The main purpose of this thesis is to develop methodological and practical improvements on robust portfolio optimization procedures. Firstly, the thesis discusses the drawbacks of classical mean-variance optimization models, and examines robust portfolio optimization procedures with CVaR and worst-case CVaR risk models by providing a clear presentation of derivation of robust optimization models from a basic VaR model. For practical purposes, the thesis introduces an open source software interface called “RobustRisk”, which is developed for producing empirical evidence for the robust portfolio optimization models. The software, which performs Monte-Carlo simulation and out-of-sample performance for the portfolio optimization, is introduced by using a hypothetical portfolio data from selected emerging markets. In addition, the performance of robust portfolio optimization procedures are discussed by providing empirical evidence in the crisis period from advanced markets. Empirical results show that robust optimization with worst-case CVaR model outperforms the nominal CVaR model in the crisis period. The empirical results encourage us to construct a forward-looking stress test procedure based on robust portfolio optimization under regime switches. For this purpose, the Markov chain process is embedded into robust optimization procedure in order to stress regime transition matrix. In addition, assets returns, volatilities, correlation matrix and covariance matrix can be stressed under pre-defined scenario expectations. An application is provided with a hypothetical portfolio representing an internationally diversified portfolio. The CVaR efficient frontier and corresponding optimized portfolio weights are achieved under regime switch scenarios. The research suggests that stressed-CVaR optimization provides a robust and forward-looking stress test procedure to comply with the regulatory requirements stated in Basel II and CRD regulations.

The main purpose of this thesis is to develop methodological and practical improvements on robust portfolio optimization procedures. Firstly, the thesis discusses the drawbacks of classical mean-variance optimization models, and examines robust portfolio optimization procedures with CVaR and worst-case CVaR risk models by providing a clear presentation of derivation of robust optimization models from a basic VaR model. For practical purposes, the thesis introduces an open source software interface called “RobustRisk”, which is developed for producing empirical evidence for the robust portfolio optimization models. The software, which performs Monte-Carlo simulation and out-of-sample performance for the portfolio optimization, is introduced by using a hypothetical portfolio data from selected emerging markets. In addition, the performance of robust portfolio optimization procedures are discussed by providing empirical evidence in the crisis period from advanced markets. Empirical results show that robust optimization with worst-case CVaR model outperforms the nominal CVaR model in the crisis period. The empirical results encourage us to construct a forward-looking stress test procedure based on robust portfolio optimization under regime switches. For this purpose, the Markov chain process is embedded into robust optimization procedure in order to stress regime transition matrix. In addition, assets returns, volatilities, correlation matrix and covariance matrix can be stressed under pre-defined scenario expectations. An application is provided with a hypothetical portfolio representing an internationally diversified portfolio. The CVaR efficient frontier and corresponding optimized portfolio weights are achieved under regime switch scenarios. The research suggests that stressed-CVaR optimization provides a robust and forward-looking stress test procedure to comply with the regulatory requirements stated in Basel II and CRD regulations.

Nesta tese discutimos abordagens que utilizam cópulas para descrever dependências entre instrumentos nanceiros e avaliamos a performance destes métodos. Muitas crises nanceiras aconteceram desde o nal da década de 90, incluindo a crise asiática (1997), a crise da dívida da Rússia (1998), a crise da bolha da internet (2000), as crises após o 9/11 (2001) e a guerra do Iraque (2003), a crise do subprime or crise nanceira global (2007-08), e a crise da dívida soberana europeia (2009). Todas estas crises levaram a uma perda maciça de riqueza nanceira e a um aumento da volatilidade observada, e enfatizaram a importância de uma política macroprudencial mais robusta. Em outras palavras, perturbações nanceiras tornam os processos econômicos altamente não-lineares, levando os principais bancos centrais a tomarem medidas contrárias para conter a angústia - nanceira. Devido aos complexos padrões de dependência dos mercados nanceiros, uma abordagem multivariada em grandes dimensões para a análise da dependência caudal é seguramente mais perspicaz do que assumir retornos com distribuição normal multivariada. Dada a sua exibilidade, as cópulas são capazes de modelar melhor as regularidades empiricamente veri cadas que são normalmente atribuídas a retornos nanceiros multivariados: (1) volatilidade condicional assimétrica com maior volatilidade para grandes retornos negativos e menor volatilidade para retornos positivos (HAFNER, 1998); (2) assimetria condicional (AIT-SAHALIA; BRANDT, 2001; CHEN; HONG; STEIN, 2001; PATTON, 2001); (3) excesso de curtose (TAUCHEN, 2001; ANDREOU; PITTIS; SPANOS, 2001); e (4) dependência temporal não linear (CONT, 2001; CAMPBELL; LO; MACKINLAY, 1997). A principal contribuição dos ensaios é avaliar se abordagens mais so sticadas do que o método da distância e o tradicional modelo de Markowitz podem tirar proveito de quaisquer anomalias/fricções de mercado. Os ensaios são uma tentativa de fornecer uma análise adequada destas questões usando conjuntos de dados abrangentes e de longo prazo. Empiricamente, demonstramos que as abordagens baseadas em cópulas são úteis em todos os ensaios, mostrando-se bené cas para modelar dependências em diferentes cenários, avaliando as medidas de risco caudais mais adequadamente e gerando rentabilidade superior a dos benchmarks utilizados. / In this thesis we discuss copula-based approaches to describe statistical dependencies within nancial instruments and evaluate its performance. Many nancial crises have occurred since the late 1990s, including the Asian crisis (1997), the Russian national debt crisis (1998), the dot-com bubble crisis (2000), the crises after 9-11 (2001) and Iraq war (2003), the subprime mortgage crisis or global nancial crisis (2007-08), and the European sovereign debt crisis (2009). All of these crises lead to a massive loss of nancial wealth and an upward in observed volatility and have emphasized the importance of a more robust macro-prudential policy. In other words, nancial disruptions make the economic processes highly nonlinear making the major central banks to take counter-measures in order to contain nancial distress. The methods for modeling uncertainty and evaluating the market risk on nancial markets are now under more scrutiny after the global nancial crisis. Due to the complex dependence patterns of nancial markets, a high-dimensional multivariate approach to tail dependence analysis is surely more insightful than assuming multivariate normal returns. Given its exibility, copulas are able to model better the empirically veri ed regularities normally attributed to multivariate nancial returns: (1) asymmetric conditional volatility with higher volatility for large negative returns and smaller volatility for positive returns (HAFNER, 1998); (2) conditional skewness (AITSAHALIA; BRANDT, 2001; CHEN; HONG; STEIN, 2001; PATTON, 2001); (3) excess kurtosis (TAUCHEN, 2001; ANDREOU; PITTIS; SPANOS, 2001); and (4) nonlinear temporal dependence (CONT, 2001; CAMPBELL; LO; MACKINLAY, 1997). The principal contribution of the essays is to assess if more sophisticated approaches than the distance method and plain Markowitz model can take advantage of any market anomalies/ fricctions. The essays are one attempt to provide a proper analysis in these issues using a long-term and comprehensive datasets. We empirically show that copula-based approaches are useful in all essays, proving bene cial to model dependencies in di erent scenarios, assessing the downside risk measures more adequately and yielding higher profitability than the benchmarks.

Nesta tese discutimos abordagens que utilizam cópulas para descrever dependências entre instrumentos nanceiros e avaliamos a performance destes métodos. Muitas crises nanceiras aconteceram desde o nal da década de 90, incluindo a crise asiática (1997), a crise da dívida da Rússia (1998), a crise da bolha da internet (2000), as crises após o 9/11 (2001) e a guerra do Iraque (2003), a crise do subprime or crise nanceira global (2007-08), e a crise da dívida soberana europeia (2009). Todas estas crises levaram a uma perda maciça de riqueza nanceira e a um aumento da volatilidade observada, e enfatizaram a importância de uma política macroprudencial mais robusta. Em outras palavras, perturbações nanceiras tornam os processos econômicos altamente não-lineares, levando os principais bancos centrais a tomarem medidas contrárias para conter a angústia - nanceira. Devido aos complexos padrões de dependência dos mercados nanceiros, uma abordagem multivariada em grandes dimensões para a análise da dependência caudal é seguramente mais perspicaz do que assumir retornos com distribuição normal multivariada. Dada a sua exibilidade, as cópulas são capazes de modelar melhor as regularidades empiricamente veri cadas que são normalmente atribuídas a retornos nanceiros multivariados: (1) volatilidade condicional assimétrica com maior volatilidade para grandes retornos negativos e menor volatilidade para retornos positivos (HAFNER, 1998); (2) assimetria condicional (AIT-SAHALIA; BRANDT, 2001; CHEN; HONG; STEIN, 2001; PATTON, 2001); (3) excesso de curtose (TAUCHEN, 2001; ANDREOU; PITTIS; SPANOS, 2001); e (4) dependência temporal não linear (CONT, 2001; CAMPBELL; LO; MACKINLAY, 1997). A principal contribuição dos ensaios é avaliar se abordagens mais so sticadas do que o método da distância e o tradicional modelo de Markowitz podem tirar proveito de quaisquer anomalias/fricções de mercado. Os ensaios são uma tentativa de fornecer uma análise adequada destas questões usando conjuntos de dados abrangentes e de longo prazo. Empiricamente, demonstramos que as abordagens baseadas em cópulas são úteis em todos os ensaios, mostrando-se bené cas para modelar dependências em diferentes cenários, avaliando as medidas de risco caudais mais adequadamente e gerando rentabilidade superior a dos benchmarks utilizados. / In this thesis we discuss copula-based approaches to describe statistical dependencies within nancial instruments and evaluate its performance. Many nancial crises have occurred since the late 1990s, including the Asian crisis (1997), the Russian national debt crisis (1998), the dot-com bubble crisis (2000), the crises after 9-11 (2001) and Iraq war (2003), the subprime mortgage crisis or global nancial crisis (2007-08), and the European sovereign debt crisis (2009). All of these crises lead to a massive loss of nancial wealth and an upward in observed volatility and have emphasized the importance of a more robust macro-prudential policy. In other words, nancial disruptions make the economic processes highly nonlinear making the major central banks to take counter-measures in order to contain nancial distress. The methods for modeling uncertainty and evaluating the market risk on nancial markets are now under more scrutiny after the global nancial crisis. Due to the complex dependence patterns of nancial markets, a high-dimensional multivariate approach to tail dependence analysis is surely more insightful than assuming multivariate normal returns. Given its exibility, copulas are able to model better the empirically veri ed regularities normally attributed to multivariate nancial returns: (1) asymmetric conditional volatility with higher volatility for large negative returns and smaller volatility for positive returns (HAFNER, 1998); (2) conditional skewness (AITSAHALIA; BRANDT, 2001; CHEN; HONG; STEIN, 2001; PATTON, 2001); (3) excess kurtosis (TAUCHEN, 2001; ANDREOU; PITTIS; SPANOS, 2001); and (4) nonlinear temporal dependence (CONT, 2001; CAMPBELL; LO; MACKINLAY, 1997). The principal contribution of the essays is to assess if more sophisticated approaches than the distance method and plain Markowitz model can take advantage of any market anomalies/ fricctions. The essays are one attempt to provide a proper analysis in these issues using a long-term and comprehensive datasets. We empirically show that copula-based approaches are useful in all essays, proving bene cial to model dependencies in di erent scenarios, assessing the downside risk measures more adequately and yielding higher profitability than the benchmarks.

Nesta tese discutimos abordagens que utilizam cópulas para descrever dependências entre instrumentos nanceiros e avaliamos a performance destes métodos. Muitas crises nanceiras aconteceram desde o nal da década de 90, incluindo a crise asiática (1997), a crise da dívida da Rússia (1998), a crise da bolha da internet (2000), as crises após o 9/11 (2001) e a guerra do Iraque (2003), a crise do subprime or crise nanceira global (2007-08), e a crise da dívida soberana europeia (2009). Todas estas crises levaram a uma perda maciça de riqueza nanceira e a um aumento da volatilidade observada, e enfatizaram a importância de uma política macroprudencial mais robusta. Em outras palavras, perturbações nanceiras tornam os processos econômicos altamente não-lineares, levando os principais bancos centrais a tomarem medidas contrárias para conter a angústia - nanceira. Devido aos complexos padrões de dependência dos mercados nanceiros, uma abordagem multivariada em grandes dimensões para a análise da dependência caudal é seguramente mais perspicaz do que assumir retornos com distribuição normal multivariada. Dada a sua exibilidade, as cópulas são capazes de modelar melhor as regularidades empiricamente veri cadas que são normalmente atribuídas a retornos nanceiros multivariados: (1) volatilidade condicional assimétrica com maior volatilidade para grandes retornos negativos e menor volatilidade para retornos positivos (HAFNER, 1998); (2) assimetria condicional (AIT-SAHALIA; BRANDT, 2001; CHEN; HONG; STEIN, 2001; PATTON, 2001); (3) excesso de curtose (TAUCHEN, 2001; ANDREOU; PITTIS; SPANOS, 2001); e (4) dependência temporal não linear (CONT, 2001; CAMPBELL; LO; MACKINLAY, 1997). A principal contribuição dos ensaios é avaliar se abordagens mais so sticadas do que o método da distância e o tradicional modelo de Markowitz podem tirar proveito de quaisquer anomalias/fricções de mercado. Os ensaios são uma tentativa de fornecer uma análise adequada destas questões usando conjuntos de dados abrangentes e de longo prazo. Empiricamente, demonstramos que as abordagens baseadas em cópulas são úteis em todos os ensaios, mostrando-se bené cas para modelar dependências em diferentes cenários, avaliando as medidas de risco caudais mais adequadamente e gerando rentabilidade superior a dos benchmarks utilizados. / In this thesis we discuss copula-based approaches to describe statistical dependencies within nancial instruments and evaluate its performance. Many nancial crises have occurred since the late 1990s, including the Asian crisis (1997), the Russian national debt crisis (1998), the dot-com bubble crisis (2000), the crises after 9-11 (2001) and Iraq war (2003), the subprime mortgage crisis or global nancial crisis (2007-08), and the European sovereign debt crisis (2009). All of these crises lead to a massive loss of nancial wealth and an upward in observed volatility and have emphasized the importance of a more robust macro-prudential policy. In other words, nancial disruptions make the economic processes highly nonlinear making the major central banks to take counter-measures in order to contain nancial distress. The methods for modeling uncertainty and evaluating the market risk on nancial markets are now under more scrutiny after the global nancial crisis. Due to the complex dependence patterns of nancial markets, a high-dimensional multivariate approach to tail dependence analysis is surely more insightful than assuming multivariate normal returns. Given its exibility, copulas are able to model better the empirically veri ed regularities normally attributed to multivariate nancial returns: (1) asymmetric conditional volatility with higher volatility for large negative returns and smaller volatility for positive returns (HAFNER, 1998); (2) conditional skewness (AITSAHALIA; BRANDT, 2001; CHEN; HONG; STEIN, 2001; PATTON, 2001); (3) excess kurtosis (TAUCHEN, 2001; ANDREOU; PITTIS; SPANOS, 2001); and (4) nonlinear temporal dependence (CONT, 2001; CAMPBELL; LO; MACKINLAY, 1997). The principal contribution of the essays is to assess if more sophisticated approaches than the distance method and plain Markowitz model can take advantage of any market anomalies/ fricctions. The essays are one attempt to provide a proper analysis in these issues using a long-term and comprehensive datasets. We empirically show that copula-based approaches are useful in all essays, proving bene cial to model dependencies in di erent scenarios, assessing the downside risk measures more adequately and yielding higher profitability than the benchmarks.