Black-Litterman är en allokeringsmodell som gör det möjligt att förena historiska avkastningar med personliga övertygelser om framtida avkastningar från en enskild investerare. Denna studie jämför två kvantitativa metoder i framtagande av felskattningen för framtida prognoser i syfte att kunna minska Black-Littermans subjektivitet. Tidigare litteratur har testat dessa metoder enskilt men aldrig ställt dem mot varandra. De metoder som undersöks använder varianser proportionella mot varianser i marknadsjämvikten, samt varianser från residualer i en faktormodel. Resultatet visar att tillämpandet av varianser framtagna av en GARCH (1,1)-modell är den metod som genererar högst avkastning, samt ger upphov till en fördelning av tillgångar som bidrar till lägst marknadskänslighet. Utifrån denna studie rekommenderas därmed tillämpningen av varianser från residualer i en faktormodel som tillägg för att minska modellens godtycklighet. / The Black-Litterman allocation model unifies historical returns with investor personal views of future returns. The study compares two quantitative methods for the estimation of uncertainty in future views with the goal to mitigate the subjectivity of the Black-Litterman model. Previous literature have investigated and tested these methods independently but a comparison has never been made between them. The two methods consist of using variances in proportion to the variances of market equilibrium and operating the residual variance of a factor model. Results show that the usage of variances estimated by a GARCH (1,1) will generate the highest average returns with an allocation distribution that contributes to least market sensitivity. Furthermore, the study recommends the implementation of variances from residuals with the addition of a factor model to diminish the subjectivity of the Black-Litterman model.

TESIS PARA OPTAR AL GRADO DE MAGISTER EN FINANZAS / Una de las labores más complicadas de un portafolio manager es sin lugar a duda la asignación eficiente de los activos de inversión que tenga bajo su administración. En un mundo que entrega un sin número de instrumentos de inversión, es primordial contar con herramientas que ayuden a tomar las mejores decisiones a la hora de invertir. Dado lo anterior este trabajo se enfocó en el estudio del modelo de Black-Littermam y su aplicación real en el Índice de precios selectivos de acciones (IPSA), dándole especial énfasis al desarrollo de las “views”. Este estudio se desarrolló desde enero del 2010 a junio de 2015. El objetivo de este trabajo fue lograr una metodología con aplicación real, que obtuviese como resultado una rentabilidad mayor al IPSA y a los principales fondos mutuos del país (para ello se consideraron los diez fondos mutuos con mayor patrimonio), cuyo foco de inversión fuera la renta variable nacional. El modelo de Black-Litterman ha tomado gran relevancia desde su creación a principios de los años 90, porque a diferencia del modelo de Markowitz, este permitió incorporar views (visiones) que tienen los inversionistas sobre un activo o sector económico en particular. Según palabras del propio Litterman, el mercado estaría en un permanente estado de equilibrio puntual, en el cual la oferta y la demanda por activos se equiparan; por tanto este equilibrio puntual puede ser comprendido como el “centro de gravedad”, del cual los mercados se desvían en todo instante, según la información que este surgiendo, pero posteriormente el mismo mercado y la información presionaran los precios para que el mercado vuelva a equilibrarse. Este equilibrio de mercado (el cual funciona como base para el modelo), es combinado con el concepto de views, permitiendo adelantarse y tomar ventajas sobre las desviaciones, antes que el mercado vuelva a su equilibrio natural. Para este trabajo se propusieron dos fuentes de información para analizar las views. Una consistente en analizar las visiones que poseen las Administradoras de Fondos de Pensión (AFPs) y otra consiste en analizar las visiones que poseen los analistas listados en bloomberg sobre empresas pertenecientes al IPSA. Los resultados de este trabajo estuvieron acordes a lo esperado, ósea se logró una metodología que pudiese tener una aplicación real y entregar una rentabilidad que estuviese sobre el mercado, además de ser una alternativa real a la estrategia buy and hold aplicada por los fondos mutuos que invierten en acciones locales.

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.

[pt] Black e Litterman propuseram um modelo de otimização de portfólio que combina visões do investidor sobre retornos esperados de ativos com o equilíbrio neutro de mercado. No entanto, especificar visões sobre uma carteira de investimentos é uma tarefa difícil, especialmente quando os investidores têm opiniões conflitantes sobre o mesmo ativo. Neste trabalho, é proposto uma nova formulação para otimização de carteiras, que é robusta diferentes à visões do investidor. A nossa abordagem foi testada em dados sintéticos e dados reais disponíveis em uma plataforma do Banco Central do Brasil. Esta plataforma consolida projeções macroeconômicas de mais de uma centena de analistas profissionais e disponibiliza para o mercado numa base semanal. Por fim, é comparado o desempenho desta formulação robusta com o modelo Black-Litterman tradicional frequentemente utilizado na indústria financeira. Os resultados mostram que a metodologia robusta pode providenciar melhor desempenho ajustado ao risco em comparação com o modelo orignial e são menos sensíveis às visões do investor. / [en] Black and Litterman proposed a portfolio optimization model that combines investor s views on future asset s returns with neutral market equilibrium. However, specifying portfolio views is a challenging task, specially when investors have conflicting opinions on the same asset. In this thesis, we suggest a new portfolio optimization formulation that is robust for investor s views. Our approach was tested on synthetic and real data available on a framework developed by Central Bank of Brazil. This online framework collects projections on main macroeconomics variables from more than a hundred professional forecasters and provides public online access on a weekly basis. The performance of this new robust formulation is compared with the traditional Black-Litterman model. The result show that our robust methodology can provide better risk adjusted performance compared to the orignial model and are less sensitive to incorrect inverstor views.

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.

[pt] Black e Litterman propuseram um modelo de seleção de portfólio que combina a visão dos investidores acerca de ativos com conceitos de equilíbrio de mercado para construir portfólios ótimos. Entretanto, a eficiência do modelo depende da qualidade da visão futura acerca do retorno dos ativos, o que é desafiador na prática. Com o objetivo de melhorar a aplicação prática do modelo Black-Litterman, o foco desse trabalho é viabilizar novas alocações com base em visões de fatores macroeconômicos que estão fora do universo de alocação. A principal vantagem é que a previsão desses fatores é amplamente fornecida por agentes de mercado. Um estudo de caso baseado nas informações disponibilizadas pelo Banco Central do Brasil é apresentado para validar a estrutura proposta. Os retornos obtidos fora da amostra e ajustados ao risco incorporando a visão de fatores macroeconômicos com a estrutura proposta superaram o modelo de média-variância tradicional e o benchmark local. / [en] Black and Litterman proposed a portfolio selection model that blends investor s views on asset returns with market equilibrium concepts to construct optimal portfolios. However, the model efficiency relies on the performance of investors views regarding tradable assets, which is challenging in practice. Focusing on improving Black-Litterman practical application, this work consists in providing new allocations based upon views on macroeconomic factors, which are largely available but not directly tradable. The main advantage is that predictions on these factors are usually provided by market players. A case study based on the information disclosed by the Brazilian Central Bank is presented to test the proposed framework. The out-of-sample risk-adjusted returns obtained incorporating the players macroeconomic expectations through the use of the proposed framework outperformed the traditional mean-variance model as well as the local 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 it in terms of potential return as well as in terms of risk adjusted return, even though its underlying theory is much simpler.

ABSTRACT PORTFOLIO SELECTION AND RETURN PERFORMANCE: An Application of the Black-Litterman Method in the Istanbul Stock Exchange Bozdemir, Mehmet Burak M.Sc, Department of Financial Mathematics Supervisor : Assist. Prof. Dr. Seza Dani

The research aims to combine various quantity models to set up a working platform that can apply to the wealth management business, including the analysis of product¡¦s return, reflection of investors' idiosyncrasy and construction of investment portfolio, building a succession of procedure hope to become the standard of the work. Regarding constructing the model, the style analysis, Black-Litterman Model and risk budget three quantitative method were adopted for three major pillars of wealth management factor model to disassemble the return of funds, allocate the assets and optimize manager structure. The materials range is from 2003 to 2007, use style analysis to disassemble the return of 115 funds that sell in Taiwan into 14 index. Incorporate investor's expectancy of market performance and suggest the assets allocation by Black-Litterman model. Join 14 index funds and 14 enhance index funds, carry on the disposition of the optimizing manager structures with the risk budget to determine the suggested fund portfolio finally. By selecting the funds with best total return in the past year forms the contrasting portfolio to compare the investment style of portfolio and characteristic of return with the models. Finding in the experience, contrasting portfolio is superior to suggested portfolio in active return only, both portfolios are similar in total return. In further consideration of the trade-off effect of return and risk in both portfolios, the suggested portfolio of the model is better than the contrasting portfolio either in IR or in Sharpe Ratio. In addition, if investors choose funds on the basis of total return, it may cause the style of whole portfolio too centralized throw the total risk in high level.

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.