基於SEC之要求，越來越多美國金融機構於其財務報表附註中揭露金融交易資產之風險值；然而計算風險值涉及到許多假設，於是導致過去部分文獻對於風險值資訊揭露之可靠性產生質疑。本研究以風險值之揭露對於報表使用者之資訊價值作為研究課題；為求與附註揭露之風險值資訊比較，本研究以公司帳列之金融交易資產(Trading Assets)、金融交易收入(Trading Revenue)為基礎，利用蒙地卡羅模擬法模擬帳列金融交易資產於次期可能產生之最大潛在損失，並且透過OLS regression及panel data model探討： (1)風險值及金融交易資產潛在可能損失是否可以預測次期金融交易收入波動 (2)風險值與金融交易資產潛在可能損失資訊之提供是否影響次期股票交易量 (3)風險值與金融交易資產潛在可能損失資訊是否可以有效預測次期股價報酬 率變異。 實證結果顯示，風險值之揭露與金融交易資產潛在可能損失之資訊對於預計次期金融交易收入之波動與股價報酬率變異均呈現顯著正相關；易言之，上述兩種資訊之揭露均提供增額之資訊價值。惟另方面，風險值之揭露與金融交易資產潛在可能損失之資訊卻與次期股票交易量呈正相關，也就是說上述兩種資訊的揭露反而會造成投資人降低長期投資持有的意願。 / Financial institutions in the United States are required by the Securities and Exchange Commission to disclose their Value at Risk (VaR) in the footnotes of the financial statements. Over the years, VaR has been used by institutional investors, industry consultants, and regulators as one of the key measures of market risk. However, there are a number of approaches to calculating VaR and some of them may involve various statistical models and assumptions. Due to the fact that different models and assumptions may be used, the VaR numbers produced by different institutions are difficult to compare with one another. The usefulness of these numbers is therefore decreased. This thesis examines the usefulness of disclosures of VaR information. In order to compare with VaR disclosures, the implied potential maximum losses of trading assets are simulated by using Monte Carlo simulation. We then employ the OLS regression and the panel data models to investigate the following research questions: (1)whether VaR and implied potential maximum losses of trading assets disclosed by financial institutions are instrumental in predicting the variability of trading revenue for the next quarter; (2)whether VaR and implied potential maximum losses of trading assets disclosed by financial institutions affect investors' investing decision; (3)how useful are VaR and implied potential maximum losses of trading assets in predicting the volatility of daily stock return next quarter. The empirical results indicate that VaR and implied potential maximum losses of trading assets are significantly related to the variability of trading revenue and the volatility of daily stock returns next quarter. This evidence suggests that both types of disclosures provide incremental information on predicting the variability of trading revenue and investment risk in the future. Nevertheless, we also find that both VaR disclosures and implied potential maximum losses of trading assets are positively associated with future average stock trading volume, implying that investors tend to trade stock more frequently when the market risk information is disclosed.

Les gérants de portefeuille pour compte de tiers sont souvent jugés par leur performance relative à celle d'un portefeuille benchmark. A ce titre, ils sont amenés très fréquemment à utiliser des modèles internes de "risk management" pour contrôler le risque de sous-performer le benchmark. Par ailleurs, ils sont de plus en plus nombreux à adopter une politique de rémunération incitative, en percevant une commission de sur-performance par rapport au benchmark. En effet, cette composante variable de leur rémunération leur permet d'augmenter leur revenu en cas de sur-performance sans contrepartie en cas de sous-performance. Or de telles pratiques ont fait récemment l'objet de nombreuses polémiques : la période récente de crise financière mondiale a fait apparaître certaines carences de plusieurs acteurs financiers en terme de contrôle de risque ainsi que des niveaux de prise de risque et de rémunération jugés excessifs. Cependant, l'étude des implications de ces pratiques reste un thème encore relativement peu exploré dans le cadre de la théorie classique des choix dynamiques de portefeuille en temps continu. Cette thèse analyse, dans ce cadre théorique, les implications de ces pratiques de "benchmarking" sur le comportement d'investissement de l'asset manager. La première partie étudie les propriétés de la stratégie dynamique optimale pour l'asset manager concerné par l'écart entre la rentabilité de son portefeuille et celle d'un benchmark fixe ou stochastique (sur ou sous-performance). Nous considérons plusieurs types d'asset managers, caractérisés par différentes fonctions d'utilité et qui sont soumis à différentes contraintes de risque de sous-performance. Nous montrons en particulier quel est le lien entre les problèmes d'investissement avec prise en compte de l'aversion à la sous-performance et avec contrainte explicite de "risk management". Dans la seconde partie, on s'intéresse à l'asset manager bénéficiant d'une rémunération incitative (frais de gestion variables, bonus de sur-performance ou commission sur encours additionnelle). On étudie, selon la forme de ses incitations financières et son degré d'aversion à la sous-performance, comment sa stratégie d'investissement s'écarte de celle de l'investisseur (ou celle de l'asset manager sans rémunération incitative). Nous montrons que le changement de comportement de l'asset manager peut se traduire soit par une réduction du risque pris par rapport à la stratégie sans incitation financière soit au contraire par une augmentation de celui-ci. Finalement, nous montrons en quoi la présence de contraintes de risque de sous-performance, imposées au gérant ou traduisant son aversion à la sous-performance, peut être bénéfique à l'investisseur donnant mandat de gestion financière.

鑒於金融市場快速的變動與日趨複雜之金融商品種類，銀行經營管理中所面臨之風險，尤以因金融市場價格變動（如市場利率、匯率、股價及商品價格之變動）造成對銀行資產負債表內及表外部位可能產生之損失，其所因應而生之市場風險須及時管控與適時因應。然而2007年因次級房貸問題引發全球性金融危機，益加彰顯風險管理制度的重要性與其再精進之處。 本研究期能藉由新巴塞爾資本協定中市場風險管理規範的探討，個案銀行之實例探究，對國內銀行在建構符合其需要的市場風險管理系統時有所助益，在建置市場風險管理系統的考量因素以及該系統的建置與應用，循序周全建構質化與量化標準之風險管理機制。 本研究由新巴塞爾資本協定規範探討銀行市場風險管理系統建置與其實際應用，歸納出研究結論顯示，市場風險管理系統架構之依循須能符合新巴塞爾資本協定之基本規範，藉由系統內建模型計算風險值以有效衡量交易簿與銀行簿之部位，及其利率、權益證券、外匯及商品四大類風險因子。市場風險管理系統需求規畫與評估，須就應用面(系統相關模組功能)、資料面(系統執行所需資料及存取介面、資料庫建置及資料完整性)與技術面(系統運作之軟體與硬體環境)予以考量。系統專案建置須有高階管理階層對市場風險管理系統專案相關執行程序的支持，前檯、中檯、後檯、資訊單位主管之配合與溝通協調。市場風險管理系統架構應考量市場風險限額管理須至各交易層級(如總行別、部門單位別、交易簿與銀行簿產品別等)，因此系統功能模組設定與管理報表規畫設計則配合系統架構分級建立。市場風險管理制度之建立，應配合市場風險管理系統之應用與管理流程結合，訂定相關管理辦法，以規範市場風險管控機制運作及程序之確實執行。 關鍵字：新巴塞爾資本協定、市場風險、衍生性金融商品、風險值 / Recently, financial market is changed quickly and types of product are more and more complicated. Operation of Bank faces many risks that are losses of in or out balance sheet by price moving. Therefore, we need to manage and monitor the market risks that result from change in interest rate, exchange rate, equity price, commodity price in the time. In 2007, global financial crisis caused by subprime mortgage storm stands out the importance of risk management and needs of improving it. On one hand, this research hopes to benefit banks to build up its market risk system satisfied the need by discussing market risk management under Basel II and looking into case study on the bank. While constructing the system, we have to pay attention to its practicability which meets standards of quantification and quality. On the other hand, this research discusses system built up and reality applying through Basel II and indicates some useful conclusion. At first, market risk system not only meets mainly criteria under Basel II but creats the value at risk (VaR) which can effectively estimate interest rate, securities, foreign exchange and commodities risks.Secondly, technology of applying, data and information should be considered into when evaluating the demands of market risk management system. Moreover, risk system constructed needs support from senior management team and cooperation between relative departments. Besides, we need to take into account whether this mentioned system can implement market risk limit management to every transaction class, for example, trading books ,banking books, product type…etc.The system function and the management reports could be able to operate with the market risk limit management, accordingly. Most of all, market risk management regulation should be thought over the application and management process of market risk management system to make sure that market risk management could be implemented certainly. Keywords: New Basel Capital Accord, Market Risk, Derivatives,Value at Risk

投資決策時，除了關注資產的報酬外，更不可忽略風險。而風險的衡量上，一般常用風險值來衡量投資所面臨的風險，這是由於風險值具有動態管理、量化風險等優點。而國內研究對於不動產風險值的文獻上多以住宅市場為主，對於商用不動產較無著墨，是故本研究欲從不同風險值模型探討投資商用不動產的風險值，並分為直接投資(北市商用不動產)與間接投資(REITs)商用不動產兩個不同次市場。實證結果發現直接投資商用不動產風險值高於間接投資商用不動產。其次，本研究試圖比較靜態與動態風險值模型在估計不動產風險值的行為表現，經回溯測試(Back Testing)檢驗後發現，發現兩個模型衡量不動產風險值時，表現差異性不大。最後，本研究並以夏普績效(Sharp Ratio)來衡量直接投資與間接投資商用不動產的投資績效，研究期間為2007年6月至2009年3月。實證結果發現，直接投資商用不動產在景氣衰退與股市劇跌時具有抗跌性；而間接投資商用不動產則與股市發生同時下跌的現象，此現象可能是我國REITs具有代理問題(Agency Problem)與系統風險(Systematic Risk)等問題所致。因此，本研究建議投資者投資REITs時，應同時考量REITs存在上述的風險與問題，以避免投資上的損失。 / When making investment strategies, aside from considering the return of investment, one cannot ignore the risk factors. In measuring risk, we usually use VaR (Value at Risk) to calculate the risks of investment because, among other reasons, VaR has dynamic and quantifiable advantages. Most of the studies regarding real estate investment risk in Taiwan focus on residential markets; thus, this paper investigates commercial real estate markets using different VaR models to determine the degree of risk, distinguishing further between direct investment markets and indirect investment markets like REITs (Real Estate Investment Trust). The result of this study reveals that direct real estate investment involves higher risks than indirect real estate investment. Furthermore, there was hardly any difference in investment risk when using either static or dynamic VaR models in the computations after using Back Testing. Finally, this study employs Sharp Ratio to calculate commercial real estate investment performance covering the period between June 2007 and March 2009. Direct real estate investment shows firmness during economic downturns or stock market crashes unlike indirect real estate investment like REITs which follows stock market trends. This phenomenon may be due to Agency Problem and Systematic Risk in Taiwan’s REITs market. Therefore this study suggests that when investing in REITs one has to take into account the risks and problems in order to avoid unnecessary investment losses.

Asset allocation is the most influential factor driving investment performance. While researchers have made substantial progress in the field of asset allocation since the introduction of mean-variance framework by Markowitz, there is little agreement about appropriate portfolio choice for multi-period long horizon investors. Nowhere this is more evident than trustees of retirement plans choosing different asset allocation strategies as default investment options for their members. This doctoral dissertation consists of four essays each of which explores either a novel or an unresolved issue in the area of asset allocation for individual retirement plan participants. The goal of the thesis is to provide greater insight into the subject of portfolio choice in retirement plans and advance scholarship in this field. The first study evaluates different constant mix or fixed weight asset allocation strategies and comments on their relative appeal as default investment options. In contrast to past research which deals mostly with theoretical or hypothetical models of asset allocation, we investigate asset allocation strategies that are actually used as default investment options by superannuation funds in Australia. We find that strategies with moderate allocation to stocks are consistently outperformed in terms of upside potential of exceeding the participant’s wealth accumulation target as well as downside risk of falling below that target by very aggressive strategies whose allocation to stocks approach 100%. The risk of extremely adverse wealth outcomes for plan participants does not appear to be very sensitive to asset allocation. Drawing on the evidence of the previous study, the second essay explores possible solutions to the well known problem of gender inequality in retirement investment outcomes. Using non-parametric stochastic simulation, we simulate iv and compare the retirement wealth outcomes for a hypothetical female and male worker under different assumptions about breaks in employment, superannuation contribution rates, and asset allocation strategies. We argue that modest changes in contribution and asset allocation strategy for the female plan participant are necessary to ensure an equitable wealth outcome in retirement. The findings provide strong evidence against gender-neutral default contribution and asset allocation policy currently institutionalized in Australia and other countries. In the third study we examine the efficacy of lifecycle asset allocation models which allocate aggressively to risky asset classes when the employee participants are young and gradually switch to more conservative asset classes as they approach retirement. We show that the conventional lifecycle strategies make a costly mistake by ignoring the change in portfolio size over time as a critical input in the asset allocation decision. Due to this portfolio size effect, which has hitherto remained unexplored in literature, the terminal value of accumulation in retirement account is critically dependent on the asset allocation strategy adopted by the participant in later years relative to early years. The final essay extends the findings of the previous chapter by proposing an alternative approach to lifecycle asset allocation which incorporates performance feedback. We demonstrate that strategies that dynamically alter allocation between growth and conservative asset classes at different points on the investment horizon based on cumulative portfolio performance relative to a set target generally result in superior wealth outcomes compared to those of conventional lifecycle strategies. The dynamic allocation strategy exhibits clear second-degree stochastic dominance over conventional strategies which switch assets in a deterministic manner as well as balanced diversified strategies.

[pt] volatilidade dos ativos financeiros reflete uma reação prosseguida dos agentes a choques no passado ou alterações nas condições dos mercados determinam mudanças na dinâmica da variável? Enquanto modelos fracionalmente integrados vêm sendo extensamente utilizados como uma descrição adequada do processo gerador de séries de volatilidade, trabalhos teóricos recentes indicaram que mudanças estruturais podem ser uma relevante alternativa empírica para o fato estilizado de memória longa. O presente trabalho investiga o que alterações nos mercados significam nesse contexto, introduzindo variações de preços como uma possível fonte de mudanças no nível da volatilidade durante algum período, com grandes quedas (ascensões) nos preços trazendo regimes persistentes de variância alta (baixa). Uma estratégia de modelagem sistemática e flexível é estabelecida para testar e estimar essa assimetria através da incorporação de retornos acumulados passados num arcabouço não-linear. O principal resultado revela que o efeito é altamente significante - estima-se que níveis de volatilidade 25% e 50% maiores estão associados a quedas nos preços em períodos curtos - e é capaz de explicar altos valores de estimativas do parâmetro de memória longa. Finalmente, mostra-se que a modelagem desse efeito traz ganhos importantes para aplicações fora da amostra em períodos de volatilidade alta. / [en] Does volatility reflect lasting reactions to past shocks or changes in the markets induce shifts in this variable dynamics? In this work, we argue that price variations are an essential source of information about multiple regimes in the realized volatility of stocks, with large falls (rises) in prices bringing persistent regimes of high (low) variance. The study shows that this asymmetric effect is highly significant (we estimate that falls of different magnitudes over less than two months are associated with volatility levels 20% and 60% higher than the average of periods with stable or rising prices) and support large empirical values of long memory parameter estimates. We show that a model based on those findings significantly improves out of sample performance in relation to standard methods {specially in periods of high volatility.

Made available in DSpace on 2010-04-20T20:51:05Z (GMT). No. of bitstreams: 3 98333.pdf.jpg: 13860 bytes, checksum: 411f2e503bdd3f85174e0db0b4bd251c (MD5) 98333.pdf: 711485 bytes, checksum: 410792964fe8e1c5a1db006b3e7fa833 (MD5) 98333.pdf.txt: 212638 bytes, checksum: 847f0564ff4a3061300b1a06e613bfd4 (MD5) Previous issue date: 2003-03-12T00:00:00Z / Este estudo faz uma revisão das origens do VaR, bem como dos conceitos e teorias que o fundamentam, e sua aplicabilidade aos fundos de pensão. Descreve as principais metodologias de cálculo e as situações nas quais o uso de cada uma é mais adequado. Revisa a literatura internacional acerca do uso do VaR como medida de risco pelos fundos de pensão. A seguir faz a previsão do VaR para as carteiras reais de três fundos de pensão brasileiros com três metodologias distintas: paramétrica, simulação histórica e simulação de Monte Carlo, esta última com duas suposições distintas para a distribuição dos retornos dos fatores de risco (normal e histórica). A partir disso, realiza um teste qualitativo, através da comparação do número de perdas efetivas realizadas pelas carteiras dos três fundos de pensão com o número de perdas correspondente admitido para os diferentes níveis de confiança utilizados no cálculo do VaR. O trabalho não encontra evidências de superioridade de nenhuma das metodologias de cálculo, sendo que todas elas superestimaram as perdas verificadas na prática (o VaR foi excedido menos vezes do que o esperado). / This study summarizes the theory underlying Value at risk, including its history, concepts and applicability to pension funds. It describes the main approaches in computing VaR, as well as the situations in which one approach is more appropriate than the other. It also revises the international literature about the use of VaR as a risk measure by pension funds. After that, VaR is computed for real portfolios of three Brazilian pension funds, applying three methods: analytical, historical simulation and Monte Carlo simulation, the last one with two different assumptions about risk factor returns’ distributions (normal and historical). Following VaR computation, a qualitative test is performed, by comparing the actual losses faced by the three pension funds’ portfolios with the associated number of losses, given the confidence level. Evidence about superiority of some of the approaches has not been found, and all of them have overestimated real losses (the VaR measure was exceeded less often than expected).

Made available in DSpace on 2010-04-20T21:00:18Z (GMT). No. of bitstreams: 3 liuyuanchun.pdf.jpg: 17401 bytes, checksum: f3f99fd1992b2110a49c01ea2b4a795c (MD5) liuyuanchun.pdf: 1060371 bytes, checksum: 3f2e7592f1f950f8abbb037eaa9e522d (MD5) liuyuanchun.pdf.txt: 115026 bytes, checksum: bba135f45d4f79bd49d73017e1c707c1 (MD5) Previous issue date: 2008-01-17T00:00:00Z / Many methodologies to measure market risk have been developed and improved in the last few decades. While some methodologies are non-parametric, others are parametric. Some methodologies are theoretical, while others are more practical. While some methodologies are original, others are hybrid. In this work, we compared methodologies to measure market risk in the Brazilian market. We evaluated non-parametric and parametric methodologies to measure VaR in a fixed income, equities and a mixture between fixed income and equities’ portfolios between 2000 and 2006. Non-parametric methodologies evaluated were: Fixed-Weight Historical Simulation, Fixed-Weight Antithetic Historical Simulation, Exponential Historical Simulation and Scenario Analysis. Parametric methodologies evaluated were: FixedWeight VaR Delta-Normal, Exponential VaR Delta-Normal (EWMA), Fixed-Weight Monte Carlo Simulation and Exponential Monte Carlo Simulation. Based on statistical measures of conservatism, accuracy and efficiency, we compared the methodologies. / Várias metodologias de mensuração de risco de mercado foram desenvolvidas e aprimoradas ao longo das últimas décadas. Enquanto algumas metodologias usam abordagens não-paramétricas, outras usam paramétricas. Algumas metodologias são mais teóricas, enquanto outras são mais práticas, usando recursos computacionais através de simulações. Enquanto algumas metodologias preservam sua originalidade, outras metodologias têm abordagens híbridas, juntando características de 2 ou mais metodologias. Neste trabalho, fizemos uma comparação de metodologias de mensuração de risco de mercado para o mercado financeiro brasileiro. Avaliamos os resultados das metodologias não-paramétricas e paramétricas de mensuração de VaR aplicados em uma carteira de renda fixa, renda variável e renda mista durante o período de 2000 a 2006. As metodologias não-paramétricas avaliadas foram: Simulação Histórica pesos fixos, Simulação Histórica Antitética pesos fixos, Simulação Histórica exponencial e Análise de Cenário. E as metodologias paramétricas avaliadas foram: VaR Delta-Normal pesos fixos, VaR Delta-Normal exponencial (EWMA), Simulação de Monte Carlo pesos fixos e Simulação de Monte Carlo exponencial. A comparação destas metodologias foi feita com base em medidas estatísticas de conservadorismo, precisão e eficiência.

Made available in DSpace on 2010-04-20T21:00:12Z (GMT). No. of bitstreams: 4 Lucas Machado Braga de Araujo.pdf.jpg: 18740 bytes, checksum: e39415b36953ced37a6d87a19c381b38 (MD5) Lucas Machado Braga de Araujo.pdf.txt: 95713 bytes, checksum: a95ad7b44ec22b2f5ba2dbfe4f6798bb (MD5) Lucas Machado Braga de Araujo.pdf: 758972 bytes, checksum: c20d926964cc37d2ee7bdfc1bdf6aafc (MD5) license.txt: 4886 bytes, checksum: f5ef202e66d94f51fd6c9a09505731a6 (MD5) Previous issue date: 2009-02-03T00:00:00Z / The aim of this work is to show that the optimization of a portfolio composed of Brazilian hedge funds presents better results when the risk measure considered is Conditional Value-at-Risk. Portfolio optimization models aim to select assets that maximize the investor‘s return for a given level of risk. Therefore the definition of an appropriate measure of risk is of fundamental importance to the allocation process. The traditional methodology of portfolio optimization, developed by Markowitz, uses the variance of assets returns as risk measure. However variance is a measure appropriate only for cases where the returns are normally distributed or that the investor utility function is quadratic. Nevertheless it will be shown that the returns of Brazilian hedge funds usually do not have a Normal distribution. Consequently, to perform the optimization of a portfolio composed by Brazilian hedge funds is necessary to use an alternative risk measure. / O objetivo do trabalho é demonstrar que a otimização de uma carteira composta por fundos multimercados brasileiros gera melhores resultados quando a medida de risco utilizada é o Conditional Value-at-Risk. Modelos de otimização de carteira têm como objetivo selecionar ativos que maximizem o retorno do investidor para um determinado nível de risco. Assim, a definição de uma medida apropriada de risco é de fundamental importância para o processo de alocação. A metodologia tradicional de otimização de carteiras, desenvolvida por Markowitz, utiliza como medida de risco a variância dos retornos. Entretanto, a variância é uma medida apenas apropriada para casos em que os retornos são normalmente distribuídos ou em que os investidores possuem funções de utilidade quadrática. Porém, o trabalho mostra que os retornos dos fundos multimercados brasileiros tendem a não apresentar distribuição normal. Logo, para efetuar a otimização de uma carteira composta por fundos multimercados brasileiros é necessário utilizar uma medida de risco alternativa.

Made available in DSpace on 2010-04-20T21:00:03Z (GMT). No. of bitstreams: 4 Fabio Nunes Barja.pdf.jpg: 2268 bytes, checksum: 3ff1d834aa6bf6835efe6dd07835326c (MD5) Fabio Nunes Barja.pdf.txt: 144718 bytes, checksum: 86d161817200706186fc58ff0c7b1cd4 (MD5) license.txt: 4712 bytes, checksum: 4dea6f7333914d9740702a2deb2db217 (MD5) Fabio Nunes Barja.pdf: 920446 bytes, checksum: 547cbd04aa1355d329be524b2fe94b1d (MD5) Previous issue date: 2009-11-30T00:00:00Z / Este trabalho aplica a teoria de cópulas à mensuração do risco de mercado, através do cálculo do Value at Risk (VaR). A função de cópula oferece uma maior flexibilidade para a agregação de riscos quando comparada com abordagens tradicionais de mensuração de risco. A teoria de cópulas permite a utilização de distribuições de probabilidade diferentes da normal para a modelagem individual dos fatores de risco. Além disso, diferentes estruturas de associação entre eles podem ser aplicadas sem que restrições sejam impostas às suas distribuições. Dessa forma, premissas como a normalidade conjunta dos retornos e a linearidade na dependência entre fatores de risco podem ser dispensadas, possibilitando a correta modelagem de eventos conjuntos extremos e de assimetria na relação de dependência. Após a apresentação dos principais conceitos associados ao tema, um modelo de cópula foi desenvolvido para o cálculo do VaR de três carteiras, expostas aos mercados brasileiros cambial e acionário. Em seguida, a sua precisão foi comparada com a das metodologias tradicionais delta-normal e de simulação histórica. Os resultados mostraram que o modelo baseado na teoria de cópulas foi superior aos tradicionais na previsão de eventos extremos, representados pelo VaR 99%. No caso do VaR 95%, o modelo delta-normal apresentou o melhor desempenho. Finalmente, foi possível concluir que o estudo da teoria de cópulas é de grande relevância para a gestão de riscos financeiros. Fica a sugestão de que variações do modelo de VaR desenvolvido neste trabalho sejam testadas, e que esta teoria seja também aplicada à gestão de outros riscos, como o de crédito, operacional, e até mesmo o risco integrado. / This study applies the theory of copulas to the measurement of market risk by doing the Value at Risk (VaR) calculation. The copula function offers a greater flexibility to aggregate the risks as compared to traditional approaches of risk measurement. The theory of copulas enables the use of probability distributions different from the normal to the individual modeling of risk factors. Furthermore, different association structures between them can be applied with no restrictions being imposed to its distributions. Thus, premises such as joint normality of returns and linearity in the dependence between risk factors can be dismissed, what enables the correct modelling of extreme joint events and of asymmetry in the dependence relation. After presenting the main concepts associated to the theme, a copula model was developed in order to calculate the VaR for three portfolios which are exposed to the Brazilian foreign exchange and stock markets. Afterwards, its accuracy was compared with that of traditional methodologies, i.e., delta-normal and historic simulation. The results showed that the model based on the theory of copulas was superior to the traditional ones at forecasting extreme events, which are represented by VaR 99%. When it comes to VaR 95%, the delta-normal model presented the best results. Finally, it was possible to conclude that the theory of copulas study is of great relevance to financial risks management. For further research, a suggestion is testing variations of the VaR model developed in this work, as well as applying this theory to managing other risks, such as credit, operational or even integrated risk.