Modern portfolio theory has its attractive characteristics of promoting diversification in a portfolio and can be seen as an easy alternative for setting optimal weights for portfolio managers. Furthermore, as portfolio managers try to beat a defined benchmark for their portfolio the Black-Litterman model allows them to include their own prospects on the future return of markets and securities. This thesis examines how the practical use of the Black-Litterman model can affect portfolios' performance. The analysis was done by calculating historical portfolio weights with investor views, without investor views, and with perfect investor views in the Black-Litterman model. Thereafter, calculating historical return and volatility for six multi-asset portfolios between 2017-09-25 and 2021-01-31. This was then compared with benchmark portfolios, which reflect the practical use. These portfolios included historically used investor views and constraints in the mean-variance optimization. The results showed that investor views had a negative effect on total return (lower return) and a positive effect on volatility (lower risk), however, an increased Sharpe ratio. The constraints in the mean-variance optimization used in the benchmark portfolios resulted in a lower total return. In conclusion, the Black-Litterman model showed robustness and did not generate unintuitive or unreasonable portfolios, and it has great potential with increasing accuracy in the investor views. / Modern portföljteori har attraktiva egenskaper vad gäller att främja diversifiering i en portfölj och kan ses som ett enkelt alternativ för att välja optimala vikter för portföljförvaltare. Eftersom portföljförvaltare försöker slå ett definierat benchmark för sin portfölj tillåter dessutom Black-Litterman modellen dem att inkludera sina egna åsikter angående förväntade avkastningar på marknader och värdepapper. Detta examensarbete undersöker hur den praktiska användningen av Black-Litterman modellen kan påverka portföljernas prestation. Analysen gjordes genom att beräkna historiska portföljvikter med Black-Litterman modellen med och utan invetserarens egna åsikter angående förväntade avkastningar, och med perfekta förväntade avkastningar. Därefter beräknades historiska avkastningar och volatiliteter för sex investeringsportföljer mellan 2017-09-25 och 2020-01-31. Detta jämfördes med benchmarkportföljer, vilka återspeglade den praktiska användningen. Dessa portföljer inkluderade historiskt använda förväntade avkastningar och restriktioner i mean-variance optimeringen. Resultaten visade att investerares åsikter angående förväntade avkastningar hade en negativ effekt på avkastningen (lägre avkastning), positiv effekt på volatiliteten (lägre risk), vilket resulterade i en högre Sharpe kvot. Restriktionerna i mean-variance optimeringen som användes i benchmarkportföjerna resulterade i en lägre totalavkastning. Sammanfattningsvis visade Black-Litterman modellen robusthet och genererade inte ointuitiva eller olämpliga portföljer, och modellen har stor potential med ökad träffsäkerhet i investerarens åsikter angående förväntade avkastningar.

This paper consolidates and compares the applicability and practicality of Black-Litterman model versus traditional Markowitz Mean-Variance model. Although well-known model such as Mean-Variance is academically sound and popular, it is rarely used among asset managers due to its deficiencies. To put the discussion into context we shed light on the improvement made by Fisher Black and Robert Litterman by putting the performance and practicality of both Black- Litterman and Markowitz Mean-Variance models into test. We will illustrate detailed mathematical derivations of how the models are constructed and bring clarity and profound understanding of the intuition behind the models. We generate two different portfolios, composing data from 10-Swedish equities over the course of 10-year period and respectively select 30-days Swedish Treasury Bill as a risk-free rate. The resulting portfolios orientate our discussion towards the better comparison of the performance and applicability of these two models and we will theoretically and geometrically illustrate the differences. Finally, based on extracted results of the performance of both models we demonstrate the superiority and practicality of Black-Litterman model, which in our particular case outperform traditional Mean- Variance model.

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.

<p>The financial portfolio model often referred to as the Black-Litterman model is analyzed using two approaches; a mathematical and a behavioral finance approach. After a detailed description of its framework, the Black-Litterman model is derived mathematically using a sampling theoretical approach. This approach generates a new interpretation of the model and gives an interpretable formula for the mystical parameter<b> τ</b>, the weight-on-views. Secondly, implications are drawn from research results within behavioral finance. One of the most interesting features of the Black-Litterman model is that the benchmark portfolio, against which the performance of the portfolio manager is evaluated, functions as the point of reference. According to behavioral finance, the actual utility function of the investor is reference-based and investors estimate losses and gains in relation to this benchmark. Implications drawn from research results within behavioral finance indicate and explain why the portfolio output given by the Black-Litterman model appears more intuitive to fund managers than portfolios generated by the Markowitz model. Another feature of the Black-Litterman model is that the user assigns levels of confidence to each asset view in the form of confidence intervals. Research results within behavioral finance have, however, shown that people tend to be badly calibrated when estimating their levels of confidence. Research has shown that people are overconfident in financial decision-making, particularly when stating confidence intervals. This is problematic. For a deeper understanding of the use of the Black-Litterman model it seems that we should turn to those financial fields in which social and organizational context and issues are taken into consideration, to generate better knowledge of the use of the Black-Litterman model.</p>

The financial portfolio model often referred to as the Black-Litterman model is analyzed using two approaches; a mathematical and a behavioral finance approach. After a detailed description of its framework, the Black-Litterman model is derived mathematically using a sampling theoretical approach. This approach generates a new interpretation of the model and gives an interpretable formula for the mystical parameter τ, the weight-on-views. Secondly, implications are drawn from research results within behavioral finance. One of the most interesting features of the Black-Litterman model is that the benchmark portfolio, against which the performance of the portfolio manager is evaluated, functions as the point of reference. According to behavioral finance, the actual utility function of the investor is reference-based and investors estimate losses and gains in relation to this benchmark. Implications drawn from research results within behavioral finance indicate and explain why the portfolio output given by the Black-Litterman model appears more intuitive to fund managers than portfolios generated by the Markowitz model. Another feature of the Black-Litterman model is that the user assigns levels of confidence to each asset view in the form of confidence intervals. Research results within behavioral finance have, however, shown that people tend to be badly calibrated when estimating their levels of confidence. Research has shown that people are overconfident in financial decision-making, particularly when stating confidence intervals. This is problematic. For a deeper understanding of the use of the Black-Litterman model it seems that we should turn to those financial fields in which social and organizational context and issues are taken into consideration, to generate better knowledge of the use of the Black-Litterman model. / QC 20101119

本篇論文主要是將Black-Litterman模型應用在組合型基金上。從一個組合型基金的基金經理人角度出發，在有限的風險下，如何進行資產配置使其達到報酬極大化的目標？第二章介紹mean-variance模型，以及其模型之缺點。第三章介紹Black-Litterman模型，其不僅可以改善mean-variace模型的缺點，此外允許投資人加入主觀看法，結合數量方法以及投資人的主觀看法是此模型的特色之一。第四章，針對兩個模型的進行比較。最後，我們發現：BLack-Litterman模型不僅符合經濟直覺，進行資產配置時也展現模型的穩定性。 / This paper applies a popular asset allocation model: the Black-Litterman model on a fund of funds. First, an overview is given of the foundations of modern portfolio theory with the mean-variance model. Next, we discuss some improvements that could be made over the mean-variance model. The Black-Litterman model addresses some of these flaws and tries to improve them. Finally, simulation has been performed to compare the performance of the Black-Litterman model to mean-variance optimization. The models have been compared in intuitiveness and stability. The conclusion can be drawn that BL-model improves the mean-variance model, in our simulation, both in intuitiveness and stability.

[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.

[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.

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

Submitted by EDISON AMERICO HUARSAYA TITO (edison.tito@gmail.com) on 2016-06-23T14:02:55Z No. of bitstreams: 1 EdisonMscFGV(20160619).pdf: 2366030 bytes, checksum: 231be2cde1e7f8e01331fddff3f227a1 (MD5) / Approved for entry into archive by GILSON ROCHA MIRANDA (gilson.miranda@fgv.br) on 2016-06-23T14:36:07Z (GMT) No. of bitstreams: 1 EdisonMscFGV(20160619).pdf: 2366030 bytes, checksum: 231be2cde1e7f8e01331fddff3f227a1 (MD5) / Approved for entry into archive by GILSON ROCHA MIRANDA (gilson.miranda@fgv.br) on 2016-06-24T12:51:11Z (GMT) No. of bitstreams: 1 EdisonMscFGV(20160619).pdf: 2366030 bytes, checksum: 231be2cde1e7f8e01331fddff3f227a1 (MD5) / Made available in DSpace on 2016-06-29T12:06:48Z (GMT). No. of bitstreams: 1 EdisonMscFGV(20160619).pdf: 2366030 bytes, checksum: 231be2cde1e7f8e01331fddff3f227a1 (MD5) Previous issue date: 2016-06-03 / This work has the objective to address the problem of asset allocation (portfolio analysis) under a Bayesian perspective. For this it was necessary to review all the theoretical analysis of the classical mean-variance model and following identify their deficiencies that compromise its effectiveness in real cases. Interestingly, its biggest deficiency this not related to the model itself, but by its input data in particular the expected return calculated on historical data. To overcome this deficiency the Bayesian approach (Black-Litterman model) treat the expected return as a random variable and after that builds a priori distribution (based on the CAPM model) and a likelihood distribution (based on market investor’s views) to finally apply Bayes theorem resulting in the posterior distribution. The expected value of the return of this posteriori distribution is to replace the estimated expected return calculated on historical data. The results showed that the Bayesian model presents conservative and intuitive results in relation to the classical model of mean-variance. / Este trabalho tem com objetivo abordar o problema de alocação de ativos (análise de portfólio) sob uma ótica Bayesiana. Para isto foi necessário revisar toda a análise teórica do modelo clássico de média-variância e na sequencia identificar suas deficiências que comprometem sua eficácia em casos reais. Curiosamente, sua maior deficiência não esta relacionado com o próprio modelo e sim pelos seus dados de entrada em especial ao retorno esperado calculado com dados históricos. Para superar esta deficiência a abordagem Bayesiana (modelo de Black-Litterman) trata o retorno esperado como uma variável aleatória e na sequência constrói uma distribuição a priori (baseado no modelo de CAPM) e uma distribuição de verossimilhança (baseado na visão de mercado sob a ótica do investidor) para finalmente aplicar o teorema de Bayes tendo como resultado a distribuição a posteriori. O novo valor esperado do retorno, que emerge da distribuição a posteriori, é que substituirá a estimativa anterior do retorno esperado calculado com dados históricos. Os resultados obtidos mostraram que o modelo Bayesiano apresenta resultados conservadores e intuitivos em relação ao modelo clássico de média-variância.