[pt] O mercado brasileiro de energia elétrica é composto basicamente de matrizes hidroelétricas e termoelétricas, sendo que seu fornecimento pode ser contratado em dois ambientes, um de contratação regulamentada e outro livre. Dessa forma o apreçamento da energia é algo complexo e com incertezas, pois seu modelo leva em consideração comportamentos de afluências futuras, além de estimar a utilização de termoelétricas, que possuem fontes de energia mais caras. No Brasil, existem quatro submercados que podem ter preços divergentes. Algumas comercializadoras se utilizam dessa diferença buscando aferir ganhos extraordinários fazendo Swaps. Essa operação consiste em compra e venda de uma mesma quantidade de energia com liquidação fixada em uma determinada data com o preço à vista entre diferentes submercados. Essas empresas utilizam medidas de otimização de carteiras e controle de risco para fazerem operações ótimas, onde há maior probabilidade de maximizar o lucro, tendo o prejuízo máximo sob controle. Esse trabalho tem como objetivo encontrar a carteira de Swaps de energia que maximiza a medida Ômega, usada como avaliador de desempenho, tendo uma expectativa de lucro e com uma restrição de risco com um limite para o Conditional Value at Risk (CVaR), assim auxiliando as comercializadoras a maximizarem seu lucro não ultrapassando seu limite de risco. O estudo levou em consideração valores de previsão reais feitos por modelos fornecidos por órgãos especializados, levando em consideração os dados para os anos de 2012 e 2013 sendo estudadas todas as combinações possíveis de Swaps para a composição da carteira ótima para cada um dos anos estudados. A carteira ótima foi encontrada, no entanto, pode-se concluir que sua composição varia de acordo com os dados simulados não existindo assim uma carteira ótima única devendo essa ser calculada caso a caso. / [en] The Brazilian energy market is composed basically by hydroelectric and thermoelectric energy sources, which can be contracted in two different environments, one regulated and the other free. In this way, the pricing of energy is something complex and uncertain, because its model takes in consideration the behavior of future water affluences, besides estimating the more expensive thermal units. In Brazil, there are four submarkets that have diverging prices and some traders use this difference to reach extraordinary gains by entering into Swap operations. This operation consists of buying and selling a same amount of energy with its liquidation fixed at pre-determined date, at a spot price between different submarkets. These companies use portfolio optimization and risk management methods to reach optimal operations, in which there is a greater probability of maximizing profits, while measuring risk. This study aim to find the portfolio of Swaps that`s maximize the Omega measurement as the performance measurement, has a estimated profit and uses the conditional Value at Risk (CVaR) as the restriction for the risk that can be taken. Its objective is to help traders maximize their profit without exceeding their risk limit. The study took in consideration values from real previsions made by models provided by specialized agencies, taking in consideration all the data for the years of 2012 and 2013, with all the combinations of Swaps being studied. The optimal portfolio was achieved in both cases however, it`s possible to conclude that this composition varies according the input data, not existing thereby a unique optimal portfolio should that be calculated by case.

[pt] A seleção de um portfolio de renda fixa é um problema comumente enfrentado pelos agentes do mercado financeiro. A alocação ótima destes ativos melhora o nível de rentabilidade e lucratividade da instituição. Um dos trade-offs rotineiramente encontrado pelos gestores destas carteiras é decidir entre a compra de títulos pré-fixados e pós-fixados de curto prazo ou longo prazo, sendo que estes últimos no geral rendem mais devido ao prêmio de risco. Tais títulos, apesar de terem a sua rentabilidade já definida no momento da compra, podem ser vendidos a qualquer momento e sua nova rentabilidade estará sujeitas às marcações a mercado. O retorno da carteira composta por estes títulos é portanto uma variável aleatória que torna necessário o controle dos riscos de perda deste portfolio. O presente estudo teve por objetivo desenvolver um modelo de otimização da rentabilidade de uma carteira composta somente por títulos prefixados do tesouro nacional, com restrições ao nível de risco expresso através do Conditional Value at Risk. Após tal, foram realizados backtests para medir o desempenho do modelo e comparar a sua rentabilidade com o índice CDI. Os testes mostraram que o modelo apresenta resultados bons em rentabilidade e resultados satisfatórios em termos de controle de risco. / [en] Fixed-income portfolio selection is a common problem faced by financial market agents. The optimal allocation of these assets improves the profitability of institutions. A trade-off routinely found by the managers of these portfolios is deciding between buying floating rate securities or short-term or long-term fixed-rate securities, while the latter generally has a higher yield due to risk premium. Despite fixed rate securities have their return already set at the moment of purchase, they can be sold at any time and the new return will be subject to the current market prices. Since the return of a portfolio holding these securities is a random variable, we argue for the importance of a risk assessment and control a fixed income security portfolio. This study aimmed to develop an optimization model of return with a portfolio composed only on fixed and floating rate bonds from Brazil s sovereign treasury, using risk restrictions expressed on the Conditional Value at Risk measure. After that, backtestswere performed to measure model efficiency and compare its return to the Brazilian s Interbank rate. The tests have shown good results in profitability and risk control.

Modern portfolio theory (MPT) is an investment theory which was introduced by Harry Markowitz in 1952 and describes how risk averse investors can optimize their portfolios. The objective of MPT is to assemble a portfolio by maximizing the expected return given a level of market risk or minimizing the market risk given an expected return. Although MPT has gained popularity over the years it has also been criticized for several theoretical and empirical shortcomings such as using variance as a measure of risk, measuring the dependence with linear correlation and assuming that returns are normally distributed when in fact empirical data suggests otherwise. When moving away from the assumption that returns are elliptical distributed, for example normally distributed, we can not use linear correlation as a measure of dependence in an accurate way. Copulas are a flexible tool for modeling dependence of random variables and enable us to separate the marginals from any joint distribution in order to extract the dependence structure. The objective of this paper was to examine the applicability of a copula-CVaR framework in portfolio optimization compared to the traditional MPT. Further, we studied how the presence of memory, when calibrating the copulas, affects portfolio optimization. The marginals for the copula based portfolios were constructed using Extreme Value Theory and the market risk was measured by Conditional Value at Risk. We implemented a dynamic investing strategy where the portfolios were optimized on a monthly basis with two different length of rolling calibration windows. The portfolios were backtested during a sample period from 2000-2016 and compared against two benchmarks; Markowitz portfolio based on normally distributed returns and an equally weighted, non optimized portfolio. The results demonstrated that portfolio optimization is often preferred compared to choosing an equally weighted portfolio. However, the results also indicated that the copula based portfolios do not always beat the traditional Markowitz portfolio. Furthermore, the results indicated that the choice of length of calibration window affects the selected portfolios and consequently also the performance. This result was supported both by the performance metrics and the stability of the estimated copula parameters.

No description available.

Title: Almost stochastic dominance Author: Adam Štefánik Department: Probability and Mathematical Statistics Supervisor: RNDr. Ing. Miloš Kopa, PhD. Department of Probability and Mathematical Statistics, MFF UK Abstract: In the presented work we study the almost stochastic dominance and it's properties. Almost stochastic dominance is a relaxation of stochastic dominance. Almost stochastic dominance also deals with paradox situations occurring in case of stochastic dominance. This is a situation when stochastic dominance determines indifferent relation- ship between two portfolios, but in fact almost all investors can choose the better one. The original almost stochastic dominance presented by Leshno and Levy (2002) is compu- tationally expensive. Lizyayev and Ruszczy'nski (2012) suggested an alternative approach. This work introduces both approaches. The most interesting part of this work is a search for efficient portfolio with respect to the almost stochastic dominance by the simple linear programming. Lizyayev and Ruszczy'nski (2012) approach is applied to Kopa and Chovanec (2008) quantile approach for portfolio efficiency testing with respect to second order stochastic dominance. Keywords: almost stochastic dominance, efficiency, CVaR

Submitted by Mário Guerreiro Ribeiro (mariogr@poli.ufrj.br) on 2017-07-24T19:59:43Z No. of bitstreams: 1 Tese_MGuerreiro_Versao final.pdf: 1679486 bytes, checksum: 41cba20a3ce6b5eaeeb08b44f89fd439 (MD5) / Approved for entry into archive by Marcia Bacha (marcia.bacha@fgv.br) on 2017-07-27T13:48:10Z (GMT) No. of bitstreams: 1 Tese_MGuerreiro_Versao final.pdf: 1679486 bytes, checksum: 41cba20a3ce6b5eaeeb08b44f89fd439 (MD5) / Made available in DSpace on 2017-07-27T13:48:38Z (GMT). No. of bitstreams: 1 Tese_MGuerreiro_Versao final.pdf: 1679486 bytes, checksum: 41cba20a3ce6b5eaeeb08b44f89fd439 (MD5) Previous issue date: 2017-05-22 / The portfolio optimization analysis for quite some time was built around the variance measure. This approach is adequate when the assets returns are normaly distributed. However, in asymmetric or heavy-tailed distributions, the same weight cannot be given to the two tails of the distribution, what requires the use of other risk measures. One of the most known and widespread is VaR, but it cannot capture extreme events, is not a coherent measure and has optimization problems. For these reasons, the dissertation addresses the CVaR on the portfolio optimization for the Brazilian electric power sector. / A análise da otimização de carteiras por muito tempo foi pautada na medida da variância. Essa abordagem é propícia quando os retornos dos ativos são normais. Porém, em distribuições assimétricas ou com caudas pesadas não se pode dar o mesmo peso para as duas extremidades da distribuição, levando a necessidade da utilização de outras medidas de risco. Uma das mais conhecidas e difundidas é o VaR, porém o mesmo não consegue capturar eventos extremos, além de não ser uma medida coerente e possuir problemas de otimização. Por esses motivos, o CVaR é abordado para o caso da otimização de portfólios do setor de energia elétrica brasileiro.

L’objet de cette thèse est d’analyser comment traiter le problème de renouvellement du parc en tenant compte de la durabilité, tout en se plaçant dans une perspective de gestion du risque. Cette thèse apporte une double contribution, au niveau de la politique de gestion du parc et à celui de la méthode utilisée pour appliquer cette politique. Au niveau de la politique, elle étudie l’effet de l’adoption de nouveaux véhicules, disposant d’une technologie de pointe, sur le risque et le coût escompté du système de gestion du parc. Au niveau méthodologique, cette thèse apporte trois contributions. Tout d’abord, elle comporte une étude de la nouvelle formulation du problème du parc en utilisant une programmation stochastique à deux étapes et à multiples étapes et une valeur à risque conditionnelle (CVaR), prenant ainsi en considération l’incertitude dans le processus de décision. En outre, elle élabore une formulation récursive de la CVaR, qui tient compte de la cohérence dans le temps, et elle examine ses propriétés de convergence, dans un cadre dynamique. Enfin, la thèse modélise l’impact sur le profit et le risque de l’utilisation des contrats à option sur le problème de remplacement du parc. / The purpose of this thesis is to conduct an analysis of how the fleet replacement problem can be addressed from both sustainability and risk management perspectives, simultaneously. The contribution of this thesis has two components, in fleet management policy and in the method used to apply it. At a policy level, this thesis addresses the effect of adoption of new technological advanced vehicles on the risk and expected cost of the fleet management system. At a methodological level, this thesis presents three contributions: First, it studies the new formulation of the fleet problem by using a two stage and a multi stage stochastic programming and conditional value at risk (CVaR), which accounts for the uncertainty in the decision process. Second, it models a recursive formulation of CVaR, which takes into account the time consistency, and studies its convergence properties, in a dynamic setting. Third, it models the impact on profit and risk from using option contracts on the fleet replacement problem.

Depuis quelques années, la recherche financière s'inscrit dans une nouvelle dynamique. La nécessité de mieux modéliser le comportement des rendements des actifs financiers et les risques sur les marchés pousse les chercheurs à trouver des mesures de risque plus adéquates. Ce travail de recherche se situe dans cette évolution, ayant admis les caractéristiques des séries financières par des faits stylisés tels que la non normalité des rendements. A travers cette thèse nous essayons de montrer l'importance d'intégrer des mesures de risque qui tiennent compte de la non normalité dans le processus d'évaluation et d'allocation des actifs financiers sur le marché français. Cette thèse propose trois chapitres correspondant chacun à un article de recherche académique. Le premier article propose de revisiter les modèles d'évaluation en prenant en compte des moments d'ordres supérieurs dans un cadre de downside risk. Les résultats indiquent que les downside co-moments d'ordres supérieurs sont déterminants dans l'explication des variations des rendements en coupe transversale. Le second chapitre propose de mettre en relation la rentabilité financière et le risque mesuré par la VaR ou la CVaR. Nous trouvons que la VaR présente un pouvoir explicatif plus élevé que celui de la CVaR et que l'approche normale est plus intéressante que l'approche basée sur l'expansion de Cornish-Fisher (1937). Ces deux résultats contredisent les prédictions théoriques mais nous avons pu démontrer qu'ils sont inhérents au marché français. Le troisième chapitre propose une autre piste, nous revisitons le modèle moyenne-CVaR dans un cadre dynamique et en présence des coûts de transaction / This dissertation is part of an ongoing researches looking for an adequate model that apprehend the behavior of financial asset returns. Through this research, we propose to analyze the relevance of risk measures that take into account the non-normality in the asset pricing and portfolio allocation models on the French market. This dissertation is comprised of three articles. The first one proposes to revisit the asset pricing model taking into account the higher-order moments in a downside framework. The results indicate that the downside higher order co-moments are relevant in explaining the cross sectional variations of returns. The second paper examines the relation between expected returns and the VaR or CVaR. A cross sectional analysis provides evidence that VaR is superior measure of risk when compared to the CVaR. We find also that the normal estimation approach gives better results than the approach based on the expansion of Cornish-Fisher (1937). Both results contradict the theoretical predictions but we proved that they are inherent to the French market. In the third paper, we review the mean-CVaR model in a dynamic framework and we take into account the transaction costs. The results indicate that the asset allocation model that takes into account the non-normality can improve the performance of the portfolio comparing to the mean-variance model, in terms of the average return and the return-to CVaR ratio. Through these three studies, we think that it is possible to modify the risk management framework to apprehend in a better way the risk of loss associated to the non-normality problem

Cette thèse a pour objectif d’évaluer et de comparer la performance des stratégies d’assurance de portefeuille pour tenter de définir quelles stratégies doivent être privilégiées par les investisseurs. Nous comparons de nombreuses stratégies d’assurance (OBPI, CPPI, put synthétique et Stop-loss) entre elles mais également avec quelques autres stratégies de référence. Nous utilisons différents critères de comparaison qui comprennent: 1. Les distributions de pay-off, le niveau de protection, la dominance stochastique et le coût d’assurance dans différentes conditions de marché identifiées par des modèles à changements de régime markovien. 2. Les mesures de la performance ajustée au risque qui peuvent refléter les préférences des investisseurs vis-à-vis du risque et de la rentabilité. 3. Les préférences des investisseurs en intégrant la théorie cumulative des perspectives (TCP). Nos résultats semblent mettre en évidence une dominance des stratégies CPPI dans la majorité des cas et pour la majorité des critères de comparaison. / This thesis is set out with the objective of evaluating and comparing the performance of portfolio insurance strategies. We try to figure out when and why one portfolio insurance strategy should be preferred by investors in practice. To meet this objective, main portfolio insurance strategies (OBPI, CPPI, Synthetic put and Stop-loss) are compared relatively to each other and to some benchmark strategies. Portfolio insurance strategies are applied within different implementation scenarios and compared according to various criteria that include:1. The payoff functions, stochastic dominance, the level of protection and the cost of insurance under bull and bear market conditions. 2. Various risk adjusted performance measures that reflect different investors’ preferences toward risk and return. 3. The preferences of investors who act according to cumulative prospect theory (CPT). Our results reveal a dominant role of CPPI strategy at the majority of cases and according to the majority of comparison criteria.

The market for decentralised financial instruments, more commonly known as cryptocurrencies, has gained momentum over the past recent years and the application areas are many. Modern portfolio theory has for years demonstrated its applicability to traditional assets, such as equities and other instruments, but to some extent omitted the application of mathematical portfolio theory with respect for cryptocurrencies. This master's thesis aims to evaluate both traditional and DeFi assets from a modern optimization perspective. The focus area includes whichallocation structures that minimize the risk-adjusted return. The optimizations strategies are based on the risk measures, standard deviation, Conditional Value at Risk and First linear partial moment. The method has its structure in different scenarios where the outcome is optimized for traditional assets, DeFi assets and a hybrid set of these. The input data for the optimization methodology is based on weekly and adjusted price data for the assets. The output variables are weight-distribution, risk levels, return, maximum drawdown and graphic visualizations. Our results show that there is a value in incorporating parts of assets from the decentralized financial world in a portfolio provided that the risk-adjusted ratio increases through but through both higher returns and higher potential risk. These results are based on incorporation of certain parts of the new landscape where more established assets such as Bitcoin, Ethereum etc. have proven to perform well while other assets that are less traded shows a significantly worse result relative to risk. / Marknaden för decentraliserade finansiella instrument, mer känt som kryptovalutor, har tagit sin fart de senaste åren och applikationsområdena är många. Modern portföljteori har i åratal visat sin tillämpbarhet på traditionella tillgångar, såsom aktier och andra instrument, men till en viss grad utelämnat applicering av matematisk portföljteori med avseende på kryptovalutor. Denna master uppsats ämnar till att utvärdera både traditionella och DeFi tillgångar ur ett modernt optimerings-perspektiv. Fokusområdet innefattar vilka allokeringsstrukturer som minimerar den risk justerade avkastningen. Optimeringsstrategierna baseras på riskmåtten, standardavvikelse, Conditional Value at Risk samt First linear partial moment. Metodiken har sin grundstruktur i olika scenarion där man studerat optimerade utfall för traditionella tillgångar, DeFi tillgångar samt en hybrid uppsättning av dessa.  Ingångsdatan till optimeringsmetodiken baseras på veckovis och justerad prisdata för tillgångarna. Utgångsvariablerna är allkokeringsfördelning, risknivåer, avkastning, maximum drawdown samt grafiska visualiseringar.  Våra resultat visar att det finns det finns ett värde i att omstrukturera sin portfölj med delar av tillgångar från den decentraliserade finansvärlden under förutsättningarna att riskjusterade kvoten ökar genom men genom både högre avkastning och högre potentiell risk. Dessa resultat bygger på inkorporering av vissa delar av de nya landskapet där mer etablerade tillgångar som Bitcoin, Ethereum etc. har visat sig prestera bra medans andra tillgångar som är mindre omsatta visar ett avsevärt sämre resultat relativt risk.