Black-Litterman Research Articles

Intelligent portfolio construction via news sentiment analysis

In this study, we apply deep learning and natural language processing methods to construct the view distribution in the Black–Litterman model. We implement this approach for portfolio allocation and perform statistical analysis to assess portfolio performance. The empirical analysis yields two main results. For the three deep learning models, we use mean square error to compare the model prediction results. The gated recurrent unit (GRU) model outperforms the other two models in the price prediction of seven stock assets. Moreover, it is more effective in capturing future trends and stock prices. The long short-term memory (LSTM) model outperforms the recurrent neural network (RNN) model. Moreover, in the comparison of the portfolio models, the Black–Litterman model, constructed by using Google’s Bidirectional Encoder Representations from Transformers (BERT) to measure news sentiment and by using the GRU model to predict stock prices, yields the highest annualized return rate of 46.6%. In addition, it has the highest Sharpe and Sortino ratios of 13.0% and 17.9%, respectively, which means that under a certain degree of risk, the Black–Litterman model still outperforms other constructed portfolios.

View Fusion Vis-à-Vis a Bayesian Interpretation of Black–Litterman for Portfolio Allocation

The Black–Litterman model extends the framework of the Markowitz modern portfolio theory to incorporate investor views. The authors consider a case in which multiple view estimates, including uncertainties, are given for the same underlying subset of assets at a point in time. This motivates their consideration of data fusion techniques for combining information from multiple sources. In particular, they consider consistency-based methods that yield fused view and uncertainty pairs; such methods are not common to the quantitative finance literature. They show a relevant, modern case of incorporating machine learning model-derived view and uncertainty estimates, and the impact on portfolio allocation, with an example subsuming arbitrage pricing theory. Hence, they show the value of the Black–Litterman model in combination with information fusion and artificial intelligence–grounded prediction methods.

Risk‐return optimised energy asset allocation in transmission‐distribution system using tangency portfolio and Black–Litterman model

AbstractThe application of Markowitz and tangency portfolio and Black–Litterman models is extended by the authors to energy portfolio selection in transmission‐distribution environments with high penetration of renewable energy. As Transmission System Operator (TSO) and Distribution System Operator (DSO) contextually take mutualistic or conflicting positions in their portfolio selection process, their risk‐return interactions and behaviours depend on their subjective views on generation and operation. Here, the financial portfolio allocation tool Black–Litterman Model is adapted to incorporate subjective views of the operators to arrive at more intuitive portfolios. The best portfolios are searched within the acceptable risk‐return search space of each operator defined by their Markowitz efficient frontiers (EF), for Pareto‐optimising their profits. The tangency portfolio approach, which is generally used to determine the portfolio of risky and risk‐free assets in finance, is used here to determine the portfolio of renewable (energy‐risky) and fuel‐based sources (energy‐risk‐free). The proposed methodology is adopted in an HV–MV interconnected test system operated by one TSO and two DSOs, having wind, solar, coal, gas and nuclear generation technologies. It is observed that completely customisable portfolios can be constructed for TSO and DSO based on their inherent financial and energy risk‐return behaviours and posterior views.

The optimal portfolio of islamic stocks using the markowitz and black-litterman models

The portfolio with the best combination of profit and risk or the investor's choice is called the optimal portfolio. The Black-Litterman and Markowitz models were used to determine the optimal portfolio during the covid-19 pandemic. Sharia stock data, that is consistent with the Jakarta Islamic Index for the 2019-2021 period, is used in this research. The stock combination of the Markowitz model is better than the Black-Litterman model. The expected value of the portfolio obtained is 0.0066, which is greater than the risk-free asset return of 0.0011 on the day of broadcast. The portfolio risk of the Markowitz model is smaller than the Black-Litterman model, which are 0.0010972 and 0.0013917, respectively. so it can be said that the Markowitz model is better than the Black-Litterman model in the formation of a Sharia stock portfolio during the covid-19 pandemic.

Diversification with international assets and cryptocurrencies using Black-Litterman

PurposeThe aim of the study was to analyze the performance of Black-Litterman (BL) portfolios using a views estimation procedure that simulates investor forecasts based on technical analysis.Design/methodology/approachIbovespa, S&P500, Bitcoin and interbank deposit rate (IDR) indexes were respectively considered proxies for the national, international, cryptocurrency and fixed income stock markets. Forecasts were made out of the sample aiming at incorporating them in the BL model, using several portfolio weighting methods from June 13, 2013 to August 30, 2022.FindingsThe Sharpe, Treynor and Omega ratios point out that the proposed model, considering only variable return assets, generates portfolios with performances superior to their traditionally calculated counterparts, with emphasis on the risk parity portfolio. Nonetheless, the inclusion of the IDR leads to performance losses, especially in scenarios with lower risk tolerance. And finally, given the impact of turnover, the naive portfolio was also detected as a viable alternative.Practical implicationsThe results obtained can contribute to improve investors practices, specifically by validating both the performance improvement – when including foreign assets and cryptocurrencies –, and the application of the BL model for asset pricing.Originality/valueThe main contributions of the study are: performance analysis incorporating cryptocurrencies and international assets in an uncertain recent period; the use of a methodology to compute the views simulating the behavior of managers using technical analysis; and comparing the performance of portfolio management strategies based on the BL model, taking into account different levels of risk and uncertainty.

Asset allocation based on LSTM and the Black–Litterman model

ABSTRACT We propose a novel ranking-based approach combined with long short-term memory (LSTM) networks to generate investor views in the well-known Black – Litterman (BL) model. This approach can effectively distinguish high-quality assets with the potential for future growth. In addition, it discards any information contained in the absolute differences between asset prices to mitigate the negative impact of these estimation errors on the BL model. Our findings suggest that the BL model based on our approach can achieve better out-of-sample performance.

A Novel Black-Litterman Model with Time-Varying Covariance for Optimal Asset Allocation of Pension Funds

The allocation of pension funds has important theoretical value and practical significance, which improves the level of pension investment income, achieves the maintenance and appreciation of pension funds, and resolves the pension payment risk caused by population aging. The asset allocation of pension funds is a long-term asset allocation problem. Thus, the long-term risk and return of the assets need to be estimated. The covariance matrix is usually adopted to measure the risk of the assets, while calculating the long-term covariance matrix is extremely difficult. Direct calculations suffer from the insufficiency of historical data, and indirect calculations accumulate short-term covariance, which suffers from the dynamic changes of the covariance matrix. Since the returns of main assets are highly autocorrelated, the covariance matrix of main asset returns is time-varying with dramatic dynamic changes, and the errors of indirect calculation cannot be ignored. In this paper, we propose a novel Black–Litterman model with time-varying covariance (TVC-BL) for the optimal asset allocation of pension funds to address the time-varying nature of asset returns and risks. Firstly, the return on assets (ROA) and the covariance of ROA are modeled by VARMA and GARCH, respectively. Secondly, the time-varying covariance estimation of ROA is obtained by introducing an effective transformation of the covariance matrix from short-term to long-term. Finally, the asset allocation decision of pension funds is achieved by the TVC-BL model. The results indicate that the proposed TVC-BL pension asset allocation model outperforms the traditional BL model. When the risk aversion coefficient is 1, 1.5, and 3, the Sharp ratio of pension asset allocation through the TVC-BL pension asset allocation model is 13.0%, 10.5%, and 12.8% higher than that of the traditional BL model. It helps to improve the long-term investment returns of pension funds, realize the preservation and appreciation of pension funds, and resolve the pension payment risks caused by the aging of the population.

USE OF THE BLACK-LITTERMAN MODEL IN PORTFOLIO OPTIMIZATION FOR ACTIVE INVESTORS ON STOCKS IN LQ45 INDEX

In these modern era, it is very easy to create an investment portfolio, an investment portfolio can be formed by buying a shares. By creating portfolio investation, our can expect score return which makes it an advantage. However, there is also a risk value that will be obtained when buy shares. In the formation of an investment portfolio for active investors, it is expected to create an optimal investment portfolio, there are many models that can be used to create an optimal investment portfolio. In this final project, will discusses the use of the Black-Litterman Model in optimizing portfolios for active investors. The Black-Litterman model is one of the models that can be used to optimize the investment portfolio, the Black-Litterman model provides additional information for the return and risk values based on the views of experts. This model builds on the MV and CAPM using a Bayesian framework that allows investors to effectively incorporate their views of the market into the allocation process asset. Based on several tests that have been carried out during the research with different days, the value of the investor's view will always be different every day, the value of an optimistic view will have a good impact on the stock, even though the stock price is falling, if the investor's view is expressed optimism, the weight of the shares will remain high.

REDESIGNING USER INTERFACE OF TEMAN BUS APPLICATION USING GOAL-DIRECTED DESIGN

In these modern era, it is very easy to create an investment portfolio, an investment portfolio can be formed by buying a shares. By creating portfolio investation, our can expect score return which makes it an advantage. However, there is also a risk value that will be obtained when buy shares. In the formation of an investment portfolio for active investors, it is expected to create an optimal investment portfolio, there are many models that can be used to create an optimal investment portfolio. In this final project, will discusses the use of the Black-Litterman Model in optimizing portfolios for active investors. The Black-Litterman model is one of the models that can be used to optimize the investment portfolio, the Black-Litterman model provides additional information for the return and risk values based on the views of experts. This model builds on the MV and CAPM using a Bayesian framework that allows investors to effectively incorporate their views of the market into the allocation process asset. Based on several tests that have been carried out during the research with different days, the value of the investor's view will always be different every day, the value of an optimistic view will have a good impact on the stock, even though the stock price is falling, if the investor's view is expressed optimism, the weight of the shares will remain high.

Research on Optimization Strategy of Quantitative Investment Scheme Based on Black-Litterman Model

In today's trading market, for every investor, they want to obtain a higher rate of return within their own controllable risks. And how to obtain a maximum yield is undoubtedly a complex and difficult challenge. In order to help investors obtain a higher return in gold and bitcoin investment, we have integrated XGBoost, ESN, Black-Litterman and other models to establish a more optimized quantitative investment plan. Task 1: For the model, first use the optimized XGBoost-ESN model to predict the prices of gold and Bitcoin on the second day, and then use the Black-Litterman model to help investors make more accurate quantitative investments. From the initial $1,000 to the final $20,278.14, the annualized rate of return: 82.56%. Task 2: In order to predict the accuracy of the price, we use two different price prediction methods for prediction. The weights of the two are determined by the least squares method, and the optimized model is obtained. And in order to understand that our investment cycle is the optimal solution, we used different trading cycles of 5 days, 15 days, and 30 days for gold and Bitcoin to conduct a single-variable comparison test, and obtained different optimal transactions between the two cycle. Task 3: We conduct a dynamic analysis of transaction costs, and determine the optimal transaction cost range for gold and Bitcoin by understanding different transaction costs. Task 4: Since different investors have different risk acceptance levels, we have added var risk prediction content. In order to reduce the loss of income, we set a profit and loss line to ensure the safety of funds. Finally, we discuss the problems that may arise in the process of practical application of the model, and use the validity test to verify the validity of the established model. In addition, we provide a reasonable evaluation of the strengths and weaknesses of the model.

Asymmetric Asset Allocation by a Black-Litterman Model

Asymmetric Asset Allocation by a Black-Litterman Model

The impact of global economic policy uncertainty on portfolio optimization: A Black–Litterman approach

This paper investigates the asymmetric impact of global economic policy uncertainty (GEPU) on global asset allocation. We employ the Double Asymmetric GARCH-MIDAS (DAGM) model to examine the asymmetric effect of GEPU shocks on long-term volatilities of global equities, bonds, commodities, clean energy and Bitcoin. The GEPU-based volatility is used as a proxy for the uncertainty of the investor’s views in the Black-Litterman (BL) framework. Empirical results show that the BL model with GEPU-based views yields higher out-of-sample risk-adjusted returns than other traditional benchmarks in most cases. The findings suggest that investors should consider the influence of GEPU when making portfolio decisions.

Fuzzy incorporated Black–Litterman model for renewable energy portfolio optimization

Fuzzy incorporated Black–Litterman model for renewable energy portfolio optimization

Black-Litterman model with copula-based views in mean-CVaR portfolio optimization framework with weight constraints

This study examines the portfolio optimization problem by exploiting daily data of 10 international Exchange Trade Funds (ETF) from 2012 to 2022. We extend the Black-Litterman (BL) approach using ARMA-GARCH-copula-based expected returns as a proxy for investor views and use the CVaR metric as a risk measure in the optimization procedure. The BL approach provides a Bayesian methodology for combining the equilibrium returns and the investor views to produce expected returns. We use Regular Vine (R-vine) copula since it provides a flexible multivariate dependency modeling. The suggested approach is compared against the copula-CVaR portfolio, which likewise a BL copula approach avoids excessive corner solutions that many optimization approaches would generate in case of extreme values of estimated parameters. We compare the performance of these two approaches using out-of-sample back-testing against two benchmarks: Mean–Variance optimizations (MV) and equal weights portfolio (EW). To further reduce the sensitivity of considered strategies to input parameters, we evaluate out-of-sample performance at three levels of maximum weight constraints: 30%, 40%, and 50%. Moreover, in this paper, we consider different levels of view confidence—τ in the Black-Litterman model as it significantly affects the obtained results and inferences. We calculate and report the portfolios’ tail risks, maximum drawdown, turnover, and the break-even point for all optimization approaches. Our empirical analysis indicates better performance for the CBL portfolio regarding lower tail risk and higher risk-adjusted returns, and the copula-CVaR portfolio is better regarding lower turnover and higher break-even point.

Integrating Zakat and Purification in a Modified Black–Litterman Model for Shariah-Compliant Stock Portfolios

Many articles demonstrate the advantages of applying Shariah principles in economic and financial activities, which motivates model development for Shariah investment. The development of the capital asset pricing model (CAPM) and mean-variance (MV) for Shariah portfolios shows various efforts within a Shariah framework. But the MV model has diversification weaknesses, and the Black–Litterman (BL) model solves this problem. According to Islamic principles, the CAPM’s use in the BL model is problematic due to the risk-free rate. This study aims to introduce a modified BL model adapted to Islamic principles. We propose a modified BL model with a Shariah-compliant asset pricing model (SCAPM) that considers the zakat obligation and purification rate to develop the model with Islamic principles. The proposed model was implemented in the Indonesian stock market. A portfolio’s Sharpe ratio using the BL-SCAPM outperforms BL-CAPM. This finding supports the idea that the modified BL model can be applied as a new alternative for a Sharia portfolio model.

Intelligent Black–Litterman Portfolio Optimization Using a Decomposition-Based Multi-Objective DIRECT Algorithm

It is agreed that portfolio optimization is of great importance for the financial market. However, input sensitivity and highly-concentrated portfolios have posed a challenge. In this paper, a random forest-based Black–Litterman model is developed, aiming to further enhance the portfolio performance, which adopts a novel method for generating investor views on the basis of random forests. More specifically, the view vector is generated based on the predicted asset returns obtained by random forests, and the confidence matrix which contains the uncertainty of each view is measured by the difference in the predicted values of multiple trees. Furthermore, motivated by decomposition strategy, a novel multi-objective DIRECT algorithm is introduced to effectively resolve the proposed model. Through the construction of a unique indicator, the algorithm possesses the capacity to select potentially-optimal hyperrectangles in all reference directions simultaneously, which will further improve the exploratory nature. Experimental results have demonstrated that the proposed algorithm achieves a better performance over NSGA-II and MOEA/D on the MOP and DTLZ benchmark problems. It is also experimentally verified that the random forest-based Black–Litterman model can obtain higher cumulative returns and Sharpe ratios in the application of Chinese stock markets when compared to the classic MV model.

Dynamic Black Litterman portfolios with views derived via CNN-BiLSTM predictions

We use daily price and technical indicators' data for the ten MSCI Asia Pacific sector indices for the past 20 years and find that our hybrid multivariate Convolutional Neural Network - Bidirectional Long Short-Term Memory (CNN-BiLSTM) deep learning model gives reasonably better predictions when predicting index closing prices out-of-sample than using either CNN or BiLSTM alone. After utilizing these predictions as investor views inside the Black-Litterman model with time variation in the conditional distribution of returns, we find that the portfolios generated outperform all benchmark model portfolios by a considerable margin in terms of financial efficiency and diversification.

On the Black–Litterman Model: Learning to Do Better

In this article, the authors study the performance of the Black–Litterman model (BLM) and compare it to the traditional mean–variance theory (MVT) of Markowitz (1952) and Sharpe (1964). They begin with the standard Bayesian learning on which the BLM is based (but the existing literature does not follow). Then, they perform a series of tests of the BLM using machine learning tools and view specifications consistent with the existing literature. Their empirical evidence (which uses 30 years of monthly data from January 1991 till December 2020) suggests that the BLM is highly sensitive to the specification of the view. Given that the view is arbitrary (even though in our article, they are rule based), it is quite a challenge to use the BLM in an actual situation. A great amount of caution must be exercised in specifying the view and its corresponding required return. This validates the previous result that BLM specification of views is very important and there is no consistent manner how one can specify a winning portfolio.

INVESTIGATION OF GENDER DIFFERENCES IN FAMILIAR PORTFOLIO CHOICE

The prevailing assumption holds that investors include in their portfolios securities that they know well, are located near their place of residence, or align with their fields of interest. This article analyse familiarity in investment through gender perspective and their fields of interest. Women and men field of interest is defined by enabling online magazines’ article’s themes. The aim of this paper is to investigate gender-based behavioural differences in investment decisions – i.e. to define women’s and men’s fields of interests and value investment portfolios. Portfolios differ according to whether they are formed from securities that are consistent with women’s fields of interest, men’s fields of interest or both women’s and men’s fields of interest. Textual analysis was employed to identify men’s and women’s fields of interest. Investment portfolios were built using mean variance (MV) and Black–Litterman (BL) models. The analysis revealed that portfolios built from men’s fields of interests are more diversified than are portfolios built either from women’s fields of interests or from both men’s and women’s fields of interest. Analysing 12 portfolios’ efficiency revealed that women’s portfolio returns are more stable than are men’s. Moreover, the study demonstrated that time impacts investment portfolio returns to a greater extent than do gendered fields of interest. The article complements the existing knowledge about bias in investor familiarity, which results from differences in men’s and women’s fields of interest.

Exploiting the Black-Litterman framework through error-correction neural networks

The Black-Litterman (BL) model is a particularly essential analytical tool for effective portfolio management in financial services sector since it enables investment analysts to integrate investor views into market equilibrium returns. In this research, we define and study the continuous-time BL portfolio optimization (CTBLPO) problem as a time-varying quadratic programming (TVQP) problem. The investor’s views in the CTBLPO problem are regarded as a forecasting problem, and they are generated by a novel neural network (NN) model. More precisely, employing a novel multi-function activated by a weights-and-structure-determination for time-series (MAWTS) algorithm, a 3-layer feed-forward NN model, called MAWTSNN, is proposed for handling time-series modeling and forecasting problems. Then, using real-world datasets, the CTBLPO problem is approached by two different TVQP NN solvers. These solvers are the zeroing NN (ZNN) and the linear-variational-inequality primal–dual NN (LVI-PDNN). The experiment findings illustrate and compare the performances of the ZNN and LVI-PDNN in three various portfolio configurations, as well as indicating that the MAWTSNN is an excellent alternative to the traditional approaches. To promote and contend the outcomes of this research, we created two MATLAB repositories for the interested user, that are publicly accessible on GitHub.