portfolios are not efficient and despite of this, the number of shares required to achieve a certain level of diversification is similar across countries. The results found are in agreement with the literature researched both internationally and nationally. / Este trabalho tem dois objetivos: verificar se o risco sistemático é diferente entre países comparando a relação risco retorno dos portfólios de mercado com portfólios igualmente ponderados (1/N) para verificar sua eficiência e se os níveis de diversificação entre os países mostrando o comportamento do risco com o aumento da diversificação. Foram selecionados retornos mensais em dólares das quarenta (40) maiores ações de catorze (14) índices de mercados de capitais das principais economias desenvolvidas e emergentes no período de 30 de Junho de 2011 á 31 de Maio de 2016 para construir portfólios igualmente ponderados (1/N) e compará-los aos portfólios de mercado. Partindo dos pressupostos da Teoria Moderna do Portfólio (MPT) os ensaios empíricos realizados neste trabalho revelaram evidências de que os riscos sistêmicos são diferentes entre os mercados de capitais das principais economias desenvolvidas e emergentes, que os portfólios de mercados não são eficientes e apesar disso, o número de ações necessárias para adquirir certo nível de diversificação é semelhante entre os países. Os resultados encontrados estão de acordo com a literatura pesquisada tanto internacionalmente quanto nacionalmente.

>Magister Scientiae - MSc / In this thesis, we discuss methods for optimising the expected rate of return of a portfolio with minimal risk. As part of the work we look at the Modern Portfolio Theory which tries to maximise the portfolio's expected rate of return for a cer- tain amount of risk. We also use Quadratic Programming to optimise portfolios. Generally it is recognised that portfolios with a high expected return, carry higher risk. The Modern Portfolio Theory assists when choosing portfolios with the lowest possible risk. There is a nite number of assets in a portfolio and we therefore want to allocate them in such a way that we're able to optimise the expected rate of return with minimal risk. We also use the Markowian approach to allocate these assets. The Capital Asset Pricing Model is also used, which will help us to reduce our e cient portfolio to a single portfolio. Furthermore we use the Black-Litterman model to try and optimise our portfolio with a view to understanding the current market conditions, as well as considering how the market will perform in the future. An additional tool we'll use is Value at Risk. This enables us to manage the market risk. To this end, we follow the three basic approaches from Jorion [Value at Risk. USA: McGraw-Hills, 2001]. The Value at Risk tool has become essential in calcu- lating a portfolio's risk over the last decade. It works by monitoring algorithms in order to nd the worst possible scenarios within the portfolio. We perform several numerical experiments in MATLAB and Microsoft Excel and these are presented in the thesis with the relevant descriptions.

This thesis is focused on the analysis of performance of chosen russian mutual funds on the basis of achieved yield and risk. After short introduction to the russian market of mutual funds, the paper deals with a theoretical background underlying the performance indicators. Risk perception and following construction of indicators are discussed in detail from the perspective of modern and post-modern portfolio theory. The indicators are interpreted and appropriateness of their application is assessed. The analytic part is devoted to the application of discussed methods on 10 open-ended equity mutual funds. Based on the result, the funds are compared with each other and with selected market index.