Search

This study investigates the profitability of portfolios that integrate asymmetric fractality within the Black–Litterman (BL) framework. It predicts 10-day-ahead exchange-traded fund (ETF) prices using recurrent neural networks (RNNs) based on historical price information and technical indicators; these predictions are utilized as BL views. While constructing the BL portfolio, the Hurst exponent obtained from the asymmetric multifractal detrended fluctuation analysis is employed to determine the uncertainty associated with the views. The Hurst exponent describes the long-range persistence in time-series data, which can also be interpreted as the uncertainty in time-series predictions. Additionally, uncertainty is measured using asymmetric fractality to account for the financial time series' asymmetric characteristics. Then, backtesting is conducted on portfolios comprising 10 countries' ETFs, rebalanced on a 10-day basis. While benchmarking to a Markowitz portfolio and the MSCI world index, profitability is assessed using the Sharpe ratio, maximum drawdown, and sub-period analysis. The results reveal that the proposed model enhances the overall portfolio return and demonstrates particularly strong performance during negative trends. Moreover, it identifies ongoing investment opportunities, even in recent periods. These findings underscore the potential of fractality in adjusting uncertainty for diverse portfolio optimization applications. [ABSTRACT FROM AUTHOR]

Generally, the Black-Litterman portfolio model relies heavily on the expert investment opinions, where high-quality investment opinions would improve model performance whereas low-quality investment opinions would result in poor model performance. Essentially, expert investment opinions are highly subjective, sourcing from these financial experts' information and knowledge. ChatGPT, as an advanced generative AI model, could extract and analyze information from huge multi-modal data, which is beneficial to build AI investment opinions for Black-Litterman portfolio model. In this study, we construct and analyze the large language model-based Black-Litterman portfolios, ChatGPT-BL and BARD-BL, where the goals of minimum variance and mean-variance trade-off are taken into account. Computational results show that the ChatGPT-based portfolios tend to be conservative, which is suitable for risk-averse investors, while the BARD-based portfolios are aggressive, which is appropriate for risk-seeking investors. Also, the superiority of Black-Litterman model using investor views generating from gradient boosting regression and GJR-GARCH algorithm is illustrated by the efficient frontiers. [ABSTRACT FROM AUTHOR]

Purpose – The 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/approach – Ibovespa, 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. Findings – The 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 implications – The 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/value – The 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.

This study investigates the profitability of portfolios that integrate asymmetric fractality within the Black–Litterman (BL) framework. It predicts 10-day-ahead exchange-traded fund (ETF) prices using recurrent neural networks (RNNs) based on historical price information and technical indicators; these predictions are utilized as BL views. While constructing the BL portfolio, the Hurst exponent obtained from the asymmetric multifractal detrended fluctuation analysis is employed to determine the uncertainty associated with the views. The Hurst exponent describes the long-range persistence in time-series data, which can also be interpreted as the uncertainty in time-series predictions. Additionally, uncertainty is measured using asymmetric fractality to account for the financial time series’ asymmetric characteristics. Then, backtesting is conducted on portfolios comprising 10 countries’ ETFs, rebalanced on a 10-day basis. While benchmarking to a Markowitz portfolio and the MSCI world index, profitability is assessed using the Sharpe ratio, maximum drawdown, and sub-period analysis. The results reveal that the proposed model enhances the overall portfolio return and demonstrates particularly strong performance during negative trends. Moreover, it identifies ongoing investment opportunities, even in recent periods. These findings underscore the potential of fractality in adjusting uncertainty for diverse portfolio optimization applications.

The Black-Litterman portfolios based on the predictions provided by Gaussian Process are constructed in this study. Besides the expert views generated by the Gaussian Process, an customized algorithm quantifying the confidence level of the given investor opinions is also designed, which can be inputted into the Black-Litterman framework to revise the posterior parameters estimations. Low-risk anomaly is observed from the numerical experiments through the grouping method base on stock β, demonstrating the potential irrationality for even giant companies and brands on the advanced market. Empirical analysis shows that Gaussian Process is able to model the low β stock effectively, while not feasible for stocks with high volatility. Thus, the proposed BLGPlo portfolio outperform the benchmarks in terms of cumulative excess return and Sharpe ratio. Moreover, the BLGPlo performance can be further improved by allocating higher confidence level for the Gaussian Process-derived investor opinions. [ABSTRACT FROM AUTHOR]

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.

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. [ABSTRACT FROM AUTHOR]

Generation mix in the power system implies the combination of various sources of energy, renewable and conventional, where each of these sources behaves as a different asset class. The generation from renewable sources is highly variable due to the uncertainty in their primary source of energy. These uncertainties affect the expected returns from a portfolio corresponding to a generation mix. To apply any theories in finance to the energy spectrum for further clarity, the risk and reward have to be clearly defined. Since taking any single parameter will not justify the complete sense of reward and risk, expected returns, defined as a fuzzy index by combining the monthly percentage output of a generation asset, the Levelized Cost of Electricity and the expected profit the generation company produces by bidding that source in power market. The generation mix is then optimized by using Black–Litterman model. [ABSTRACT FROM AUTHOR]

• Study of the CTBLPO problem through Error-Correction Neural Networks. • Investor's views are regarded as a forecasting problem. • Proposal of a feed-forward MAWTSNN model for time-series forecasting problems. • Four other high-performing NN models are compared to the MAWTSNN model. • The use of TVQP NN solvers, i.e. ZNN and LVI-PDNN, to finance. • Experiments in three distinct portfolio configurations using real-world datasets. 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper transfers and adapts the Black-Litterman portfolio management model and its subsequent generalizations to the characteristics and specificities of assets quoted on sports betting markets. The results show that these assets are suitable for the application of portfolio management models with the possible inclusion of investors' opinions. Information based on the variability of market prices and the attention received by NBA teams in Google Trends is successfully used to simulate the opinions expressed by a hypothetical portfolio manager. Furthermore, the assets are suitable for inclusion in portfolios in which managers are seeking returns uncorrelated with other assets. [ABSTRACT FROM AUTHOR]

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.

Generation error is one of the shortcomings of the classical mean-variance portfolio selection model which would result in unstable performance in out-of-sample data sets. Machine learning provides several potential solutions for reducing the generalization error, such as adding penalty terms and random sampling. Due to some significant advantages of machine learning algorithms, we implement Black- Litterman (BL for short) series portfolio models integrated with quantitative opinions generating from machine learning algorithms in this paper. And, the fundamental factors in the Fama-French model form the basis of quantitative opinions. Considering the non-linearity among fundamental factors, we construct high-order terms and cross terms of basic features by the approach of dimension-increasing transformation. A multi-period portfolio strategy is designed in our work for the timeliness of quantitative opinions, the experimental results reveal that the optimal BL model with investor opinion generating from Random Forest gained over 20% average annual return and a Sharpe Ratio of 1.25. By comparison, S&P 500 index gained about 14.94% annual return and a Sharpe Ratio of 1.00, the 1/N strategy gained about 15.92% annual return and the Sharpe Ratio of 0.99. Moreover, the BL series models are more diversified and robust, about 30% to 60% of assets are selected to construct the portfolio. Even when the transaction cost is taken into account, our proposed models still obtained higher cumulative returns than S&P 500 if the transaction cost is lower than 30%%. [ABSTRACT FROM AUTHOR]

Classic mean–variance optimization is very sensitive to expected returns. An alternative and more robust approach is to calculate the implied returns given the current portfolio allocation and risk profile. Portfolio managers can then do a reality check on the implied returns and find opportunities for better allocations. The most common implied return calculation assumes normal distribution and unlimited leverage, and use volatility as risk measure and covariance matrix as model input. However, practitioners usually have leverage constraints, often use non-parametric risk models, and care about portfolio tail risk. This paper presents a new approach to calculate expected returns with leverage constraints. This approach is flexible enough to alleviate normal distribution assumption, connect with non-parametric risk models, and use tail risk measures, such as conditional VaR. [ABSTRACT FROM AUTHOR]

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.

The portfolio process of optimization search for the best portfolio through the risk measures and return, Markowitz model has worked on that selection under median-variance portfolio, that model has been criticized because it is based on historic information, leaving some aspects unaccounted for, such as the state of the market, lower diversification, among others; in order to improve this model, Fischer Black and Robert Litterman provided information about financial assets assignment based on the assumption of the equilibrium and the investor opinion concerning the future investment asset. Because of the uncertainty in the optimization process, it is proposed to make the use of fuzzy techniques for its treatment. This article is the result of the Master Degree in Finances, "Aplication of fuzzy techniques to the selection's model of the Black-Litterman portfolio: Colombian Case Coleqty index" that evaluate the optimization process of contributions of portfolio in Black-Litterman Model, based on diffuse techniques in stocks of Coleqty index of Colombia, resulting risk-return base on triangular and trapezoidal functions, obtaining some different portfolios concerning with diversification, it will be compared with Sharpe, Treynor and Jensen's Alpha performance indicators, portfolio with best return and less risk will be important, in order to choose the best optimization process, Black-Litterman classic or Black Litterman fuzzy techniques. [ABSTRACT FROM AUTHOR]

This study develops a behavioral portfolio selection model that uses a robust estimator for expected returns in order to produce portfolios with less need to change over consecutive periods. We also consider investor attitudes toward risk through spectral risk measure as well as investor expectations on future returns by means of the Black–Litterman model, and finally, our model includes a varying risk aversion depending on investor behavioral biases and his latest realized return. In order to evaluate the proposed model and make comparisons possible, we conducted a survey on investor biases and attitudes along with market data of Tehran Stock Exchange. The results reveal that although our model is not mean–variance efficient, it recommends portfolios that are robust, well diversified, and have less utility loss compared to a famous behavioral portfolio model. [ABSTRACT FROM AUTHOR]

The Colombian pension model is characterized by being intergenerational, reason why it has been affected by three major structural problems: inequality, low coverage and financial unsustainability, to which the Colombian government has reacted with regulatory measures that have somewhat relieved these problems. However, these prudential regulations have a negative effect on the inherent purpose of the investment fund, which is the generation of wealth to guarantee the intertemporal consumption of the Colombian elderly population. Therefore, the pension funds in Colombia requires that under the framework of the stablished regulations, new alternatives for structuring their portfolios be studied that allow them into better and more efficient management of retirement resources for Colombian people. In this sense, an efficient portfolio and frontier were built through a Support Vector Machine and the Black Litterman model to the Colombian Mandatory Pension Funds, with the aim to test the applicability of machine learning in financial fields. Results show that its applicability to the Black-Litterman portfolio structuring model is suitable through the improvement to the a priori distribution matrix, specifically with the use of Support Vector Regression, the model generated better diversified portfolios in comparison to the Markowitz model and shows to be adaptable to the Colombian Mandatory Pension Funds. [ABSTRACT FROM AUTHOR]

• Fear/greed indicator predictions act a valuable proxy for future investor sentiment and constructing relative Black-Litterman views. • A hybrid CEEMDAN-GRU deep learning model gives the most accurate predictions for this indicator. • The XGBoost ensemble algorithm is used to predict relative outperformance in returns when constructing Black-Litterman views. • The proposed Black-Litterman approach outperforms eight other established portfolio strategies. We introduce a new dimension in constructing relative investor views for the Black-Litterman model by incorporating fear/greed technical indicator predictions as a proxy for investor sentiment in the portfolio construction process. We apply a hybrid CEEMDAN-GRU deep learning model to forecast this indicator and the XGBoost ensemble learning algorithm to forecast returns for ten country ETFs and create relative views for the Black-Litterman model. These models beat several benchmark forecasting models. Our empirical results show that the proposed approach outperforms the Markowitz, minimum-variance, equally-weighted and risk-parity strategies along with four other Black-Litterman approaches from the literature for six investment periods. [ABSTRACT FROM AUTHOR]

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.

There is apparent persistent confusion over certain aspects of Black-Litterman expected returns, with a number of publications offering various explanations, clarifications, and criticisms as to how the model works in practice. The parameter tau ( τ) has proved to be a particularly confounding feature of the model: A wide range of opinions and suggestions on how to interpret and quantify tau has accumulated in the literature and includes some harsh condemnation of Black-Litterman specifically related to tau. This article presents a simple interpretation of tau, shows that it is directly related to the level of active risk implicit in the Black-Litterman model, and is easily calibrated so that Black-Litterman expected returns produce portfolios with targeted levels of active risk. The main contribution is an alternative derivation of Black-Litterman that affords a direct way to target active risk without requiring a specific value for tau. This derivation reveals that portfolio construction using Black-Litterman is equivalent to creating a mean-variance optimal portfolio of active strategies that is then overlaid onto a benchmark portfolio, and by targeting active risk directly, users of the Black-Litterman model do not need to consider tau at all. [ABSTRACT FROM AUTHOR]

The Black-Litterman method is widely used in the investment management industry to incorporate views in investment portfolios. The method applies when views are expressed as expected returns over the horizon for which allocation decisions are made, i.e., the investment horizon. In practice, however, the investor's views are typically formulated for the near future while the investor's investment horizon is much longer. To incorporate such views, we introduce the time-dependent Black-Litterman method and show that, in a time-dependent setting, a distinction should be made between unconditional and conditional views. Furthermore, we demonstrate its use for buy and hold investors. In an example, we show that the investor's views have a plausible impact on resulting allocation decisions. [ABSTRACT FROM AUTHOR]

This paper uses a novel numerical optimization technique – robust optimization – that is well suited to solving the asset–liability management (ALM) problem for pension schemes. It requires the estimation of fewer stochastic parameters, reduces estimation risk and adopts a prudent approach to asset allocation. This study is the first to apply it to a real-world pension scheme, and the first ALM model of a pension scheme to maximize the Sharpe ratio. We disaggregate pension liabilities into three components – active members, deferred members and pensioners, and transform the optimal asset allocation into the scheme's projected contribution rate. The robust optimization model is extended to include liabilities and used to derive optimal investment policies for the Universities Superannuation Scheme (USS), benchmarked against the Sharpe and Tint, Bayes–Stein and Black–Litterman models as well as the actual USS investment decisions. Over a 144-month out-of-sample period, robust optimization is superior to the four benchmarks across 20 performance criteria and has a remarkably stable asset allocation – essentially fix-mix. These conclusions are supported by six robustness checks. [ABSTRACT FROM AUTHOR]

The Black–Litterman model aims to enhance asset allocation decisions by overcoming the problems of mean-variance portfolio optimization. We propose a sample-based version of the Black–Litterman model and implement it on a multi-asset portfolio consisting of global stocks, bonds, and commodity indices, covering the period from January 1993 to December 2011. We test its out-of-sample performance relative to other asset allocation models and find that Black–Litterman optimized portfolios significantly outperform naïve-diversified portfolios (1/Nrule and strategic weights), and consistently perform better than mean-variance, Bayes–Stein, and minimum-variance strategies in terms of out-of-sample Sharpe ratios, even after controlling for different levels of risk aversion, investment constraints, and transaction costs. The BL model generates portfolios with lower risk, less extreme asset allocations, and higher diversification across asset classes. Sensitivity analyses indicate that these advantages are due to more stable mixed return estimates that incorporate the reliability of return predictions, smaller estimation errors, and lower turnover. [ABSTRACT FROM PUBLISHER]

In this paper we introduce an intra-sector dynamic trading strategy that captures mean-reversion opportunities across liquid U.S. stocks. Our strategy combines the Avellaneda and Lee methodology (AL; Quant. Financ. 2010, 10, 761–782) within the Black and Litterman framework (BL; J. Fixed Income, 1991, 1, 7–18; Financ. Anal. J. 1992, 48, 28–43). In particular, we incorporate the s-scores and the conditional mean returns from the Orstein and Ulhembeck (Phys. Rev. 1930, 36, 823–841) process into BL. We find that our combined strategy ALBL has generated a 45% increase in Sharpe Ratio when compared to the uncombined AL strategy over the period from January 2, 2001 to May 27, 2010. These new indices, built to capture dynamic trading strategies, will definitely be an interesting addition to the growing hedge fund index offerings. This paper introduces our first “focused-core” strategy, namely, U.S. Equity Mean-Reversion.

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.

Stochastic optimisation has found a fertile ground for applications in finance. One of the greatest challenges remains to incorporate a set of scenarios that accurately model the behaviour of financial markets, and in particular their behaviour during crashes and crises, without sacrificing the tractability of the optimal investment policy. This paper shows how to incorporate return predictions and crash predictions as views into continuous time asset allocation models. [ABSTRACT FROM PUBLISHER]

• CNN is efficient in feature extraction and BiLSTM is efficient in long-term multivariate time series prediction. • CNN-BiLSTM gives the best predictions when compared to CNN, LSTM, BiLSTM and CNN-LSTM. • The predictions from the CNN-BiLSTM model are used as investor views inside a Black-Litterman model with time variation in the conditional distribution of returns. • The Dynamic Black-Litterman model with CNN-BiLSTM predictions as views outperforms three benchmark models by a significant margin in terms of financial efficiency and diversification. 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. [ABSTRACT FROM AUTHOR]

Among the several financial theories related with the optimal portfolio selection, Black-Litterman proposal is the only one that considers the future expectation of investors over the assets that are being considered in the portfolio allocation problem. This works presents the Black-Litterman portfolio proposal as a tool that improves the optimal portfolio selection and also shows how the results obtained with this model could be used as an input to the classical Markowitz portfolio selection model. Besides the theorical presentation of the Black-Litterman portfolio model, a portfolio analysis over the COLCAP index in the Colombian Capital Market is presented, in this case the expectations of investors are taking into account and the results obtained from the Black-Litterman model are used to improve an optimal portfolio that consider the previous expectations under the Markowitz portfolio selection model, either under minimum variance and maximum return optimization. [ABSTRACT FROM AUTHOR]