Within the scope of this thesis, the Black-Litterman Asset Allocation Model (as presented in He & Litterman, 1999) is compared to the classical mean-variance framework by simulating past performance of portfolios constructed by both models using identical input data. A quantitative investment strategy which favours stocks with high dividend yield rates is used to generate private views about the expected excess returns for a fraction of the stocks included in the sample. By comparing the ex-post risk-return characteristics of the portfolios and performing ample sensitivity analysis with respect to the numerical values assigned to the input variables, we evaluate the two models’ suitability for different categories of portfolio managers. As a neutral benchmark towards which both portfolios can be measured, a third market-capitalization-weighted portfolio is constructed from the same investment universe. The empirical data used for the purpose of our simulations consists of total return indices for 23 of the 30 stocks included in the OMXS30 index as of the 21st of February 2014 and stretches between January of 2003 and December of 2013.   The results of our simulations show that the Black-Litterman portfolio has delivered risk-adjusted return which is superior not only to that of its market-capitalization-weighted counterpart but also to that of the classical mean-variance portfolio. This result holds true for four out of five simulated strengths of the investment strategy under the assumption of zero transaction costs, a rebalancing frequency of 20 trading days, an estimated risk aversion parameter of 2.5 and a five per cent uncertainty associated with the CAPM prior. Sensitivity analysis performed by examining how the results are affected by variations in these input variables has also shown notable differences in the sensitivity of the results obtained from the two models. While the performance of the Black-Litterman portfolio does undergo material changes as the inputs are varied, these changes are nowhere near as profound as those exhibited by the classical mean-variance portfolio.   In the light of our empirical results, we also conclude that there are mainly two aspects which the portfolio manager ought to consider before committing to one model rather than the other. Firstly, the nature behind the views generated by the investment strategy needs to be taken into account. For the implementation of views which are of an α-driven character, the dynamics of the Black-Litterman model may not be as appropriate as for views which are believed to also influence the expected return on other securities. Secondly, the soundness of using market-capitalization weights as a benchmark towards which the final solution will gravitate needs to be assessed. Managers who strive to achieve performance which is fundamentally uncorrelated to that of the market index may want to either reconsider the benchmark weights or opt for an alternative model.

Submitted by Ricardo Porto (ricardoporto@bancobbm.com.br) on 2010-08-23T15:32:21Z No. of bitstreams: 1 DISSERTAÇÃO RICARDO PORTO.pdf: 454076 bytes, checksum: 66bba39f53ab22d9842749c2713ec606 (MD5) / Approved for entry into archive by Vitor Souza(vitor.souza@fgv.br) on 2010-08-23T15:34:47Z (GMT) No. of bitstreams: 1 DISSERTAÇÃO RICARDO PORTO.pdf: 454076 bytes, checksum: 66bba39f53ab22d9842749c2713ec606 (MD5) / Made available in DSpace on 2010-08-23T17:42:59Z (GMT). No. of bitstreams: 1 DISSERTAÇÃO RICARDO PORTO.pdf: 454076 bytes, checksum: 66bba39f53ab22d9842749c2713ec606 (MD5) Previous issue date: 2010-05-26 / The Black-Litterman model calculates the expected market returns as a combination of a set of investor views and a neutral reference point. The model uses Bayesian approach to blend both sources of information. The results from the Black-Litterman model, in contrast to the traditional approach, are quite intuitive, stable and consistent with the investors views. The purpose of this thesis is to provide a detailed analysis of each component of the Black-Litterman model and verify if the use of the Black-Litterman model, introducing the views of the market based on the Central Bank report, FOCUS, outperforms brasilians Hegde Funds. / O modelo Black-Litterman calcula os retornos esperados de mercado como uma combinação de um conjunto de expectativas específicas de cada investidor e um ponto de referência neutro. A combinação dessas duas fontes de informações são feitas pelo modelo utilizando a abordagem bayesiana. Os resultados obtidos a partir do modelo Black-Litterman, ao contrário da abordagem tradicional, são bastante intuitivos, estáveis e consistentes em relação as expectativas dos investidores. O objetivo dessa dissertação é fazer uma análise detalhada de cada um dos componentes do modelo Black-Litterman e verificar se a utilização o modelo de Black-Litterman, introduzindo as opiniões de mercado com base no relatório FOCUS do Banco Central, supera o retorno dos fundos multimercados brasileiros.

yes / This paper uses a novel numerical optimization technique – robust optimization – that is well suited to solving the asset–liability management (ALM) problem for pension schemes. It requires the estimation of fewer stochastic parameters, reduces estimation risk and adopts a prudent approach to asset allocation. This study is the first to apply it to a real-world pension scheme, and the first ALM model of a pension scheme to maximize the Sharpe ratio. We disaggregate pension liabilities into three components – active members, deferred members and pensioners, and transform the optimal asset allocation into the scheme’s projected contribution rate. The robust optimization model is extended to include liabilities and used to derive optimal investment policies for the Universities Superannuation Scheme (USS), benchmarked against the Sharpe and Tint, Bayes–Stein and Black–Litterman models as well as the actual USS investment decisions. Over a 144-month out-of-sample period, robust optimization is superior to the four benchmarks across 20 performance criteria and has a remarkably stable asset allocation – essentially fix-mix. These conclusions are supported by six robustness checks.

The Black-Litterman model is analyzed in three steps seeking to investigate, develop and test the B-L model in an applied perspective. The first step mathematically derives the Black-Litterman model from a sampling theory approach generating a new interpretation of the model and an interpretable formula for the parameter weight-on-views.  The second step draws upon behavioural finance and partly explains why managers find B-L portfolios intuitively accurate and also comments on the risk that overconfident managers state too low levels-of-unconfidence. The third step, a case study, concerns the implementation of the B-L model at a bank. It generates insights about the key-features of the model and their interrelations, the importance of understanding the model when using it, alternative use of the model, differences between the model and reality and the influence of social and organisational context on the use of the model. The research implies that it is not the B-L model alone but the combination model-user-situation that may prove rewarding. Overall, the research indicates the great distance between theory and practice and the importance of understanding the B-L model to be able to keep a critical attitude to the model and its output. The research points towards the need for more research concerning the use of the B-L model taking cultural, social and organizational contexts into account. / QC 20101202

In an ever-changing global environment, the ability to adapt to the current economic climate is essential for a company to prosper and survive. Numerous previous re- search state that better risk management and low overall risks will lead to a higher firm value. The purpose of this study is to examine if portfolio theory, made for fi- nancial portfolios, can be used to compose product portfolios in order to minimize risk and optimize returns. The term contingent hedge is defined as an optimal portfolio that can be identified today, that in the future will yield a stable stream of returns at a low level of risk. For companies that might engage in costly hedging activities on the futures market, the benefits of creat- ing a contingent hedge are several. These include creating an optimized portfolio that minimizes risk and avoid trading contracts on futures markets that would incur hefty transaction costs and risks. Using quantitative financial models, product portfolio compositions are generated and compared with the returns and risks profile of individual commodities, as well as the actual product portfolio compositions of publicly traded mining companies. Us- ing Modern Portfolio Theory an efficient frontier is generated, yielding two inde- pendent portfolios, the minimum risk portfolio and the tangency portfolio. The Black-Litterman model is also used to generate yet another portfolio using a Bayesian approach. The portfolios are generated by historic time-series data and compared with the actual future development of commodities; the portfolios are then analyzed and compared. The results indicate that the minimum risk portfolio provides a signif- icantly lower risk than the compositions of all mining companies in the study, as well as the risks of individual commodities. This in turn will lead to several benefits for company management and the firm’s shareholders that are discussed throughout the study. However, as for a return-optimizing portfolio, no significant results can be found. Furthermore, the analysis suggests a series of improvements that could potentially yield an even greater result. The recommendation is that mining companies can use the methods discussed throughout this study as a way to generate a costless contin- gent hedge, rather than engage in hedging activities on futures markets.

[pt] A alocação de ativos é uma das mais importantes decisões financeiras para investidores. No entanto, as decisões humanas não são totalmente racionais. Sabemos que as pessoas cometem muitos erros sistemáticos como, excesso de confiança, aversão à perda irracional e mau uso da informação entre outros. Nesta tese desenvolvemos duas metodologias distintas para enfrentar esse problema. A primeira abordagem é qualitativa, utiliza o modelo de Black-Litterman e tenta mapear a visão que o investidor tem do mercado. Esse método tenta mitigar a irracionalidade na tomada de decisão tornando mais fácil para um investidor demonstrar suas preferências em relação aos ativos. Black e Litterman desenvolveram um método para otimização de carteiras com a proposta de melhorar o modelo Markowitz, utilizando a construção de visões para representar a opinião do investidor sobre o futuro. No entanto, a forma de construir essas visões é bastante confusa e exige que o investidor estime vários parâmetros que são subjetivos. Assim, propomos uma nova forma de criar essas visões, utilizando Análise Verbal de Decisão. A segunda pesquisa envolve métodos quantitativos para resolver o problema de alocação de ativos com múltiplos estágios com premissas mais realistas. Embora a Programação Dinâmica Dual Estocástica (PDDE) seja uma técnica promissora para a solução de problemas de grande porte, não é adequada para o problema de alocação de ativos devido à dependência temporal associada aos retornos dos ativos. PDDE assume que o processo estocástico tem independência por estágio assegurando uma função única de custo futuro para cada estágio. No problema de alocação de ativos, a dependência do tempo é tipicamente não-linear e no lado esquerdo, o que torna PDDE tradicional não aplicável. Propomos uma variação do PDDE usando modelo oculto de Markov com estados discretos para resolver problemas reais de alocação de ativos com múltiplos períodos e dependência no tempo. Ambas as abordagens foram testadas em dados reais e empiricamente analisadas. As principais contribuições são as metodologia desenvolvidas para simplificar a construção de portfólios e para resolver o problema de alocação de ativos com múltiplos estágios. / [en] Asset allocation is one of the most important financial decisions made by investors. However, human decisions are not fully rational, and people make several systematic mistakes due to overconfidence, irrational loss aversion and misuse of information, among others. In this thesis, we developed two distinct methodologies to tackle this problem. The first approach has a more qualitative view, trying to map the investor s vision of the market. It tries to mitigate irrationality in decision-making by making it easier for an investor to demonstrate his/her preferences for specirfic assets. This first research uses the Black-Litterman model to construct portfolios. Black and Litterman developed a method for portfolio optimization as an improvement over the Markowitz model. They suggested the construction of views to represent an investor s opinion about future stocks returns. However, constructing these views has proven difficult, as it requires the investor to quantify several subjective parameters. This work investigates a new way of creating these views by using Verbal Decision Analysis. The second research focuses on quantitative methods to solve the multistage asset allocation problem. More specifically, it modifies the Stochastic Dynamic Dual Programming (SDDP) method to consider real asset allocation models. Although SDDP is a consolidated solution technique for large-scale problems, it is not suitable for asset allocation problems due to the temporal dependence of returns. Indeed, SDDP assumes a stagewise independence of the random process assuring a unique cost-to-go function for each time stage. For the asset allocation problem, time dependency is typically nonlinear and on the left-hand side, which makes traditional SDDP inapplicable. This thesis proposes an SDDP variation to solve real asset allocation problems for multiple periods, by modeling time dependence as a Hidden Markov Model with concealed discrete states. Both approaches were tested in real data and empirically analyzed. The contributions of this thesis are the methodology to simplify portfolio construction and the methods to solve real multistage stochastic asset allocation problems.

Submitted by Diego de Carvalho Martins (diego.cmartins@gmail.com) on 2015-03-03T17:37:26Z No. of bitstreams: 1 Dissertação Diego Martins Vf.pdf: 5717457 bytes, checksum: 7b47eb855a437b18798c842352f083b8 (MD5) / Rejected by Renata de Souza Nascimento (renata.souza@fgv.br), reason: Prezado Diego, Encaminharei por e-mail o que deve ser alterado, para que possamos aceita-lo junto à biblioteca. Att Renata on 2015-03-03T21:33:00Z (GMT) / Submitted by Diego de Carvalho Martins (diego.cmartins@gmail.com) on 2015-03-03T22:13:33Z No. of bitstreams: 1 Dissertação Diego Martins Vf.pdf: 5717977 bytes, checksum: 446abdc648b62abddb519b99648b6a3a (MD5) / Approved for entry into archive by Renata de Souza Nascimento (renata.souza@fgv.br) on 2015-03-04T17:27:29Z (GMT) No. of bitstreams: 1 Dissertação Diego Martins Vf.pdf: 5717977 bytes, checksum: 446abdc648b62abddb519b99648b6a3a (MD5) / Made available in DSpace on 2015-03-04T18:27:00Z (GMT). No. of bitstreams: 1 Dissertação Diego Martins Vf.pdf: 5717977 bytes, checksum: 446abdc648b62abddb519b99648b6a3a (MD5) Previous issue date: 2015-02-06 / This work aims to analyze the performance of regularized mean-variance portfolios, employing financial assets available in Brazilian markets. In particular, regularized portfolios are obtained by restricting the norm of the portfolio-weights vector, following DeMiguel et al. (2009). Additionally, we analyze the performance of portfolios that take into account information about the group structure of assets with similar characteristics, as proposed by Fernandes, Rocha and Souza (2011). While the covariance matrix employed is the sample one, the expected returns are obtained by reverse optimization of market equilibrium portfolio proposed by Black and Litterman (1992). The empirical analysis out of the sample for the period between January 2010 and October 2014 indicates that, in line with previous studies, penalizing the norm of weights can (depending on the chosen standard and intensity of the restriction) lead to portfolios having best performances in terms of return and Sharpe, when compared to portfolios obtained via Markowitz models. In addition, the inclusion of group information can also be beneficial in order to calculate optimal portfolios, when compared to both Markowitz portfolios or without using group information. / Este trabalho se dedica a analisar o desempenho de modelos de otimização de carteiras regularizadas, empregando ativos financeiros do mercado brasileiro. Em particular, regularizamos as carteiras através do uso de restrições sobre a norma dos pesos dos ativos, assim como DeMiguel et al. (2009). Adicionalmente, também analisamos o desempenho de carteiras que levam em consideração informações sobre a estrutura de grupos de ativos com características semelhantes, conforme proposto por Fernandes, Rocha e Souza (2011). Enquanto a matriz de covariância empregada nas análises é a estimada através dos dados amostrais, os retornos esperados são obtidos através da otimização reversa da carteira de equilíbrio de mercado proposta por Black e Litterman (1992). A análise empírica fora da amostra para o período entre janeiro de 2010 e outubro de 2014 sinaliza-nos que, em linha com estudos anteriores, a penalização das normas dos pesos pode levar (dependendo da norma escolhida e da intensidade da restrição) a melhores performances em termos de Sharpe e retorno médio, em relação a carteiras obtidas via o modelo tradicional de Markowitz. Além disso, a inclusão de informações sobre os grupos de ativos também pode trazer benefícios ao cálculo de portfolios ótimos, tanto em relação aos métodos tradicionais quanto em relação aos casos sem uso da estrutura de grupos.

Submitted by Guilherme Atem (guiatem@gmail.com) on 2013-03-19T16:02:06Z No. of bitstreams: 1 Dissertação - Guilherme Atem.pdf: 2045602 bytes, checksum: 3d2427a0fdd1376baf5c274252a390a2 (MD5) / Approved for entry into archive by Suzinei Teles Garcia Garcia (suzinei.garcia@fgv.br) on 2013-03-19T16:04:40Z (GMT) No. of bitstreams: 1 Dissertação - Guilherme Atem.pdf: 2045602 bytes, checksum: 3d2427a0fdd1376baf5c274252a390a2 (MD5) / Made available in DSpace on 2013-03-19T16:24:11Z (GMT). No. of bitstreams: 1 Dissertação - Guilherme Atem.pdf: 2045602 bytes, checksum: 3d2427a0fdd1376baf5c274252a390a2 (MD5) Previous issue date: 2013-02-05 / Neste trabalho, comparamos algumas aplicações obtidas ao se utilizar os conhecimentos subjetivos do investidor para a obtenção de alocações de portfólio ótimas, de acordo com o modelo bayesiano de Black-Litterman e sua generalização feita por Pezier e Meucci. Utilizamos como medida de satisfação do investidor as funções utilidade correspondentes a um investidor disciplinado, isto é, que é puramente averso a risco, e outro que procura risco quando os resultados são favoráveis. Aplicamos o modelo a duas carteiras de ações que compõem o índice Ibovespa, uma que replica a composição do índice e outra composta por pares de posições long&short de ações ordinárias e preferenciais. Para efeito de validação, utilizamos uma análise com dados fora da amostra, dividindo os dados em períodos iguais e revezando o conjunto de treinamento. Como resultado, foi possível concluir que: i) o modelo de Black-Litterman não é suficiente para contornar as soluções de canto quando o investidor não é disciplinado, ao menos para o modelo utilizado; ii) para um investidor disciplinado, o P&L médio obtido pelos modelos de média-variância e de Black-Litterman é consideravelmente superior ao do benchmark para as duas carteiras; iii) o modelo de Black Litterman somente foi superior ao de média-variância quando a visão do investidor previu bem os resultados do mercado. / On this work, we compare results obtained when the investor chooses to use his subjective views on the market to calculate the allocation optimization of a given portfolio, according to the bayesian model of Black-Litterman (BLACK; LITTERMAN, 1992) and the generelization provided by Pezier (PEZIER, 2007) and Meucci (MEUCCI, 2008). As a measure of satisfaction of the investor, we use utility functions describing an investor with discipline that is always risk-averse and other function for an investor who seeks risk when the results are favourable. The model is applied to two portfolios consisting of stock from the Ibovespa index: one of them consists of all stocks from the index, with time horizon of half an year, and the other presents four long short positions betwen ordinary and preferential stocks and time horizon of one month. The results are validated with out of sample data, according to a 10-fold cross validation. As a result, we conclude that: i) the Black-Litterman model may not be enougth to avoid corner solutions when the investor has no discipline, according to our model; ii) both the Black-Litterman and the Mean-Variance models perform better then the benchmarks; iii) but the winner model depends on the forecast power of the investor views.