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In recent years, the number of Indonesian investors has rapidly increased during the COVID-19 pandemic which happened all around the world. There have been a massive number of influencers in social media who were promoting investment. Although stocks and warrants are interesting choices, mutual funds still become the main ones for beginners. Therefore, this research focuses on the development of a stock portfolio model using the Black-Litterman method which involves the investor’s views towards the stock returns. The research refers to one of the largest equity funds in Indonesia, that is Sucorinvest Equity Fund, by using the top ten of its stocks that are majority in the fund (as of April 28, 2023). Furthermore, this research also constructs a structured warrant portfolio, but it is separated from the initially constructed stock portfolio. Structured warrants could be an appropriate choice for low-budget investors. It was newly introduced in Indonesia in September 2022 so it is interesting to be observed. Based on the results and the implemented assumptions, the return obtained from the stock portfolio is superior to the observed fund’s return. Meanwhile, call structured warrant portfolio using the existing product in the market yields a negative return, because the exercise price and warrant offered price were too high. Thus, structured warrants could be considered overpriced at the moment, so the chance of obtaining profit is extremely small. Due to its similar properties to call and put options, we propose the warrant pricing and use it in simulations, so in the future, structured warrants may become an attractive instrument for the investors.

Introduction: This article focuses on the study and application of the Black Litterman (BL) model to six companies on the Colombian Stock Exchange (BVC), considering historical returns, market capitalizations, and perspectives on the future behavior of assets. in order to obtain the expected returns. Methodology: the results of this approach are compared with the Markowitz and CAMP models, the study period covers from February 28, 2018, to February 24, 2023. The research is quantitative, descriptive, and longitudinal, it is used the risk-free rate TFIT16240724 and the ICOLCAP index as measures of market risk. Results: were obtained, they were evaluated, concluding that the Markowitz model presented the most optimistic and profitable individual returns, while the BL and CAMP models presented very low expected returns. Portfolio returns optimized for the Markowitz and Black Litterman models have a similar insight into stock trends but differ in their perception of risk., Introducción: Este artículo se centra en el estudio y la aplicación del modelo Black Litterman (BL) a seis empresas de la bolsa de valores de Colombia (BVC), se consideran los retornos históricos, las capitalizaciones de mercado y las perspectivas sobre el comportamiento futuro de los activos con el fin de obtener los rendimientos esperados. Metodología: se comparan los resultados de este enfoque con los modelos de Markowitz y el CAMP, el periodo de estudio comprende desde el 28 de febrero de 2018 al 24 de febrero de 2023. La investigación es de tipo cuantitativo, descriptivo y longitudinal, se utiliza la tasa libre de riesgo TFIT16240724 y el índice ICOLCAP como medidas de riesgo del mercado. Resultados: estos fueron evaluados, concluyéndose que el modelo de Markowitz presentó los rendimientos individuales más optimistas y rentables, mientras que los modelos de BL y CAMP presentaron rendimientos esperados muy bajos. Los rendimientos de los portafolios optimizados para los modelos de Markowitz y Black Litterman tienen una percepción similar sobre las tendencias de las acciones, pero difieren en su percepción del riesgo.

The concept of portfolio optimization has been widely studied in the academy and implemented in the financial markets since its introduction by Markowitz 70 years ago. The problem of the mean-variance optimization framework caused by input uncertainty has been one of the foci in the previous research. In this study, several models (linear shrinkage and Black-Litterman) based on Bayesian approaches are studied to improve the estimation of inputs. Moreover, a new framework based on robust optimization is presented to mitigate the input uncertainty further. An out-of-sample test is specially designed, and the results show that Bayesian models in this study can improve the optimization results in terms of higher Sharpe ratios (the quotient between portfolio returns and their risks). Both covariance matrix estimators based on the linear shrinkage method contain less error and provide better optimization results, i.e. higher Sharpe ratios. The Black-Litterman model with a proper choice of inputs can significantly improve the portfolio return. The new framework based on the combination of shrinkage estimators, Black-Litterman, and robust optimization presents a better way for portfolio optimization than the classical framework of mean-variance optimization.

This thesis investigates how neural networks can be used to produce investors' views for the Black-Litterman market model. The study uses two data sets, one with global stock market indexes and one with stock market data from the S&P 500. The task of the neural networks is to produce forecasts for the returns for the next quarter and the following year. The neural network will have to predict whether the market will move up or down and determine if the market movement is less than or equal to one standard deviation, creating four different scenarios. The forecasts are used as input to the Black-Litterman model to generate new portfolios, which are backtested from 2017 until 2022. The index data set was compared to a benchmark portfolio and a portfolio with naive risk diversification, while the S&P 500 data set was compared to market capitalization-weighted and naive portfolios. This resulted in eight different backtests where the neural networks obtained AUC values in the range of 0.56-0.73 and prediction accuracies in the range of 20.9% - 42.1%. The network used for yearly predictions on the index data set was the only network to outperform the benchmark portfolio. It obtained a Sharpe ratio of 1.782, a Sortino ratio of 2.165, and a maximum drawdown of -30.9% compared to the benchmark portfolio, where the corresponding metrics were 1.544, 1.879, and -32.8%., Detta examensarbete undersöker hur neurala nätverk kan användas för att generera investerares åsikt till Black-Littermans marknadsmodell. Studien använder två dataset, en med globala börsindex och en med börsdata från S6P 500. De neurala nätverkens uppgift är att generera prognoser för avkastning för nästa kvartal samt nästkommande år. Det neurala nätverket måste förutsäga om marknaden kommer att röra sig uppåt eller nedåt, och avgöra om marknadsrörelsen är mindre än eller lika med en standaravvikelse, vilket skapar fyra olika scenarier. Prognoserna användas som input till Black-Litterman-modellen för att generera nya portföljer, som backtestas från 2017 till 2022. Portföljerna som skapades med globala börsindex jämfördes med en benchmarkportfölj och en portfölj med naiv riskspridning. Datasetet med data från S&P 500 jämfördes med marknadsvärdesviktade och naiva portföljer. Detta resulterade i åtta olika simuleringar där de neurala nätverken fick AUC-värden i intervallet 0,56-0,73 och prediktionsnoggrannheter i intervallte 20,9% - 42,1%. Nätverket som användes för årliga prognoser om globala börsindex var det enda nätverket som överträffade jämförelseportföljen. Den fick en Sharpekvot på 1, 782, Sortinokvot på 2,165 och en största kumulativa nedgång på -30,9% jämfört med jämförelseportföljen där motsvarande mätvärden var 1, 544, 1, 879 och -32,8%.

El acceso a diferentes activos de inversión, la búsqueda de alternativas de diversificación y la cuantificación y cobertura de los riesgos asociados a los portafolios, son factores de alta relevancia a la hora de construir y administrar portafolios de inversión con alcance internacional. De ahí, que el objetivo del presente trabajo se centra en la aplicación del modelo Black-Litterman para la construcción de un portafolio de renta fija global, compuesto por activos ETFs high yield e investment grade, así como por bonos soberanos de países desarrollados. Asimismo, con el fin de aumentar la cobertura, la capacidad de diversificación y minimizar el riesgo, se presenta un benchmark construido con base en diferentes índices de renta fija global y activos de la misma categoría. Finalmente, se propondrá la utilización de una estrategia de cobertura vía forwards con el fin de mitigar el riesgo inherente a la devaluación de la divisa., The access to different investment assets, the search for diversification, and the application of measures as for quantification and hedging risk are relevant factors for building and managing international investment portfolios. Therefore, the objective of the present paper aims to the application of Black-Litterman portfolio model on building a global fixed income portfolio, which is made up of high yield and investment grade ETFs, as well as developed countries government bonds. Furthermore, in order to increase hedging, diversification ratio, and to minimize risk, a benchmark, which is made up of both global fixed income indices and assets from the same category will be built. Finally, a hedging strategy will be proposed through forwards in order to minimize the inherent risk due to currency depreciation.

This thesis investigates how neural networks can be used to produce investors' views for the Black-Litterman market model. The study uses two data sets, one with global stock market indexes and one with stock market data from the S&P 500. The task of the neural networks is to produce forecasts for the returns for the next quarter and the following year. The neural network will have to predict whether the market will move up or down and determine if the market movement is less than or equal to one standard deviation, creating four different scenarios. The forecasts are used as input to the Black-Litterman model to generate new portfolios, which are backtested from 2017 until 2022. The index data set was compared to a benchmark portfolio and a portfolio with naive risk diversification, while the S&P 500 data set was compared to market capitalization-weighted and naive portfolios. This resulted in eight different backtests where the neural networks obtained AUC values in the range of 0.56-0.73 and prediction accuracies in the range of 20.9% - 42.1%. The network used for yearly predictions on the index data set was the only network to outperform the benchmark portfolio. It obtained a Sharpe ratio of 1.782, a Sortino ratio of 2.165, and a maximum drawdown of -30.9% compared to the benchmark portfolio, where the corresponding metrics were 1.544, 1.879, and -32.8%., Detta examensarbete undersöker hur neurala nätverk kan användas för att generera investerares åsikt till Black-Littermans marknadsmodell. Studien använder två dataset, en med globala börsindex och en med börsdata från S6P 500. De neurala nätverkens uppgift är att generera prognoser för avkastning för nästa kvartal samt nästkommande år. Det neurala nätverket måste förutsäga om marknaden kommer att röra sig uppåt eller nedåt, och avgöra om marknadsrörelsen är mindre än eller lika med en standaravvikelse, vilket skapar fyra olika scenarier. Prognoserna användas som input till Black-Litterman-modellen för att generera nya portföljer, som backtestas från 2017 till 2022. Portföljerna som skapades med globala börsindex jämfördes med en benchmarkportfölj och en portfölj med naiv riskspridning. Datasetet med data från S&P 500 jämfördes med marknadsvärdesviktade och naiva portföljer. Detta resulterade i åtta olika simuleringar där de neurala nätverken fick AUC-värden i intervallet 0,56-0,73 och prediktionsnoggrannheter i intervallte 20,9% - 42,1%. Nätverket som användes för årliga prognoser om globala börsindex var det enda nätverket som överträffade jämförelseportföljen. Den fick en Sharpekvot på 1, 782, Sortinokvot på 2,165 och en största kumulativa nedgång på -30,9% jämfört med jämförelseportföljen där motsvarande mätvärden var 1, 544, 1, 879 och -32,8%.

The concept of portfolio optimization has been widely studied in the academy and implemented in the financial markets since its introduction by Markowitz 70 years ago. The problem of the mean-variance optimization framework caused by input uncertainty has been one of the foci in the previous research. In this study, several models (linear shrinkage and Black-Litterman) based on Bayesian approaches are studied to improve the estimation of inputs. Moreover, a new framework based on robust optimization is presented to mitigate the input uncertainty further. An out-of-sample test is specially designed, and the results show that Bayesian models in this study can improve the optimization results in terms of higher Sharpe ratios (the quotient between portfolio returns and their risks). Both covariance matrix estimators based on the linear shrinkage method contain less error and provide better optimization results, i.e. higher Sharpe ratios. The Black-Litterman model with a proper choice of inputs can significantly improve the portfolio return. The new framework based on the combination of shrinkage estimators, Black-Litterman, and robust optimization presents a better way for portfolio optimization than the classical framework of mean-variance optimization.

Los derivados financieros, con exposición en el mercado internacional por medio de futuros que repliquen los índices bursátiles, generan una gran oportunidad de inversión en el mercado colombiano, por medio de instrumentos de especulación y mayores rendimientos esperados. Bajo este marco, y con el interés de utilizar vehículos de inversión alternativos, la presente investigación busca la construcción de un portafolio de activos, compuesto por contratos de futuros de índices bursátiles a partir del modelo Black-Litterman, evaluando la generación de exceso de rendimientos frente a una estrategia pasiva como benchmark., Financial derivatives, with exposure in the international market through futures that replicate stock indexes, generate a great investment opportunity in the colombian market, through speculation instruments and higher expected returns. Under this framework, and with the interest of using alternative investment vehicles, this research seeks the construction of a portfolio of assets composed of futures contracts of stock indexes based on the Black-Litterman model, evaluating the generation of excess returns against to a passive strategy as a benchmark.

Portfolio allocation theories have been studied and used ever since the mid 20th century. Nevertheless, many investors still rely on personal expertise and information gathered from the market when building their investment portfolios. The purpose of this master’s thesis is to examine how personal preferences and expertise perform compared to mathematical portfolio alloca- tion theories and how the risk between these di↵erent strategies di↵er. Using two portfolio allocation theories, the Black-Litterman model and mod- ern portfolio theory (Markowitz), a portfolio managed by the investment firm Placerum Kapitalf ̈orvaltning in Ume ̊a will be compared and challenged to investigate which strategy gives the best risk adjusted return. Using scenario modelling, the portfolios can be compared using both historical data and future forecasted scenarios to analyze the past, present and future of the allocation theories and Placerum’s investment strategy. The first allocation theory, the Black-Litterman model, combines historical information from the market with views and preferences of the investor to select the optimal allocations derived from return and volatility. The second allocation theory, the modern portfolio theory (Markowitz), only uses histori- cal data to derive correlations and returns which are then used to select the optimal allocations. By analysing several risk measures applied on the portfolios historical and forecasted data as well as comparing the performance of the portfolios, it is shown that the investment strategy used at Placerum succeeds with its intentions to achieve relatively high return while reducing the risk. However, the portfolios given using the two allocation theories results in higher potential returns but at the cost of taking on a higher risk. Comparing the two studied allocation theories, it is shown that when using the Black-Litterman model with the assumptions and views defined in this project, modern allocation theory actually beats

Portfolio allocation theories have been studied and used ever since the mid 20th century. Nevertheless, many investors still rely on personal expertise and information gathered from the market when building their investment portfolios. The purpose of this master’s thesis is to examine how personal preferences and expertise perform compared to mathematical portfolio alloca- tion theories and how the risk between these di↵erent strategies di↵er. Using two portfolio allocation theories, the Black-Litterman model and mod- ern portfolio theory (Markowitz), a portfolio managed by the investment firm Placerum Kapitalf ̈orvaltning in Ume ̊a will be compared and challenged to investigate which strategy gives the best risk adjusted return. Using scenario modelling, the portfolios can be compared using both historical data and future forecasted scenarios to analyze the past, present and future of the allocation theories and Placerum’s investment strategy. The first allocation theory, the Black-Litterman model, combines historical information from the market with views and preferences of the investor to select the optimal allocations derived from return and volatility. The second allocation theory, the modern portfolio theory (Markowitz), only uses histori- cal data to derive correlations and returns which are then used to select the optimal allocations. By analysing several risk measures applied on the portfolios historical and forecasted data as well as comparing the performance of the portfolios, it is shown that the investment strategy used at Placerum succeeds with its intentions to achieve relatively high return while reducing the risk. However, the portfolios given using the two allocation theories results in higher potential returns but at the cost of taking on a higher risk. Comparing the two studied allocation theories, it is shown that when using the Black-Litterman model with the assumptions and views defined in this project, modern allocation theory actually beats

The Black-Litterman model combines the market equilibrium with the investor's personal views and gives optimal portfolio weights. In this paper we will review the original Black-Litterman model, we will modify the model such that it fits in a Bayesian framework by considering the investors' personal views to be a direct prior on the means of the returns and by including a typical Inverse Wishart prior on the covariance matrix of the returns. We will then consider Leonard and Hsu's (1992) idea for a prior on the logarithm of the covariance matrix. We encountered both running time and memory allocation problems when we applied the latter version to the whole S&P 500. To overcome such computational problems, Bayesian factor models are considered for the analysis. This choice was also motivated by the strong connection between Black-Litterman and the Capital Asset Pricing Model, which itself can be seen as a factor model. Sensitivity analyses for the level of confidence that investors have in their own personal views were performed and performance of the models was assessed on a test data set consisting of returns over the month of January 2018.

The Black-Litterman model combines the market equilibrium with the investor's personal views and gives optimal portfolio weights. In this paper we will review the original Black-Litterman model, we will modify the model such that it fits in a Bayesian framework by considering the investors' personal views to be a direct prior on the means of the returns and by including a typical Inverse Wishart prior on the covariance matrix of the returns. We will then consider Leonard and Hsu's (1992) idea for a prior on the logarithm of the covariance matrix. We encountered both running time and memory allocation problems when we applied the latter version to the whole S&P 500. To overcome such computational problems, Bayesian factor models are considered for the analysis. This choice was also motivated by the strong connection between Black-Litterman and the Capital Asset Pricing Model, which itself can be seen as a factor model. Sensitivity analyses for the level of confidence that investors have in their own personal views were performed and performance of the models was assessed on a test data set consisting of returns over the month of January 2018.

An investor wants to maximize return at the cost of as little risk as possible and theBlack-Litterman model can help see that this condition is met. This thesis willinvestigate whether a portfolio created by using modern portfolio theory can beat thebenchmark index in terms of risk-adjusted return during a five year backtest period(2013-2017). Harry Markowitz provides the mean variance optimization frameworkwhile the practical Black-Litterman model adds the opportunity to tweak performancewith views on stock returns. The method for producing views for the Black-Littermanmodel can vary a lot and is what makes this thesis, for all that we know, unique. Theviews in our model stem from regression on the summed up earnings per share forthe last four quarters multiplied by the corresponding historical price earnings ratioand the historical stock price. The regressions provide data on how over orundervalued the stocks are. Backtesting our modified Black-Litterman model yieldsimpressive results in terms of risk-adjusted return and we encourage other studentsof the financial market to further investigate the performance of our modified portfolio.However most of the results are not statistically significant on a 5% significance leveldue to the need for more data points. This method is purely quantitative and can befully replicated to yield the same results for any interested investor.

An investor wants to maximize return at the cost of as little risk as possible and theBlack-Litterman model can help see that this condition is met. This thesis willinvestigate whether a portfolio created by using modern portfolio theory can beat thebenchmark index in terms of risk-adjusted return during a five year backtest period(2013-2017). Harry Markowitz provides the mean variance optimization frameworkwhile the practical Black-Litterman model adds the opportunity to tweak performancewith views on stock returns. The method for producing views for the Black-Littermanmodel can vary a lot and is what makes this thesis, for all that we know, unique. Theviews in our model stem from regression on the summed up earnings per share forthe last four quarters multiplied by the corresponding historical price earnings ratioand the historical stock price. The regressions provide data on how over orundervalued the stocks are. Backtesting our modified Black-Litterman model yieldsimpressive results in terms of risk-adjusted return and we encourage other studentsof the financial market to further investigate the performance of our modified portfolio.However most of the results are not statistically significant on a 5% significance leveldue to the need for more data points. This method is purely quantitative and can befully replicated to yield the same results for any interested investor.

This thesis is an implementation project of a portfolio optimization model, with the purpose of creating a decision support tool. It aims to provide quantitative input to the portfolio construction process at Handelsbanken Fonder, by applying Konno & Yamazaki’s Mean Absolute Deviation method, with a Feinstein & Thapa modification. Additionally, the Black-Litterman model is implemented to approximate the input of expected return. The linear optimization problem was then solved by the Simplex algorithm. The main deliverable is a model that can assist portfolio managers in making investment decisions. Back-testing of the model showed that it did not outperform the benchmark portfolios, which is likely a result of only allowing long positions in the model. Nevertheless, the model provides value by giving the user a second opinion on the efficient frontier, for any given investment decision., Den här uppsatsen är ettimplementationsprojekt av enportföljoptimerings-modell, med syftet att skapaett beslutsstödjande verktyg. Den strävar efter att ge ett kvantitativt bidragtill portföljallokerings-processen på Handelsbanken Fonder, genom att användaKonno & Yamazaki’s Mean Absolute Deviation-metod med en Feinstein &Thapa-modifiering. Vidare har Black-Littermanmodellen implementerats för attapproximera den förväntade avkastningen. Det linjära optimeringsproblemetlöstes sedan med Simplex-algorithmen. Det huvudsakliga resultatet är en modellsom kan assisterafondförvaltare i investeringsbeslut. Utförda utfallstestvisade att modellen inte överträffade de använda benchmark-fonderna, vilketsannolikt är ett resultat av att modellen enbart tillåterlånga positioner.Likväl, kan modellen vara värdefull genom att erbjuda användaren ett alternativpå den effektiva fronten, för ett givet investeringsbeslut.

This thesis is an implementation project of a portfolio optimization model, with the purpose of creating a decision support tool. It aims to provide quantitative input to the portfolio construction process at Handelsbanken Fonder, by applying Konno & Yamazaki’s Mean Absolute Deviation method, with a Feinstein & Thapa modification. Additionally, the Black-Litterman model is implemented to approximate the input of expected return. The linear optimization problem was then solved by the Simplex algorithm. The main deliverable is a model that can assist portfolio managers in making investment decisions. Back-testing of the model showed that it did not outperform the benchmark portfolios, which is likely a result of only allowing long positions in the model. Nevertheless, the model provides value by giving the user a second opinion on the efficient frontier, for any given investment decision., Den här uppsatsen är ettimplementationsprojekt av enportföljoptimerings-modell, med syftet att skapaett beslutsstödjande verktyg. Den strävar efter att ge ett kvantitativt bidragtill portföljallokerings-processen på Handelsbanken Fonder, genom att användaKonno & Yamazaki’s Mean Absolute Deviation-metod med en Feinstein &Thapa-modifiering. Vidare har Black-Littermanmodellen implementerats för attapproximera den förväntade avkastningen. Det linjära optimeringsproblemetlöstes sedan med Simplex-algorithmen. Det huvudsakliga resultatet är en modellsom kan assisterafondförvaltare i investeringsbeslut. Utförda utfallstestvisade att modellen inte överträffade de använda benchmark-fonderna, vilketsannolikt är ett resultat av att modellen enbart tillåterlånga positioner.Likväl, kan modellen vara värdefull genom att erbjuda användaren ett alternativpå den effektiva fronten, för ett givet investeringsbeslut.

2 Abstract This paper deploys methodology typically utilized in financial econometrics, namely univariate and multivariate GARCH-M forecasting techniques, as inputs into the Black-Litterman asset allocation process. While previous works have examined the usefulness in deploying select GARCH specifications as a source for the required Black-Litterman views vector, to the best of our knowledge, this is the first such work comparing the effects of select GARCH specification on asset allocation volatility. This paper draws parallels with Beach and Orlov (2007) and Duqi, Franci, and Torluccio (2014) in finding improved portfolio financial performance after the incorporation of GARCH-derived views relative to market equilibrium weighting. Financial performance is further improved with the incorporation of the multivariate DCC models. While this increase in performance is accompanied by an increase in asset allocation instability, the multivariate portfolios provide a better return-to-risk relationship for the associated degree of allocation volatility. In both the univariate and multivariate specifications the more simple GARCH(1,1) provides superior performance relative to the asymmetric GJR model.

2 Abstract This paper deploys methodology typically utilized in financial econometrics, namely univariate and multivariate GARCH-M forecasting techniques, as inputs into the Black-Litterman asset allocation process. While previous works have examined the usefulness in deploying select GARCH specifications as a source for the required Black-Litterman views vector, to the best of our knowledge, this is the first such work comparing the effects of select GARCH specification on asset allocation volatility. This paper draws parallels with Beach and Orlov (2007) and Duqi, Franci, and Torluccio (2014) in finding improved portfolio financial performance after the incorporation of GARCH-derived views relative to market equilibrium weighting. Financial performance is further improved with the incorporation of the multivariate DCC models. While this increase in performance is accompanied by an increase in asset allocation instability, the multivariate portfolios provide a better return-to-risk relationship for the associated degree of allocation volatility. In both the univariate and multivariate specifications the more simple GARCH(1,1) provides superior performance relative to the asymmetric GJR model.

This paper develops a multiple-goal investment strategy for sovereign wealth funds. In our investment strategy, we embed the Black-Litterman (B-L) model into the mean variance mental accounting (MVMA) approach. The B-L method provides a means of modeling return expectations, and the MVMA framework allows the derivation of the optimal asset allocation from a global investment perspective, in a response to a specific macroeconomic environment.

Dentro de las diversas teorías financieras que se enfocan en la asignación óptima de recursos en un portafolio de inversión, la propuesta de Black-Litterman es la única que incorpora las expectativas futuras que tienen los inversionistas sobre los activos en los cuales destinarán sus recursos. En este trabajo se presenta la propuesta de Black-Litterman como una herramienta para mejorar la selección óptima de portafolios y como un insumo que mejora la estructuración de portafolios a través del modelo clásico propuesto por Markowitz. Además de la presentación teórica del modelo de Black-Litterman, se realiza un análisis de caso estructurando un portafolio óptimo sobre el índice COLCAP del mercado de valores colombiano, los resultados muestran que además de permitir incorporar las visiones de los inversionistas, los resultados obtenidos mediante Black-Litterman ayudan a crear mejores portafolios de inversión a través del modelo de Markowitz, tanto en maximización de rendimientos como de minimización de varianza.

This paper develops a multiple-goal investment strategy for sovereign wealth funds. In our investment strategy, we embed the Black-Litterman (B-L) model into the mean variance mental accounting (MVMA) approach. The B-L method provides a means of modeling return expectations, and the MVMA framework allows the derivation of the optimal asset allocation from a global investment perspective, in a response to a specific macroeconomic environment.

Dentro de las diversas teorías financieras que se enfocan en la asignación óptima de recursos en un portafolio de inversión, la propuesta de Black-Litterman es la única que incorpora las expectativas futuras que tienen los inversionistas sobre los activos en los cuales destinarán sus recursos. En este trabajo se presenta la propuesta de Black-Litterman como una herramienta para mejorar la selección óptima de portafolios y como un insumo que mejora la estructuración de portafolios a través del modelo clásico propuesto por Markowitz. Además de la presentación teórica del modelo de Black-Litterman, se realiza un análisis de caso estructurando un portafolio óptimo sobre el índice COLCAP del mercado de valores colombiano, los resultados muestran que además de permitir incorporar las visiones de los inversionistas, los resultados obtenidos mediante Black-Litterman ayudan a crear mejores portafolios de inversión a través del modelo de Markowitz, tanto en maximización de rendimientos como de minimización de varianza.

We develop two dynamic Bayesian portfolio allocation models that address questions of learning and model uncertainty by taking model-specific shortcomings into account.In our first model, we formulate a multi-period portfolio choice problem in which the investor is uncertain about parameters of the model, can learn these parameters over time from observing asset returns, but is also concerned about robustness. To address these concerns, we introduce an objective function which can be regarded as a Bayesian version of relative regret. The optimal portfolio is characterized and shown to involve a ``tilted'' posterior, where the tilting is defined in terms of a family of stochastic benchmarks. We have found this model to perform at least as well as a benchmark given the true market parameters, while outperforming it when the market assets have the same trend.Our next model extends the Black-Litterman portfolio choice model by taking several potential errors into account. We extend Black-Litterman to multiple periods, which allows for us to take into account the pairs of expert forecasts and the realized return. By doing so, we can then perform inference on these experts and discover whether they may have any bias for or against any specific assets. We can also perform similar inference on the market equilibrium distribution, which is typically represented by the capital asset pricing model (CAPM). The result is a model that is analytically intractable but may be solved numerically via Gibbs sampling. Controlled tests show our model performs favorably when Black-Litterman's model assumptions about the market equilibrium and expert views are violated. Backtests shed light on the model's ability to account for CAPM's shortcomings.

We develop two dynamic Bayesian portfolio allocation models that address questions of learning and model uncertainty by taking model-specific shortcomings into account.In our first model, we formulate a multi-period portfolio choice problem in which the investor is uncertain about parameters of the model, can learn these parameters over time from observing asset returns, but is also concerned about robustness. To address these concerns, we introduce an objective function which can be regarded as a Bayesian version of relative regret. The optimal portfolio is characterized and shown to involve a ``tilted'' posterior, where the tilting is defined in terms of a family of stochastic benchmarks. We have found this model to perform at least as well as a benchmark given the true market parameters, while outperforming it when the market assets have the same trend.Our next model extends the Black-Litterman portfolio choice model by taking several potential errors into account. We extend Black-Litterman to multiple periods, which allows for us to take into account the pairs of expert forecasts and the realized return. By doing so, we can then perform inference on these experts and discover whether they may have any bias for or against any specific assets. We can also perform similar inference on the market equilibrium distribution, which is typically represented by the capital asset pricing model (CAPM). The result is a model that is analytically intractable but may be solved numerically via Gibbs sampling. Controlled tests show our model performs favorably when Black-Litterman's model assumptions about the market equilibrium and expert views are violated. Backtests shed light on the model's ability to account for CAPM's shortcomings.

This thesis applies the Black-Litterman (BL) model on the stocks that makes up the Swedish stock index OMXS30 during the year of 2012. Public information in the form of stock recommendations from financial institutions has been used as views in the BL-framework. A method of estimating confidence in these views has been analyzed and further clarified. The testing consists of two BL-portfolios along with two Mean Variance-portfolios, allowing me to compare the performance difference that the BL-model has. The two portfolios differ in terms of short selling restrictions. Although the results show a difference in total returns in favor of the restricted BL-portfolio, no significant difference were found compared to the other portfolios or the stock market index, both in terms of returns and in terms of Sharpe ratios.

This thesis applies the Black-Litterman (BL) model on the stocks that makes up the Swedish stock index OMXS30 during the year of 2012. Public information in the form of stock recommendations from financial institutions has been used as views in the BL-framework. A method of estimating confidence in these views has been analyzed and further clarified. The testing consists of two BL-portfolios along with two Mean Variance-portfolios, allowing me to compare the performance difference that the BL-model has. The two portfolios differ in terms of short selling restrictions. Although the results show a difference in total returns in favor of the restricted BL-portfolio, no significant difference were found compared to the other portfolios or the stock market index, both in terms of returns and in terms of Sharpe ratios.

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

This thesis investigates the applicability of the Black-Litterman portfolio allocation model on the Swedish stock market for the time period January 2008 to April 2012 and aims to bring clarity to the implementation process of the model. We also implement a new estimation approach for the confidence in analyst views. The portfolio of 36 companies used in the research was selected in order to benchmark against the Nordea Sverigefond. Also a Mean-Variance portfolio will be used for comparison purposes. Both a restricted and an unrestricted version of the Black-Litterman model are used in order to test differences in outcome when short selling is allowed. Results indicate that that the restricted model is more suitable than the unrestricted. However we find no significant differences in the performance of our benchmark portfolio and the Black-Litterman portfolio. We also find results that indicate longer positions in assets were the level of confidence is higher.

This thesis investigates the applicability of the Black-Litterman portfolio allocation model on the Swedish stock market for the time period January 2008 to April 2012 and aims to bring clarity to the implementation process of the model. We also implement a new estimation approach for the confidence in analyst views. The portfolio of 36 companies used in the research was selected in order to benchmark against the Nordea Sverigefond. Also a Mean-Variance portfolio will be used for comparison purposes. Both a restricted and an unrestricted version of the Black-Litterman model are used in order to test differences in outcome when short selling is allowed. Results indicate that that the restricted model is more suitable than the unrestricted. However we find no significant differences in the performance of our benchmark portfolio and the Black-Litterman portfolio. We also find results that indicate longer positions in assets were the level of confidence is higher.

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

La optimización de portafolios de inversión es un aspecto central en el mundo financiero. El modelo de Markowitz ha logrado éxito a nivel teórico en el medio de las finanzas, en cuanto a la estructuración de portafolios y en la búsqueda de la diversificación implícita en el análisis de inversiones. Sin embargo, en la práctica, se presentan dificultades e inconvenientes, que han influido notoriamente en el poco éxito de su aplicación. En este artículo se hace un estudio reflexivo sobre las desventajas de este modelo en situaciones reales, y se presenta el modelo de Black-Litterman como alternativa metodológica que contribuye a neutralizar algunas de esas desventajas y permite maximizar el rendimiento esperado, generando un portafolio más eficiente, estable y diversificado.

La optimización de portafolios de inversión es un aspecto central en el mundo financiero. El modelo de Markowitz ha logrado éxito a nivel teórico en el medio de las finanzas, en cuanto a la estructuración de portafolios y en la búsqueda de la diversificación implícita en el análisis de inversiones. Sin embargo, en la práctica, se presentan dificultades e inconvenientes, que han influido notoriamente en el poco éxito de su aplicación. En este artículo se hace un estudio reflexivo sobre las desventajas de este modelo en situaciones reales, y se presenta el modelo de Black-Litterman como alternativa metodológica que contribuye a neutralizar algunas de esas desventajas y permite maximizar el rendimiento esperado, generando un portafolio más eficiente, estable y diversificado.

La optimización de portafolios de inversión es un aspecto central en el mundo financiero. El modelo de Markowitz ha logrado éxito a nivel teórico en el medio de las finanzas, en cuanto a la estructuración de portafolios y en la búsqueda de la diversificación implícita en el análisis de inversiones. Sin embargo, en la práctica, se presentan dificultades e inconvenientes, que han influido notoriamente en el poco éxito de su aplicación. En este artículo se hace un estudio reflexivo sobre las desventajas de este modelo en situaciones reales, y se presenta el modelo de Black-Litterman como alternativa metodológica que contribuye a neutralizar algunas de esas desventajas y permite maximizar el rendimiento esperado, generando un portafolio más eficiente, estable y diversificado.

La optimización de portafolios de inversión es un aspecto central en el mundo financiero. El modelo de Markowitz ha logrado éxito a nivel teórico en el medio de las finanzas, en cuanto a la estructuración de portafolios y en la búsqueda de la diversificación implícita en el análisis de inversiones. Sin embargo, en la práctica, se presentan dificultades e inconvenientes, que han influido notoriamente en el poco éxito de su aplicación. En este artículo se hace un estudio reflexivo sobre las desventajas de este modelo en situaciones reales, y se presenta el modelo de Black-Litterman como alternativa metodológica que contribuye a neutralizar algunas de esas desventajas y permite maximizar el rendimiento esperado, generando un portafolio más eficiente, estable y diversificado.

La optimización de portafolios de inversión es un aspecto central en el mundo financiero. El modelo de Markowitz ha logrado éxito a nivel teórico en el medio de las finanzas, en cuanto a la estructuración de portafolios y en la búsqueda de la diversificación implícita en el análisis de inversiones. Sin embargo, en la práctica, se presentan dificultades e inconvenientes, que han influido notoriamente en el poco éxito de su aplicación. En este artículo se hace un estudio reflexivo sobre las desventajas de este modelo en situaciones reales, y se presenta el modelo de Black-Litterman como alternativa metodológica que contribuye a neutralizar algunas de esas desventajas y permite maximizar el rendimiento esperado, generando un portafolio más eficiente, estable y diversificado.

La optimización de portafolios de inversión es un aspecto central en el mundo financiero. El modelo de Markowitz ha logrado éxito a nivel teórico en el medio de las finanzas, en cuanto a la estructuración de portafolios y en la búsqueda de la diversificación implícita en el análisis de inversiones. Sin embargo, en la práctica, se presentan dificultades e inconvenientes, que han influido notoriamente en el poco éxito de su aplicación. En este artículo se hace un estudio reflexivo sobre las desventajas de este modelo en situaciones reales, y se presenta el modelo de Black-Litterman como alternativa metodológica que contribuye a neutralizar algunas de esas desventajas y permite maximizar el rendimiento esperado, generando un portafolio más eficiente, estable y diversificado.

La optimización de portafolios de inversión es un aspecto central en el mundo financiero. El modelo de Markowitz ha logrado éxito a nivel teórico en el medio de las finanzas, en cuanto a la estructuración de portafolios y en la búsqueda de la diversificación implícita en el análisis de inversiones. Sin embargo, en la práctica, se presentan dificultades e inconvenientes, que han influido notoriamente en el poco éxito de su aplicación. En este artículo se hace un estudio reflexivo sobre las desventajas de este modelo en situaciones reales, y se presenta el modelo de Black-Litterman como alternativa metodológica que contribuye a neutralizar algunas de esas desventajas y permite maximizar el rendimiento esperado, generando un portafolio más eficiente, estable y diversificado.

La optimización de portafolios de inversión es un aspecto central en el mundo financiero. El modelo de Markowitz ha logrado éxito a nivel teórico en el medio de las finanzas, en cuanto a la estructuración de portafolios y en la búsqueda de la diversificación implícita en el análisis de inversiones. Sin embargo, en la práctica, se presentan dificultades e inconvenientes, que han influido notoriamente en el poco éxito de su aplicación. En este artículo se hace un estudio reflexivo sobre las desventajas de este modelo en situaciones reales, y se presenta el modelo de Black-Litterman como alternativa metodológica que contribuye a neutralizar algunas de esas desventajas y permite maximizar el rendimiento esperado, generando un portafolio más eficiente, estable y diversificado.

La optimización de portafolios de inversión es un aspecto central en el mundo financiero. El modelo de Markowitz ha logrado éxito a nivel teórico en el medio de las finanzas, en cuanto a la estructuración de portafolios y en la búsqueda de la diversificación implícita en el análisis de inversiones. Sin embargo, en la práctica, se presentan dificultades e inconvenientes, que han influido notoriamente en el poco éxito de su aplicación. En este artículo se hace un estudio reflexivo sobre las desventajas de este modelo en situaciones reales, y se presenta el modelo de Black-Litterman como alternativa metodológica que contribuye a neutralizar algunas de esas desventajas y permite maximizar el rendimiento esperado, generando un portafolio más eficiente, estable y diversificado.

La optimización de portafolios de inversión es un aspecto central en el mundo financiero. El modelo de Markowitz ha logrado éxito a nivel teórico en el medio de las finanzas, en cuanto a la estructuración de portafolios y en la búsqueda de la diversificación implícita en el análisis de inversiones. Sin embargo, en la práctica, se presentan dificultades e inconvenientes, que han influido notoriamente en el poco éxito de su aplicación. En este artículo se hace un estudio reflexivo sobre las desventajas de este modelo en situaciones reales, y se presenta el modelo de Black-Litterman como alternativa metodológica que contribuye a neutralizar algunas de esas desventajas y permite maximizar el rendimiento esperado, generando un portafolio más eficiente, estable y diversificado.

La optimización de portafolios de inversión es un aspecto central en el mundo financiero. El modelo de Markowitz ha logrado éxito a nivel teórico en el medio de las finanzas, en cuanto a la estructuración de portafolios y en la búsqueda de la diversificación implícita en el análisis de inversiones. Sin embargo, en la práctica, se presentan dificultades e inconvenientes, que han influido notoriamente en el poco éxito de su aplicación. En este artículo se hace un estudio reflexivo sobre las desventajas de este modelo en situaciones reales, y se presenta el modelo de Black-Litterman como alternativa metodológica que contribuye a neutralizar algunas de esas desventajas y permite maximizar el rendimiento esperado, generando un portafolio más eficiente, estable y diversificado.

La optimización de portafolios de inversión es un aspecto central en el mundo financiero. El modelo de Markowitz ha logrado éxito a nivel teórico en el medio de las finanzas, en cuanto a la estructuración de portafolios y en la búsqueda de la diversificación implícita en el análisis de inversiones. Sin embargo, en la práctica, se presentan dificultades e inconvenientes, que han influido notoriamente en el poco éxito de su aplicación. En este artículo se hace un estudio reflexivo sobre las desventajas de este modelo en situaciones reales, y se presenta el modelo de Black-Litterman como alternativa metodológica que contribuye a neutralizar algunas de esas desventajas y permite maximizar el rendimiento esperado, generando un portafolio más eficiente, estable y diversificado.

La optimización de portafolios de inversión es un aspecto central en el mundo financiero. El modelo de Markowitz ha logrado éxito a nivel teórico en el medio de las finanzas, en cuanto a la estructuración de portafolios y en la búsqueda de la diversificación implícita en el análisis de inversiones. Sin embargo, en la práctica, se presentan dificultades e inconvenientes, que han influido notoriamente en el poco éxito de su aplicación. En este artículo se hace un estudio reflexivo sobre las desventajas de este modelo en situaciones reales, y se presenta el modelo de Black-Litterman como alternativa metodológica que contribuye a neutralizar algunas de esas desventajas y permite maximizar el rendimiento esperado, generando un portafolio más eficiente, estable y diversificado.

La optimización de portafolios de inversión es un aspecto central en el mundo financiero. El modelo de Markowitz ha logrado éxito a nivel teórico en el medio de las finanzas, en cuanto a la estructuración de portafolios y en la búsqueda de la diversificación implícita en el análisis de inversiones. Sin embargo, en la práctica, se presentan dificultades e inconvenientes, que han influido notoriamente en el poco éxito de su aplicación. En este artículo se hace un estudio reflexivo sobre las desventajas de este modelo en situaciones reales, y se presenta el modelo de Black-Litterman como alternativa metodológica que contribuye a neutralizar algunas de esas desventajas y permite maximizar el rendimiento esperado, generando un portafolio más eficiente, estable y diversificado.

La optimización de portafolios de inversión es un aspecto central en el mundo financiero. El modelo de Markowitz ha logrado éxito a nivel teórico en el medio de las finanzas, en cuanto a la estructuración de portafolios y en la búsqueda de la diversificación implícita en el análisis de inversiones. Sin embargo, en la práctica, se presentan dificultades e inconvenientes, que han influido notoriamente en el poco éxito de su aplicación. En este artículo se hace un estudio reflexivo sobre las desventajas de este modelo en situaciones reales, y se presenta el modelo de Black-Litterman como alternativa metodológica que contribuye a neutralizar algunas de esas desventajas y permite maximizar el rendimiento esperado, generando un portafolio más eficiente, estable y diversificado.

La optimización de portafolios de inversión es un aspecto central en el mundo financiero. El modelo de Markowitz ha logrado éxito a nivel teórico en el medio de las finanzas, en cuanto a la estructuración de portafolios y en la búsqueda de la diversificación implícita en el análisis de inversiones. Sin embargo, en la práctica, se presentan dificultades e inconvenientes, que han influido notoriamente en el poco éxito de su aplicación. En este artículo se hace un estudio reflexivo sobre las desventajas de este modelo en situaciones reales, y se presenta el modelo de Black-Litterman como alternativa metodológica que contribuye a neutralizar algunas de esas desventajas y permite maximizar el rendimiento esperado, generando un portafolio más eficiente, estable y diversificado.

La optimización de portafolios de inversión es un aspecto central en el mundo financiero. El modelo de Markowitz ha logrado éxito a nivel teórico en el medio de las finanzas, en cuanto a la estructuración de portafolios y en la búsqueda de la diversificación implícita en el análisis de inversiones. Sin embargo, en la práctica, se presentan dificultades e inconvenientes, que han influido notoriamente en el poco éxito de su aplicación. En este artículo se hace un estudio reflexivo sobre las desventajas de este modelo en situaciones reales, y se presenta el modelo de Black-Litterman como alternativa metodológica que contribuye a neutralizar algunas de esas desventajas y permite maximizar el rendimiento esperado, generando un portafolio más eficiente, estable y diversificado.

La optimización de portafolios de inversión es un aspecto cen-tral en el mundo financiero. El modelo de Markowitz ha logrado éxito a nivel teórico en el medio de las finanzas, en cuanto a la es-tructuración de portafolios y en la búsqueda de la diversificación implícita en el análisis de inversiones. Sin embargo, en la práctica, se presentan dificultades e inconvenientes, que han influido noto-riamente en el poco éxito de su aplicación. En este artículo se hace un estudio reflexivo sobre las desventajas de este modelo en situa-ciones reales, y se presenta el modelo de Black-Litterman como al-ternativa metodológica que contribuye a neutralizar algunas de esas desventajas y permite maximizar el rendimiento esperado, generando un portafolio más eficiente, estable y diversificado., The optimization of investment portfolios is a central aspect in the financial world. Markowitz's model has been successful on a theoretical level in the middle of finance, about the structuring of portfolios and the search of implicit diversify in the investment analysis. However, in practice, there are difficulties and disad-vantages that has been a notable influence on the limited success of its implementation. In this article is done a reflective study of the disadvantages of this model in real situations, and presents the Black-Litterman model as an alternative methodology that helps to neutralize some of these disadvantages and maximizing the expected return, generating a more efficient, stable and diversified portfolio.

La optimización de portafolios de inversión es un aspecto central en el mundo financiero. El modelo de Markowitz ha logrado éxito a nivel teórico en el medio de las finanzas, en cuanto a la estructuración de portafolios y en la búsqueda de la diversificación implícita en el análisis de inversiones. Sin embargo, en la práctica, se presentan dificultades e inconvenientes, que han influido notoriamente en el poco éxito de su aplicación. En este artículo se hace un estudio reflexivo sobre las desventajas de este modelo en situaciones reales, y se presenta el modelo de Black-Litterman como alternativa metodológica que contribuye a neutralizar algunas de esas desventajas y permite maximizar el rendimiento esperado, generando un portafolio más eficiente, estable y diversificado.