Black-Litterman Research Articles

Using Markov-Switching Models in US Stocks Optimal Portfolio Selection in a Black–Litterman Context (Part 1)

In this study, we tested the benefit of using Markov-Switching (M-S) models to forecast the views of the 26 most traded stocks in the US in a Black–Litterman (B–L) optimal selection context. With weekly historical data of these stocks from 1 January 1980, we estimated and simulated (from 7 January 2000, to 7 February 2022) three portfolios that used M-S views in each stock and blended them with the market equilibrium views in a B–L context. Our position was that the B–L optimal portfolios could generate alpha (extra return) against a buy-and-hold and an actively managed portfolio with sample portfolio parameters (à la Markowitz, SampP). Our results suggest that the outperformance of the B–L managed portfolios holds only in the short term. In the long-term, the performance of the B–L portfolios, the SampP, and the market portfolio are statistically equal in terms of returns or their mean–variance efficiency in an ex-ante or ex-post analysis.

Searching for higher-performance, income-generating assets: a mutual fund assessment on asset-backed securities

PurposeIn the search for alternative income-generating assets, the paper addresses the following question, one that the literature has yet to answer: what is a reasonable allocation, if any, to asset-backed securities within a 60–40% stock-bond balanced portfolio of mutual funds?Design/methodology/approach The authors apply the Black–Litterman model of Modern Portfolio Theory to test the efficacy of adding asset-backed securities to the classic 60–40% stock-bond portfolio of mutual funds. The authors use out-of-sample tests of one, three, five, and ten years to determine a reasonable asset allocation. The data are monthly and range from January 2000 through September 2021.FindingsThe statistical evidence indicates a modest reward-risk added value from the addition of asset-backed securities, as measured by the Sharpe “reward-to-variability” ratio, in holding periods of three, five, and ten years. Based on the findings, the authors conclude that a reasonable asset allocation for income-seeking, risk-averse investors who follow the classic 60%–40% stock-bond allocation is 8%–10%.Research limitations/implicationsThe findings apply to a stock-bond balanced portfolio of mutual funds. Other fund combinations could produce different results.Practical implicationsInvestors and money managers can use the findings to improve portfolio performance.Originality/valueFor investors seeking higher income-generating securities in the current record-low interest rate environment, the authors determine a reasonable asset allocation range on asset-backed securities. This study is the first to provide such direction to these investors.

Analisis Sensitivitas Model Black-Litterman Menggunakan Treynor Ratio pada Portofolio Saham

Investment is an activity that can not separate from return and risk, so that forming portfolio is important to risk minimizing and profit optimizing. One of way to optimizing portfolio is using Black-Litterman model. This model is model that combine equilibrium return by CAPM eith investor’s views about return an asset. Purpose of this research are to form Black-Litterman model with tau calibration and measure the best portfolio performance with treynor ratio. This research used secondary data stock in LQ-45 index during August 2019-January 2020. Selecting portfolio by selecting high return expected CAPM are CPIN, WIKA, ADRO and CTRI. Forming portfolio using Black-Litterman model by calibration so obtain the best measure performance by Treynor Ratio are 0,12142 with =1 and potfolio return 0,26445

Toward the Black–Litterman with Shariah-compliant asset pricing model: a case study on the Indonesian stock market during the COVID-19 pandemic

Purpose This research aims to demonstrate portfolio modeling, which leads to Sharia compliance in encountering crises because of COVID-19. The authors proposed modifying the Black–Litterman (BL) model adapted to the Sharia principle. The implementation of BL on Shariah-compliant stock data with capital asset pricing model (CAPM) requires adjustment because of the interest rate in the calculation. Thus, the objective of this study is to develop and evaluate the modified BL for Shariah-compliant stock portfolios in the financial crisis caused by the COVID-19 pandemic. Design/methodology/approach The Sharia-compliant asset pricing model (SCAPM) with the inflation rate was regarded as the new starting point in the BL model. This proposed model was implemented in Indonesia using monthly returns from the Jakarta Islamic Index (JII) list collected from February 2014 to June 2019. Furthermore, the portfolio performance of BL-SCAPM was compared with two reference portfolios, the mean-variance method and BL-CAPM. Findings The result presents that the portfolio performance of BL-SCAPM outperformed the MV and BL-CAPM. The impact of the Sharpe ratio of BL-SCAPM was more significant than the reference portfolio. The equal benefit was procured from both portfolios in July and August 2019. After the COVID-19 outbreak was officially declared in January 2020, the performance of BL-SCAPM was still above the BL. Despite a decline in portfolio value before and during the outbreak, the reference portfolio losses were higher than those of BL-SCAPM. Hence, this study manifested that BL-SCAPM outperformed the reference portfolio. Practical implications The results illustrate the empirical study which can be implemented for the Shariah-compliant stock market in Indonesia. By evaluating portfolio value on the COVID crisis for long investment, replacing CAPM with SCAPM in the BL model can transform the asset proportion. It decreased the portfolio loss during the crisis. Future research can be developed more from the open problems in this implementation to deliver the portfolio model into the Shariah framework with varied SCAPM in BL. Originality/value The attention to BL studies on portfolio building with Sharia-compliant stocks is rarely focused on the Islamic perspective. Hence, the novelty of this research is the idea of modifying the BL model with a Shariah starting point. More generally, this research enriches Shariah financial literacy regarding the stock market and, specifically, its implementation in the Indonesian stock market.

The diversification benefits of cryptocurrency asset categories and estimation risk: pre and post Covid-19

We examine the diversification benefits of cryptocurrency asset categories. To mitigate the effects of estimation risk, we employ the Bayes-Stein model with no short-selling and variance-based constraints. We estimate the inputs using lasso regression and elastic net regression, employing the shrunk Wishart stochastic volatility model and Gaussian random projection. We consider nine cryptocurrency asset categories, and find that all but two provide significant out-of-sample diversification benefits. The lower is investor risk aversion, the more beneficial are cryptocurrencies as portfolio diversifiers. During uncertain economic environments, such as the post-Covid-19 period, cryptocurrencies provide the same diversification benefits as in more stable environments. Our results are robust to different portfolio benchmarks, regression technique, transaction cost, portfolio constraints, higher moments and Black–Litterman models.

Research on Black-Litterman Index Enhancement Strategy——Based on the Ledoit-Wolf Compression Estimation Method to Optimize the CSI 500 Index Enhancement Strategy

Financial risks may often lead to significant losses. A reasonable capital management model can prevent financial risks and enhance financial services to the real economy. The Black-Litterman model can reduce risks through asset allocation. This paper uses the Black-Litterman model to construct an enhanced strategy applied to the CSI 500 Index, and selects the backtest from December 1, 2019 to December 1, 2021. Through the strategy backtest, it can be found that: whether it is considered or not Transaction costs, using analysts’ consensus target price as the input point of view of the BL model, can provide excess returns for the index enhancement strategy under relatively stable conditions within the sample interval, and improve the sharpness ratio, information ratio, maximum drawdown, etc. Within the risk-return parameters. 
 
 In order to solve the problem of model instability and extreme values of configuration weights in the first step, this paper adjusts the covariance based on the Leodit-wolf compression estimation, thereby optimizing the exponential enhancement model. The backtest results showed that although the volatility and maximum drawdown of the optimized enhanced index model increased slightly, it showed a higher excess return rate and information ratio. Therefore, the BL model optimized based on the compression estimation method can make the model applicable to a wider range, and can be extended to large-scale assets and multi-asset allocation, so that investors have more choices in quantitative investment strategies.

A Short Review over Twenty Years on the Black- Litterman Model in Portfolio Optimization

This paper review aims to explain how the Black-Litterman approach for portfolio optimization works based on many references and perspectives. The explanation of the expected return of Black Litterman is derived from many developments in both theory and practice. For over two decades, the Black-Litterman model has many extensions that have been generated from the data, methods, or portfolio performance. We summarize the relevant articles, from concept-centric and author-centric, to discover the potential areas in developing the original model. In the final section, we classify the extension of the Black-Litterman model based on the modified formula for the Black-Litterman return and propose future research.

Distributionally Robust Mean-Variance Portfolio Selection with Wasserstein Distances

We revisit Markowitz’s mean-variance portfolio selection model by considering a distributionally robust version, in which the region of distributional uncertainty is around the empirical measure and the discrepancy between probability measures is dictated by the Wasserstein distance. We reduce this problem into an empirical variance minimization problem with an additional regularization term. Moreover, we extend the recently developed inference methodology to our setting in order to select the size of the distributional uncertainty as well as the associated robust target return rate in a data-driven way. Finally, we report extensive back-testing results on S&P 500 that compare the performance of our model with those of several well-known models including the Fama–French and Black–Litterman models. This paper was accepted by David Simchi-Levi, finance.

Practical Applications of Weak Supervision and Black–Litterman for Automated ESG Portfolio Construction

In Weak Supervision and Black–Litterman for Automated ESG Portfolio Construction, published in the Summer 2021 issue of The Journal of Financial Data Science, Alik Sokolov of SR.ai, and Kyle Caverly, Jonathan Mostovoy, Talal Fahoum, and Luis Seco of the University of Toronto’s RiskLab demonstrate the use of machine learning signals for ESG risk in portfolio optimization. The signals are created by a state-of-the-art natural language processing model applied to news articles from The New York Times. The authors demonstrate that the system achieves high accuracy across the ESG categories. They use the Black–Litterman model to combine the signals with a market-weight portfolio to find optimal portfolio weights that reflect the ESG risks. The resulting portfolio outperforms an otherwise equal non-ESG portfolio on a risk-adjusted basis. The approach is promising in that it avoids self-reported biases in the ESG data. Moreover, the results do not imply that risk-adjusted returns must be sacrificed in order to achieve ESG objectives. This area of research is particularly important as interest in ESG investing continues to grow.

Multi-asset allocation of exchange traded funds: Application of Black–Litterman model

ABSTRACT The Black–Litterman (BL) model allows investors to apply their subjective views to asset allocation optimisation. In this study, we construct a multi-asset allocation portfolio of iShares exchange traded funds (ETFs) using mean–variance (MV) and BL models. Two investment strategies, namely lump-sum investment and a systematic investment plan (SIP), are also investigated and applied to ETF portfolios. On the basis of a momentum strategy, three subjective views of investors are developed for the BL model. The contributions of this empirical study are threefold. First, under the SIP strategy, BL portfolios outperform the MV portfolio in terms of cumulative values, even when an investment starts with bad market timing (i.e., 2008). Second, the asset allocation weights of BL portfolios are demonstrated to be closely related to investors’ subjective views and significantly different from those of the MV portfolio. Third, the three BL portfolios constructed on the basis of the momentum strategy exhibit similar performance patterns in their cumulative returns during the period from 2008 to mid-2021, indicating that investors’ views are consistently reflected in the BL portfolios and consequently contribute to the similarity of the portfolios’ performance as they share similarities in the application of momentum strategies.

Decision Support for Portfolio Management by Information System with Black–Litterman Model

An algorithm is derived for the development of portfolio decision-support information service. The algorithm allows being automated evaluations for the definition and solution of portfolio problems. Small set of historical data of asset returns with limited set of assets are used for the portfolio, which is the case for no institutional portfolio manager. The algorithm applies analytical relations for decreasing the computational workload for the estimation of the market parameters due to the limited number of assets. The subjective expert views in the Black–Litterman (BL) model are defined from additional assessment of historical data of the asset returns. The algorithm makes comparisons of the results for active portfolio management from the mean variance (MV) model, the BL one and the equal-weighted investment strategy. Benefits of the algorithm are the usage of small set of historical data and limited number of assets, which are proved in investment rolling horizon.

Analysis of Portfolio Expected Returns as a Material Consideration for Investors in Choosing Investments in the Pandemic Period (Formation of Optimal Portfolios Using the Black Litterman Model on Hang Seng Stocks for the 2017-2019 Period)

. This study attempts to find out how a method of Black Litterman in the formation of stock portfolios. This research was conducted on the basis of increasing the number of investors' funds in the capital market for certain stocks, showing that it increases positive sentiment on stock investments compared to other investments. The Black Litterman Model method is one of the options that can be used in the formation of portfolio. The Black Litterman model method is a method that formulates the existence of an element of return equilibrium and investor views in an investment. By using the Black Litterman Model, investors can take advantage of all available information as the basis for forming a maximum portfolio. The object of this research is Hang Seng (HSI) stock price data for the period 2017 – 2019. The research sample is 35 companies. The results of this study resulted in 10 stocks included in the Black Litterman model portfolio with the expected return on the portfolio (which consisted of 10 stocks with the Black Litterman model) of 0.062387. Where the highest proportion of returns given by Shenzhou International Group Holdings Limited (SEHK: 2313) is 23% and the expected return is 0.017933. While the lowest level is occupied by New World Development Company Limited (SEHK: 17) with a proportion of 1% and an expected return of 0.000687.

Application of modified Black-Litterman model for active portfolio management

An active policy for portfolio optimization is developed based on repetitive application of modified Black-Litterman (BL) portfolio model and new formal definition of the expert views. New subjective views are defined which are based on the differences between the historical mean asset returns and their implied return values. An algorithm for the implementation of active management with the modified BL model is derived. The active management policy allows using short time series of historical data of assets, providing portfolio optimization with limited set of assets. New market point is evaluated, because the small set of assets does not allow market index to be used as characteristics of the market. The new formalization of the expert views allows to be compared the Mean Variance and BL portfolios on common basis. The experiments and comparisons between the Mean Variance optimization and the modified BL problem give advantages to the last one.

Does a Skew-Normal Return Find Better Bayesian Optimal Portfolios?

In the presence of asset returns’ non-normal behavior, optimal portfolio selection techniques should consider higher-moment risks. In this paper, we extend the Black-Litterman (BL) asset allocation model (Black & Litterman, 1990) by applying the hidden truncation skew-normal distribution (Arnold & Beaver, 2000). Based on Simaan’s approach (Simaan, 1993), we also develop a three-moment BL model considering skewness. Using the skew-normal returns, the skew-normal BL model provides optimal portfolios with the same expected return but less risk compared to an optimal portfolio of the classical BL model. We find that the portfolios become more negatively skewed as the expected returns of portfolios increase at any level of N (non-spherical variance), which suggests that the investors trade a negative skewness for a higher expected return. We also find the negative relation between portfolio volatility and portfolio skewness. In other words, the investors trade a lower volatility for a higher skewness or vice versa reflecting that stocks with big price declines are more volatile.

Time-varying Black–Litterman portfolio optimization using a bio-inspired approach and neuronets

The Black–Litterman model is a very important analytical tool for active portfolio management because it allows investment analysts to incorporate investor’s views into market equilibrium returns. In this paper, we define and study the time-varying Black–Litterman portfolio optimization under nonlinear constraints (TV-BLPONC) problem as a nonlinear programming (NLP) problem. More precisely, the nonlinear constraints refer to transaction costs and cardinality constraints. Furthermore, a speedy weights-and-structure-determination (WASD) algorithm for the power-activation feed-forward neuronet (PFN) is presented to solve time-series modeling and forecasting problems. Inhere, the investor’s views in the TV-BLPONC problem are considered as a forecasting problem and, thus, they are produced by the WASD-based PFN. In addition, using the beetle antennae search (BAS) algorithm a computational method is introduced to solve the TV-BLPONC problem. For all we know, this is an innovative approach that integrates modern neural network and meta-heuristic optimization methods to provide a solution to the TV-BLPONC problem in large portfolios. Our approach is tested on portfolios of up to 90 stocks with real-world data, and the results show that it is more than 30 times faster than other methods. Our technique’s speed and precision are verified in this way, showing that it is an outstanding alternative to ordinary methods. In order to support and promote the findings of this work, we have constructed two complete MATLAB packages for the interested user, which are freely available through GitHub.

LQ45 Stock Portfolio Selection using Black-Litterman Model in Pandemic Time Covid-19

The world was shocked by the emergence of a virus that spread very quickly to several countries including Indonesia at the end of 2019. This virus infection is called Corona Virus Disease 2019 (Covid-19). The outbreak of Covid-19 not only threatens human lives but also disrupts various economic, financial, and business activities, especially in Indonesia. A stock portfolio is a collection of financial assets in a unit that is held or created by an investor, investment company, or financial institution. The Black-Litterman model of the stock portfolio is a portfolio model that involves the CAPM equilibrium return and investor views. The purpose of this study is to determine the stock portfolio with the Black-Litterman model using company data listed in the LQ45 stock index from January 2020 to June 2020. Four of the twenty-nine LQ45 stocks were selected as assets in the stock portfolio. The stock portfolio containing the four stocks, namely ICBP, KLBF, MNCN, and TLKM with the Black-Litterman model resulted in an expected return of 2.07% and a risk of 2.82%.

Weak Supervision and Black-Litterman for Automated ESG Portfolio Construction

The authors propose an approach that combines modern machine learning techniques in natural language processing with portfolio optimization to incorporate views of companies’ environment, social, and governance (ESG) performance. This is automatically done through curating and subsequently converting large-scale news data into portfolio management decisions. They train a machine learning news data classifier to automatically identify several key ESG issues in news data over time. They then aggregate these issues over time to generate a views vector under the Black–Litterman portfolio framework and finally compare the performance of an ESG-tilted portfolio against a standard Black–Litterman portfolio. They also show how this can be achieved at scale, in a fully automated manner, and with consistency over large periods of time. Their methodology thus demonstrates a reasonable and agile method for asset managers to incorporate ESG considerations into their portfolios free of any exclusionary frameworks and without sacrificing performance. <b>TOPICS:</b>ESG investing, quantitative methods, statistical methods, big data/machine learning, portfolio construction <b>Key Findings</b> ▪ The authors describe a theoretical framework for using an automated NLP system to incorporate ESG criteria into portfolio optimization decisions. ▪ The authors demonstrate the technical implementation details for incorporating ESG signals into augmented portfolio weights. ▪ The authors demonstrate the competitive performance of such a portfolio through a long-term historical backtest with the S&amp;P 500 Index.

Copula-based Black–Litterman portfolio optimization

We extend the Black-Litterman (BL) approach to incorporate tail dependency in portfolio optimization and estimate the posterior joint distribution of returns using vine copulas. Our novel copula-based BL (CBL) model leads to flexibility in modeling returns symmetric and asymmetric multivariate distribution from a range of copula families. Based on a sample of the Eurostoxx 50 constituents (also for S&P 100 as robustness check), we evaluate the performance of the suggested CBL approach and portfolio optimization technique using out-of-sample back-testing. Our empirical analysis and robustness check indicate better performance for the CBL portfolios in terms of lower tail risk and higher risk-adjusted returns, compared to the benchmark strategies.

Reverse optimization and capital asset pricing model in the application of the Black Litterman portfolio

In the application of the Black Litterman model on portfolio construction, the terms of reverse optimization and Capital Asset Pricing Model (CAPM) are often associated with the Black Litterman process. This study explains the Black Litterman model from two perspectives: reverse optimization and the CAPM formula. Two portfolios are built with different starting points and without any lambda difference as a risk aversion coefficient, a scalar tau, and views return in the Black Litterman strategy. Both models are applied in the Indonesian stock market, and the empirical comparison of both portfolios are demonstrated. The result shows that both approaches can build a portfolio using the Black Litterman with a similar weight allocation.

The study of mixed assets allocation based on Black–Litterman model

With Private Funds having a new type of license for asset allocation practice in China, comprehensive asset allocation cross private equity and stock market has received more attention. However, most of the studies focus more on the stock market, and asset allocation models for private equity market that are mainly made based on experience. Thus, the joint allocation of assets crosses both markets making it a challenging research topic. This paper introduces the Black–Litterman model into the private equity market, realizing the transition from qualitative models to quantitative models. It lays a solid quantitative ground for the mixed asset allocation model in both the markets.