Orientador: Roberto Andreani / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-10T15:35:32Z (GMT). No. of bitstreams: 1 Magro_RogerioCorrea_M.pdf: 1309841 bytes, checksum: 3935050b45cf1bf5bbba46ac64603d72 (MD5) Previous issue date: 2008 / Resumo: Dado um capital C e n opções de investimento (ativos), o problema de seleção de portfolio consiste em aplicar C da melhor forma possivel para um determinado perfil de investidor. Visto que, em geral, os valores futuros destes ativos não são conhecidos, a questão fundamental a ser respondida e: Como mensurar a incerteza? No presente trabalho são apresentadas tres medidas de risco: O modelo de Markowitz, o Value-at-Risk (VaR) e o Conditional Value-At-Risk (CVaR). Defendemos que, sob o ponto de vista teorico, o Valor em Risco (VaR) e a melhor dentre as tres medidas. O motivo de tal escolha deve-se ao fato de que, para o VaR, podemos controlar a influencia que os cenários catastroficos possuem sobre nossas decisões. Em contrapartida, o processo computacional envolvido na escolha de um portfolio ótimo sob a metodologia VaR apresenta-se notadamente mais custoso do que aqueles envolvidos nos calculos das demais medidas consideradas. Dessa forma, nosso objetivo e tentar explorar essa vantagem computacional do Modelo de Markowitz e do CVaR no sentido de tentar aproximar suas decisões aquelas apontadas pela medida eleita. Para tal, consideraremos soluções VaR em seu sentido original (utilizando apenas o parametro de confiabilidade ao buscar portfolios otimos) e soluções com controle de perda (impondo uma cota superior para a perda esperada) / Abstract: Given a capital C and n investment options (assets), the problem of portfolio selection consists of applying C in the best possible way for a certain investor profile. Because, in general, the future values of these assets are unknown, the fundamental question to be answered is: How to measure the uncertainty? In the present work three risk measures are presented: The Markowitz¿s model, the Value-at-Risk (VaR) and the Conditional Value-at-Risk (CVaR). We defended that, under the theoretical point of view, the Value in Risk (VaR) is the best amongst the three measures. The reason of such a choice is due to the fact that, for VaR, we can control the influence that the catastrophic sceneries possess about our decisions. In the other hand, the computational process involved in the choice of a optimal portfolio under the VaR methodology comes notedly more expensive than those involved in the calculations of the other considered measures. In that way, our objective is to try to explore that computational advantage of the Markowitz¿s Model and of CVaR in the sense of trying to approach its decisions the those pointed by the elect measure. For such, we will consider VaR solutions in its original sense (just using the confidence level parameter when looking for optimal portfolios) and solutions with loss control (imposing a superior quota for the expected loss) / Mestrado / Otimização / Mestre em Matemática Aplicada

This thesis evaluates the mean-variance analysis framework by comparing the performance of an optimized portfolio consisting of stocks from the Dow Jones Industrial Average to the performance of the Dow Jones Industrial Average index itself. The results show that the optimized portfolio performs better than the corresponding index when evaluated on the period between 2015 and 2019. However, the variance of the returns are high and therefore it is difficult to determine if mean-variance analysis performs better than its corresponding index in the general case. Furthermore, it is shown that individual stocks can still influence the movement of an optimized portfolio significantly, even though the model is supposed to diversify firm-specific risk. Thus, the authors recommend modifying the model by restricting the amount that is allowed to be invested in a single stock, if one wishes to apply mean-variance analysis in reality. To be able to draw further conclusions, more practical research within the subject needs to be done. / Denna uppsats utvärderar ramverket ”mean-variance analysis” genom att jämföra prestandan av en optimerad portfölj bestående av aktier från Dow Jones Industrial Average med prestandan av indexet Dow Jones Industrial Average självt. Resultaten visar att att den optimerade portföljen presterar bättre än motsvarande index när de utvärderas på perioden 2015 till 2019. Dock är variansen av avkastningen hög och det är därför svårt att bedöma om mean-variance analysis generellt sett presterar bättre än sitt motsvarande index. Vidare visas det att individuella aktier fortfarande kan påverka den optimerade portföljens rörelser, fastän modellen antas diversifiera företagsspecifik risk. På grund av detta rekommenderar författarna att modifiera modellen genom att begränsa mängden som kan investeras i en individuell aktie, om man önskar att tillämpa mean-variance analysis i verkligheten. För att kunna dra vidare slutsatser så krävs mer praktisk forskning inom området.

[pt] A dissertação é composta por três ensaios empíricos que usam dados históricos de ações americanas. O primeiro avalia o desempenho de uma abordagem de otimização de carteiras baseada na otimização de Markowitz. Os resultados mostram valor econômico positivo do portfólio resultante, mesmo na presença de custos de transação. O segundo artigo visa comparar e combinar a técnica desenvolvida no artigo anterior à abordagem paramétrica e avalia o desempenho da combinação das técnicas. Os resultados mostram que o desempenho da técnica paramétrica é inferior à técnica de Markowitz modificada e pouco melhor do que o mercado agregado. Isto sugere que o valor econômico de explorar a estrutura de covariância entre as ações é superior a aumentar pesos em ações cujas características oferecem relações risco-retorno maiores até o período. O terceiro ensaio avalia modelos de previsão da variação de retornos entre ações. As estatísticas utilizadas apontam que os modelos padrão não possuem poder preditivo superior a modelos que supõem que não há variação ou que usam a média histórica. Por meio do uso tanto de combinações de modelos lineares quanto estimação restrita de modelos com muitos fatores, mostro que é possível obter resultados ligeiramente superiores. / [en] The dissertation consists of three empirical essays which use historical data of stocks listed in NYSE. The first essay evaluates a portfolio selection approach based on the Markowitz optimization. Results show the portfolios have positive economic value, even after including transaction costs. The second essay compares the technique proposed in the first essay to the parametric approach. Results show the parametric approach performs worse than the modified Markowitz approach and shlightly better than the aggregated market. This suggests that exploring the covariance structure of stocks provides better results than overweighting stocks with characteristics associated to better riskreturn ratios in the past. The third essay evaluates models that forecast the cross-sectional variation in stock returns. Given the statistics used, benchmark models do not show greater forecasting power than skeptical or naive models. By using linear model combination or lasso technique on a model with several factors, I show it is possible to obtain slightly better results.

Although nonprofit organization (NPO) leaders play crucial roles in society, financial distress and vulnerability are common for many NPO leaders, with some NPOs closing as a result of these conditions. The purpose of this single-case study was to explore the diversification strategies used by 10 leaders and senior staff of an NPO in the mid-Atlantic region of the United States through the conceptual lens of Markowitz's modern portfolio theory. Data were collected through in-depth semistructured interviews and analysis of organizational documents, internal archival data, social media, literature, and online databases. Through thematic analysis, 7 revenue diversification themes emerged: adding revenue streams; establishing an operating reserve; establishing positive financial performance; achieving financial stability, sustainability, organizational capacity, and organizational resilience; using transparency; achieving efficiency and organizational effectiveness; and using a marketing strategy. Additionally, 7 key themes emerged: documenting and implementing systematic processes, developing an approach to process improvement, implementing cross-department action plans, increasing transparency, reversing the adverse trend in forum participation, building a data-management system, and increasing individual and organizational capacity. These findings have implications for positive social change, in that they may offer NPO executives new insights and strategies to support revenue diversification, thereby helping them to reduce volatility in funding, decrease financial risk, avoid dependence on sole-source revenue, and identify opportunities to increase flexibility in support of organizational goals and objectives to increase services.

<p>Capital Asset Pricing Model (CAPM) är den prissättningsmodell som mest frekvent används av aktörer på den finansiella marknaden samt i litteratur för att förklara sambandet mellan risk och förväntad avkastning. Teorin grundades under 1960-talet av William Sharpe och tidiga empiriska tester av modellen visade att den med hög förklaringsgrad kunde estimera en framtida förväntad avkastning givet en viss risknivå. På senare år har dock CAPM fått stark kritik eftersom nya empiriska undersökningar demonstrerat att modellen inte längre verkar visa en rättvisande avkastning i förhållande till risk.</p><p>För att undersöka om den över 40 år gamla modellen fortfarande visar någorlunda rättvisande beskrivningar av verkligheten har vi ställt oss frågan: Går det att med hjälp av historiska data förutspå en riskfylld tillgångs avkastning på den svenska aktiemarknaden?</p><p>Vid besvarade av denna fråga har studien syftet Att med hjälp av portföljer studera huruvida sambandet mellan risk och avkastning, vilket postuleras av CAPM, stämmer på den nutida svenska aktiemarknaden.</p><p>Vi har utifrån vår kunskapssyn kritisk rationalism använt oss av en kvantitativ metod för att försöka ge svar på problemställningen, vilken angreps med ett deduktivt tillvägagångssätt. Den teoretiska referensramen behandlar teorier som portföljval, den effektiva marknadshypotesen och CAPM. Det empiriska materialet består av historiska aktiekurser vilka bearbetades och användes till att komponera flertalet portföljer. Dessa portföljer har sedan analyserats genom regressionsanalys och jämförts med ett aktiemarknadsindex i syfte att besvara vår problemställning.</p><p>Det som framkommit genom studien är att det till viss del med hjälp av historiska data går att förutspå en riskfylld tillgångs avkastning på den svenska aktiemarknaden. Även om vi delvis kan ge stöd åt den testade modellen anser vi inte att betavärdet, som ensamt förklarande variabel och mått på risk, bör tillämpas vid beslutsfattande av investeringar, något som CAPM förutsätter att det ska göra. Det linjära samband som CAPM postulerar bedömer vi vara bristande i tillämpbarhet på dagens komplicerade aktiemarknad eftersom fler variabler än historiska data påverkar aktiekurserna.</p>

Capital Asset Pricing Model (CAPM) är den prissättningsmodell som mest frekvent används av aktörer på den finansiella marknaden samt i litteratur för att förklara sambandet mellan risk och förväntad avkastning. Teorin grundades under 1960-talet av William Sharpe och tidiga empiriska tester av modellen visade att den med hög förklaringsgrad kunde estimera en framtida förväntad avkastning givet en viss risknivå. På senare år har dock CAPM fått stark kritik eftersom nya empiriska undersökningar demonstrerat att modellen inte längre verkar visa en rättvisande avkastning i förhållande till risk. För att undersöka om den över 40 år gamla modellen fortfarande visar någorlunda rättvisande beskrivningar av verkligheten har vi ställt oss frågan: Går det att med hjälp av historiska data förutspå en riskfylld tillgångs avkastning på den svenska aktiemarknaden? Vid besvarade av denna fråga har studien syftet Att med hjälp av portföljer studera huruvida sambandet mellan risk och avkastning, vilket postuleras av CAPM, stämmer på den nutida svenska aktiemarknaden. Vi har utifrån vår kunskapssyn kritisk rationalism använt oss av en kvantitativ metod för att försöka ge svar på problemställningen, vilken angreps med ett deduktivt tillvägagångssätt. Den teoretiska referensramen behandlar teorier som portföljval, den effektiva marknadshypotesen och CAPM. Det empiriska materialet består av historiska aktiekurser vilka bearbetades och användes till att komponera flertalet portföljer. Dessa portföljer har sedan analyserats genom regressionsanalys och jämförts med ett aktiemarknadsindex i syfte att besvara vår problemställning. Det som framkommit genom studien är att det till viss del med hjälp av historiska data går att förutspå en riskfylld tillgångs avkastning på den svenska aktiemarknaden. Även om vi delvis kan ge stöd åt den testade modellen anser vi inte att betavärdet, som ensamt förklarande variabel och mått på risk, bör tillämpas vid beslutsfattande av investeringar, något som CAPM förutsätter att det ska göra. Det linjära samband som CAPM postulerar bedömer vi vara bristande i tillämpbarhet på dagens komplicerade aktiemarknad eftersom fler variabler än historiska data påverkar aktiekurserna.

This thesis investigates a technique to estimate the risk of the mean-variance (MV) portfolio optimization problem. We call this technique the Scaling technique. It provides a better estimator of the risk of the MV optimal portfolio. We obtain this result for a general estimator of the covariance matrix of the returns which includes the correlated sampling case as well as the independent sampling case and the exponentially weighted moving average case. This gave rise to the paper, [CMcS]. Our result concerning the Scaling technique relies on the moments of the inverse of compound Wishart matrices. This is an open problem in the theory of random matrices. We actually tackle a much more general setup, where we consider any random matrix provided that its distribution has an appropriate invariance property (orthogonal or unitary) under an appropriate action (by conjugation, or by a left-right action). Our approach is based on Weingarten calculus. As an interesting byproduct of our study - and as a preliminary to the solution of our problem of computing the moments of the inverse of a compound Wishart random matrix, we obtain explicit moment formulas for the pseudo-inverse of Ginibre random matrices. These results are also given in the paper, [CMS]. Using the moments of the inverse of compound Wishart matrices, we obtain asymptotically unbiased estimators of the risk and the weights of the MV portfolio. Finally, we have some numerical results which are part of our future work.

Centralized power system planning covers time windows that range from ten to thirty years. Consequently, it is the longest and most uncertain part of power system economics. One of the challenges that power system planning faces is the inability to accurately predict random events; these random events introduce risk in the planning process. Another challenge stems from the fact that, despite having a centralized planning scheme, generation plans are set first and then transmission expansion plans are carried out. This thesis addresses these problems. A joint model for generation and transmission expansion for the vertically integrated industry is proposed. Randomness is considered in demand, equivalent availability factors of the generators, and transmission capacity factors of the transmission lines. The system expansion model is formulated as a two-stage stochastic program with fixed recourse and probabilistic constraints. The transmission network is included via a DC approximation. The mean variance Markowitz theory is used as a risk minimization technique in order to minimize the variance of the annualized estimated generating cost. This system expansion model is capable of considering the locations of new generation and transmission and also of choosing the right mixture of generating technologies. The global tendency is to move from regulated power systems to deregulated power systems. Power pool electricity markets, assuming that the independent system operator is concerned with the social cost minimization, face great uncertainties from supply and demand bids submitted by market participants. In power pool electricity markets, randomness in the cost and benefit functions through random demand and supply functions has never been considered before. This thesis considers as random all the coefficients of the quadratic cost and benefit functions and uses the mean variance Markowitz theory to minimize the social cost variance. The impacts that this risk minimization technique has on nodal prices and on the elasticities of the supply and demand curves are studied. All the mathematical models in this thesis are exemplified by the six-node network proposed by Garver in 1970, by the 21-node network proposed by the IEEE Reliability Test System Task Force in 1979, and by the IEEE 57- and 118-node systems.

Centralized power system planning covers time windows that range from ten to thirty years. Consequently, it is the longest and most uncertain part of power system economics. One of the challenges that power system planning faces is the inability to accurately predict random events; these random events introduce risk in the planning process. Another challenge stems from the fact that, despite having a centralized planning scheme, generation plans are set first and then transmission expansion plans are carried out. This thesis addresses these problems. A joint model for generation and transmission expansion for the vertically integrated industry is proposed. Randomness is considered in demand, equivalent availability factors of the generators, and transmission capacity factors of the transmission lines. The system expansion model is formulated as a two-stage stochastic program with fixed recourse and probabilistic constraints. The transmission network is included via a DC approximation. The mean variance Markowitz theory is used as a risk minimization technique in order to minimize the variance of the annualized estimated generating cost. This system expansion model is capable of considering the locations of new generation and transmission and also of choosing the right mixture of generating technologies. The global tendency is to move from regulated power systems to deregulated power systems. Power pool electricity markets, assuming that the independent system operator is concerned with the social cost minimization, face great uncertainties from supply and demand bids submitted by market participants. In power pool electricity markets, randomness in the cost and benefit functions through random demand and supply functions has never been considered before. This thesis considers as random all the coefficients of the quadratic cost and benefit functions and uses the mean variance Markowitz theory to minimize the social cost variance. The impacts that this risk minimization technique has on nodal prices and on the elasticities of the supply and demand curves are studied. All the mathematical models in this thesis are exemplified by the six-node network proposed by Garver in 1970, by the 21-node network proposed by the IEEE Reliability Test System Task Force in 1979, and by the IEEE 57- and 118-node systems.

Portfolios of contemporary integrated petroleum companies consist of a few dozen Exploration and Production (E&P) projects that are usually spread all over the world. Therefore, it is important not only to manage individual projects by themselves, but to also take into account different interactions between projects in order to manage whole portfolios. This study is the step-by-step representation of the method of optimizing portfolios of risky petroleum E&P projects, an illustrated method based on Markowitz’s Portfolio Theory. This method uses the covariance matrix between projects’ expected return in order to optimize their portfolio. The developed computer model consists of four major modules. The first module generates petroleum price forecasts. In our implementation we used the price forecasting method based on Sequential Gaussian Simulation. The second module, Monte Carlo, simulates distribution of reserves and a set of expected production profiles. The third module calculates expected after tax net cash flows and estimates performance indicators for each realization, thus yielding distribution of return for each project. The fourth module estimates covariance between return distributions of individual projects and compiles them into portfolios. Using results of the fourth module, analysts can make their portfolio selection decisions. Thus, an advanced computer model for optimization of the portfolio of petroleum assets has been developed. The model is implemented in a MATLAB® computational environment and allows optimization of the portfolio using three different return measures (NPV, GRR, PI). The model has been successfully applied to the set of synthesized projects yielding reasonable solutions in all three return planes. Analysis of obtained solutions has shown that the given computer model is robust and flexible in terms of input data and output results. Its modular architecture allows further inclusion of complementary “blocks” that may solve optimization problems utilizing different measures (than considered) of risk and return as well as different input data formats.