In this paper, I evaluate the out-of-sample performance of the portfolio optimizer relative to the naïve and market strategy on the Swedish stock market from January 1998 to December 2012. Recent studies suggest that simpler strategies, such as the naïve strategy, outperforms optimized strategies and that they should be implemented in the absence of better estimation models. Of the 12 strategies I evaluate, 11 of them significantly outperform both benchmark strategies in terms of Sharpe ratio. I find that the no-short-sales constrained minimum-variance strategy is preferred over the mean-variance strategy, and that the historical sample estimator creates better minimum-variance portfolios than the single-factor model and the three-factor model. My results suggest that there are considerable gains to optimization in terms of risk reduction and return in the context of portfolio selection.

TESIS PARA OPTAR AL GRADO DE MAGISTER EN FINANZAS / The use of the Sharpe ratio for the measurement of the performance of the financial assets is widely generalized, although there is empirical evidence of serious problems with the assumptions behind the distribution functions. This paper explores the conditions under which the Sharpe ratio is efficient to analyze the performance of financial asset portfolios, a situation that is not true in the presence of strong autocorrelation. We demonstrate the effect that autocorrelation has in determining the best means of performance measurement, defining a robustness function of the variance of the Spearman coefficient degradation, allowing to define monitoring and control criteria in the task of tracking the evolution of financial assets and makes an adequate selection of a combination of risk and return, expanding the spectrum of analysis for the performancemeasurement of the financial series, placing an alarmfor the evaluation of the performance of the financial assets.

I focus on analyzing the performance of various hedge fund strategies in my diploma thesis.

Bitcoin is an asset that demonstrated a high increase in price since it was launched in 2009, meanwhile it has been a very volatile and risky asset. Previous research has indicated that an allocation of bitcoin in investor’s portfolio could increase return as well as risk adjusted return. Furthermore, bitcoin has been observed to be uncorrelated to many markets; creating diversification opportunities and in some instances acted as a hedge against various stock markets. Due to the similarities between bitcoin and gold they have often been compared as alternative investment assets. Therefore, it is of interest for investors to understand if bitcoin could be included into a stock-portfolio in the Swedish market to increase risk adjusted returns and if bitcoin is a better alternative investment, than gold. Furthermore, if bitcoin could be used as hedge against the Swedish stock market. Three different portfolios with bitcoin were created, 1% bitcoin, 4% bitcoin and 8% bitcoin, the rest of the portfolio constitutes of Stockholm gross-index (OMXSGI). The portfolios are compared to OMXSGI and similar portfolios involving gold and OMXSGI. The portfolios are created for four different periods: 2011- 2021, 2016-2021, the bear market during the pandemic and the year 2020. Results reveals that during normal market behavior an 8% allocation of bitcoin and OMXSGI generates the highest Sharpe ratio. Also, that a small allocation of bitcoin can generate higher returns to lower risk then OMXSGI. During normal market behavior portfolio with bitcoin performs higher returns and Sharp ratio than portfolios with gold but to a higher risk. Additionally, bitcoin is not correlated to the Swedish market and implies that it possibly may be used as a hedge during normal market behavior. During the corona bear market bitcoin has a high correlation to OMXSGI and has a similar negative return but to a higher volatility. Meanwhile gold act as a safe haven during turbulent market behavior. To conclude during normal market times bitcoin creates opportunities for investors to include bitcoin to the portfolio. High allocations of 8% bitcoin might be too much risk for risk averse investors. During the corona bear market bitcoin portfolios generates worse returns to a higher risk and gold is a better asset to hold. Bitcoin and cryptocurrencies are assets which have some unique risks that cannot be measured by the Sharp ratio. Thus limit the results and analysis of the study.

This paper sets out to evaluate whether investment recommendations of South African share analysts provide any value to an investor in the Johannesburg Stock Exchange (JSE). The study focuses on the creation of a portfolio based on the recommendations by analysts between December 2002 and July 2010. The monthly returns and respective risk-adjusted returns of this portfolio are compared to those of the SATRIX Top 40 over the same period of time. The paper also evaluates the effectiveness of the SATRIX Top 40 as a performance benchmark by comparing it to a portfolio for shares of family-controlled or owner-managed companies listed on the JSE. The study utilises analyst consensus recommendations, with focus on buy and sell recommendations, to create a buy and hold portfolio that is compared to the SATRIX Top 40. The SATRIX Top 40 is further compared to ten-share portfolio of family-owned or owner-managed companies. The study finds that analysts’ recommendations lead to higher risk-adjusted returns for an investor when compared to the SATRIX Top 40. The returns are even better in a bear market environment when compared the benchmark SATRIX Top 40. It is also found that a portfolio of shares of family-controlled or owner-managed companies performs better than the SATRIX Top 40 and thus provides a better benchmark for an investor. Copyright / Dissertation (MBA)--University of Pretoria, 2010. / Gordon Institute of Business Science (GIBS) / unrestricted

En esta tesis se estudian carteras de inversión compuestas únicamente por fondos de inversión cotizados (ETF), los que utilizan un activo índice como benchmark y buscan replicar sus resultados con diversificación a bajos costos y mínimas inversiones de capital. En el caso de un inversor argentino, cuyo mercado y economía tienen un alto grado de volatilidad, con elevada inflación y permanente devaluación de la moneda, restricciones en la compra de divisas, así como también falta de estabilidad en las políticas macroeconómicas de largo plazo, podría encontrar en activos de otras economías una respuesta a todos estos inconvenientes, manteniendo el valor real de sus inversiones en el tiempo. En este trabajo se hace énfasis en ETF de diferentes mercados del mundo, asociados a activos de distinta naturaleza, los cuales son cotizados en moneda dólar estadounidense, cuya tenencia en sí misma ya puede considerarse un refugio de valor en el contexto actual. A su vez, se pretende obtener rendimientos que puedan superar la inflación anualmente en dicha moneda y generar un flujo positivo a largo plazo mediante una gestión pasiva de la misma, es decir sin una necesidad permanente de rearmado de la cartera. Metodológicamente, la investigación presenta un abordaje cuantitativo, de índole empírica con alcance correlacional, trabajando a partir de información secundaria histórica sobre los ETF seleccionados en ventanas temporales de 5 y 10 años y su comparación con la situación con Covid-19 durante el primer semestre de 2020. Sobre los datos se calculan rendimientos, volatilidades y ratios de Sharpe de las carteras para diferentes problemas de optimización. A partir de los análisis realizados se puede argumentar que para el período de análisis resulta redundante la inclusión de más de un ETF de grandes grupos de acciones, como lo son los que representan al “S&P500” (SPY), las empresas en crecimiento de pequeña capitalización (VBK), el índice russell 2000 de empresas pequeñas (IWV) y el índice que replica prácticamente la totalidad del mercado de acciones estadounidense (VTI), ya que los mismos encuentran en un índice de acciones de base tecnológica (QQQ) una cartera dominante que no da lugar a otros grupos de ETF de renta variable, solo presentándose beneficios de la diversificación en el ORO y la renta fija, con GLD y VCIT (bonos corporativos) respectivamente. En relación a los mercados internacionales emergentes y otros desarrollados no norteamericanos, el resultado es idéntico, ya que el desempeño de los ETF incluidos en este trabajo no justifica su incorporación para el rango de los últimos 5 años, siendo sus métricas de rendimiento claramente inferiores a las del mercado norteamericano. Desde el punto de vista de un inversor argentino se puede determinar que el uso de instrumentos internacionales permite una disminución considerable del riesgo de su cartera aplicando la optimización del precio del riesgo, así como también en caso de que el perfil de la persona lo amerite, un mayor rendimiento igualando la volatilidad obtenida por un portafolio integrado únicamente por activos argentinos. / In this thesis, investment portfolios composed only of listed Exchange-traded funds (ETF) are studied, those that use an asset or index as a benchmark and seek to replicate their results with diversification at low costs and minimal capital investments. In the case of an Argentine investor, whose market and economy have a high degree of volatility, with high inflation and permanent devaluation of the currency, restrictions on the purchase of foreign currency, as well as lack of stability in long-term macroeconomic policies, you could find an answer to all these inconveniences in assets from other economies, maintaining the real value of your investments over time. In this paper, emphasis is placed on ETF from different markets around the world, associated with assets of different nature, which are quoted in US dollar currency. Holding in US dollars can already be considered a refuge of value in the current context. In turn, the aim is to obtain returns that can exceed inflation annually in said currency and generate a long-term positive flow through passive management of the same. Methodologically, the research presents a quantitative approach, of an empirical nature with a correlational scope, working from secondary historical information on the ETF selected. The time windows are 5 and 10 years and their comparison with the Covid-19 situation in the first semester of 2020. Portfolio returns, volatilities and Sharpe ratios are calculated on the data for different optimization problems. Based on the analyzes carried out, it can be argued that for the period of analysis the inclusion of more than one ETF of large groups of stocks is redundant. Index representing the “S&P500” (SPY), small growth companies capitalization (VBK), the russell 2000 index of small companies (IWV) and the index that tracks practically the entire US stock market (VTI), find in a technology-based equity index (QQQ) a dominant portfolio. It does not give rise to other groups of variable income ETF, only presenting benefits from diversification in GOLD and fixed income, with GLD and VCIT (corporate bonds) respectively. In relation to emerging international markets and other non-North American developed markets, the result is identical, since the performance of the ETF included in this study does not justify their incorporation. For the range of the last 5 years, their performance metrics was clearly lower than those of the North American market. From the point of view of an Argentine investor, it can be determined that the use of international instruments allows a considerable reduction of the risk of their portfolio by applying the optimization of the risk price, as well as in case the profile of the person warrants it, a higher return equaling the volatility obtained by a portfolio made up solely of Argentine assets.

Jämfört med andra branscher har fastighetsmarknaden låg avkastning på totala tillgångar, de utnyttjar istället en hävstångsstrategi för att skapa mer effektiv utväxling på eget kapital. Det finns många riskvariabler kopplat till fastighetsbranschen och flera sätt att differentiera sig från den osystematiska risken. De kommunala fastighetsbolagen har en finansieringskälla Kommuninvest, som enbart vänder sig till allmännyttiga bolag och inte privata aktörer. Syftet med uppsatsen är att historiskt analysera hur risk och avkastning genererats av kommunala och privata fastighetsbolag. Metoden är kvantitativ, kombinerat med en deduktiv metod och som har en förklarande ansats. Utifrån teori har vi formulerat tre hypoteser för att undersöka om vi kan finna indikatorer på hur kommunala och privata fastighetsbolag skiljer sig till från varandra. För att genomföra undersökningen har uppsatsen utgått från en kvantitativ metod och statistiska test har gjorts för att kunna analysera utfallen. Resultaten indikerar på att det finns en signifikant skillnad mellan kommunala och privata fastighetsbolag i två av hypoteserna. Hur undersökningen är genomförd beskrivs i den empiriska metoden. Från de resultat som blivit har det fastställts att det finns mer att undersöka och nya förslag på fortsatt forskning har utformats. / Compared to other industries, real estate markets have historically low return on total assets, instead they use a leverage strategy to create a more efficient ratio on return on equity. There are many risk variables associated with real estate and several ways for real estate firms to differentiate themselves from the unsystematic risk. The municipal property firms have a funding source Kommuninvest, only turning to public utilities and not private actors. The purpose of this paper is to analyze the historical risk and return generated by municipal and private property firms. The method is quantitative, combined with a deductive theory, which has an explanatory approach. Based on theory we have formulated three hypotheses to explore and see if we can find indicators of how differences between municipal and private property is. To conduct the survey, the thesis has a quantitative method and statistical tests to analyze the outcomes. The results indicate that there is a significant difference in two of the hypotheses between municipal and private property. How the survey is conducted is described in the empirical method. From the results determined, the intention shows that there is more to explore, and new suggestions for further research have been suggested.

The traditional way to analyze stocks and portfolios within the area of finance have been restricted to Sharpe and Markovitz. The Omega function and its properties enlighten the field of finance and differs from the traditional ways when it comes to the volatility of the stocks. The Omega function, the Sharpe performance criteria and mean-variance model by Markovitz will be used. All calculations are done in Matlab and the data sheets are excel tables. The aim of this thesis is to investigate the nordic small cap market by using the Omega function, Sharpe performance criteria and the mean variance model by Markovitz. In order to to see how the purposed methods differs.

[pt] Nos anos 50, Henrry Markowitz criou um modelo que maximiza a razão entre a média e o desvio padrão [Markowitz, 1952 & 1959]. Esse modelo é muito utilizado até os dias de hoje. Porém ele supõe que os retornos dos ativos do portifólio sejam normalmente distribuídos, e isso não é tão comum, logo seu uso é limitado. Esse trabalho propõe um modelo mais robusto em termos de risco, que possa ser utilizado sem restrições de distribuições, não necessitando do conhecimento a priori das distribuições e que seja uma aproximação do modelo de Markowitz, caso os retornos dos ativos sejam normalmente distribuídos. Para possibilitar isso, o índice maximizado pelo modelo de Markowitz é escrito como uma função da média e da entropia. A seleção do portifólio é dada pelo portifólio que obtiver o maior índice proposto dentro da amostra selecionada. / [en] In the 50 s, Henrry Markowitz created a model that maximizes the mean to standard deviation ratio [Markowitz, 1952]. This model is largely use in the financial market. However, it assumes that portfolio s equities returns are normally distributed, and this not always happens, therefore limiting its use. This work proposes a more robust model in risk measure that can be used without any distribution constraint, however it reduces to Markowitz model if the assets returns are normal distributed. To make it possible, the index maximized by Markowitz will be written as a function of the mean and the entropy. The portfolio selection is that one witch has the largest proposed index in the selected sample.

I denna uppsats undersöker vi kryptovalutor ur ett ekonomiskt och finansiellt perspektiv. Vi skapar en optimal portfölj av de 28 största kryptovalutorna enligt marknadsvärdet den 3 mars 2020 genom av att använda oss av Markowitz (1952) portföljvalsteori. Den optimala portföljen jämförs med en marknadsportfölj som är skapad av de 100 största kryptovalutorna enligt marknadsvärdet, för att bilda oss en uppfattning om kryptovalutamarknaden och hur man kan utnyttja kryptovalutor i investeringssyfte. CAPM används för att kunna se relationen mellan risk och avkastning mellan den optimala portföljen och marknadsportföljen. Vi kommer även att undersöka om CAPM ger samma resultat som Markowitz portföljvalsteori. Den optimala portföljen jämförs dessutom med den svenska aktiemarknaden för att undersöka om den optimala kryptovalutaportföljen påverkas av trender på den svenska aktiemarknaden. / This thesis studies cryptocurrencies from an economic and financial perspective. The research is carried out by constructing an optimal portfolio of the 28 biggest cryptocurrencies according to market capital on the 3rd of March 2020 by using Markowitz (1952) portfolio optimization theory. The optimal portfolio is then compared to the market portfolio, which is constructed of the hundred largest cryptocurrencies according to market capital, to study the cryptocurrency market. CAPM is also used to find out the risk-return relationship and to see if CAPM gives us the same optimal portfolio as Markowitz portfolio optimization theory. The optimal portfolio is also compared to the Swedish stock market index, OMXS30, to study if the optimal portfolio is affected by trends in the Swedish stock market.