Multi-period Portfolio Selection Research Articles

DivFolio: a Shiny application for portfolio divestment in green finance wealth management

Abstract This paper introduces DivFolio, a multiperiod portfolio selection and analytic software application that incorporates automated and user-determined divestment practices accommodating Environmental Social Governance (ESG) and portfolio carbon footprint considerations. This freely available portfolio analytics software tool is written in R with a GUI interface developed as an R Shiny application for ease of user experience. Users can utilize this software to dynamically assess the performance of asset selections from global equity, exchange-traded funds, exchange-traded notes, and depositary receipts markets over multiple time periods. This assessment is based on the impact of ESG investment and fossil-fuel divestment practices on portfolio behavior in terms of risk, return, stability, diversification, and climate mitigation credentials of associated investment decisions. We highlight two applications of DivFolio. The first revolves around using sector scanning to divest from a specialized portfolio featuring constituents of the FTSE 100. The second, rooted in actuarial considerations, focuses on divestment strategies informed by environmental risk assessments for mixed pension portfolios in the US and UK.

Multi-period portfolio selection with interval-based conditional value-at-risk

Multi-period portfolio selection with interval-based conditional value-at-risk

Learning fused lasso parameters in portfolio selection via neural networks

AbstractIn recent years, fused lasso models are becoming popular in several fields, such as computer vision, classification and finance. In portfolio selection, they can be used to penalize active positions and portfolio turnover. Despite efficient algorithms and software for solving non-smooth optimization problems have been developed, the amount of regularization to apply is a critical issue, especially if we have to achieve a financial aim. We propose a data-driven approach for learning the regularization parameters in a fused lasso formulation of the multi-period portfolio selection problem, able to realize a given financial target. We design a neural network architecture based on recurrent networks for learning the functional dependence between the regularization parameters and the input data. In particular, the Long Short-Term Memory networks are considered for their ability to process sequential data, such as the time series of the asset returns. Numerical experiments performed on market data show the effectiveness of our approach.

An uncertainty theory based tri-objective behavioral portfolio selection model with loss aversion and reference level using a modified evolutionary root system growth algorithm

The outbreak of uncertain events, e.g., financial crisis, regional conflict and abrupt contagion, has a significant impact on residents’ income. Hence, the wealth management and portfolio selection become more and more important. In addition, the behavioral finance believes that decision-making process of the investors not only depend on utility maximization, but also on who to compare with. It differs from the traditional finance based on rational cognitive acquiring and decision-making of agents, in this paper, we consider both investment uncertainty and investment utility with reference level for portfolio selection. First, we introduce the uncertainty theory and loss aversion utility with reference level based on behavioral finance. Then we study an uncertain multi-period portfolio selection problem. Moreover, we formulate an uncertain behavioral portfolio selection model with three objective functions for which we propose an equivalent program consisting of a main model and two auxiliary models for tri-objective optimization model. Thereafter, we use a modified evolutionary root system growth algorithm to solve the transformed models. Finally, a numerical simulation allows to show the practicability of proposed models and validity of modified algorithm.

The cost of delay as risk measure in target-based multi-period portfolio selection models

Abstract Accepted by: Aris Syntetos Increasingly, in recent years, the fund management industry has evolved towards so-called goal-based investing paradigms, under which investors are assumed to base their portfolio strategies on pre-specified targets to be attained in the future. A similar decision model is common in the wealth management and the life insurance industries where targets may be associated with long-term investment horizons and retirement planning problems. Based on this evidence, we propose in this article a novel risk measure explicitly focusing on the financial cost that may be associated with a delay in reaching those targets. We show that the definition of this risk measure is both rather natural and effective to capture investors’ risk preferences. A dynamic portfolio selection model is developed to assess the effectiveness of the risk measure from financial and risk control perspectives. The introduced risk measure has good properties and it is related to the Value-at-Risk with a given confidence level. Under sufficiently general statistical assumptions, we derive a closed form solution to a mean-risk formulation of the portfolio problem in which the cost of delay is taken as risk measure. Finally, a set of numerical tests validate the proposed portfolio selection model and show a set of comparative results with respect to a classical dynamic mean-variance model.

Responsible Investing: A Multi-period Portfolio Selection Model

Responsible Investing: A Multi-period Portfolio Selection Model

Regularization methods for sparse ESG-valued multi-period portfolio optimization with return prediction using machine learning

In the context of global sustainable development, environmental, social, and governance (ESG) investment has become a frontier topic in the field of asset management. This paper focuses on ESG-valued multi-period portfolio selection problem which incorporates ESG factor into traditional portfolio optimization. Using ESG-valued returns instead of traditional returns, we propose an ESG-valued fused LASSO model to promote an optimal sparse multi-period portfolio strategy. The objective of the model is to minimize a combination of returns and risks with respect to ESG ratings based on classical Markowitz mean–variance framework. The sparsity of the portfolio at each period and the turnover across periods is achieved by the ℓ1 regularization approach. To improve the out-of-sample performance of the ESG-valued model, we introduce two machine learning methods, namely random forest and support vector regression, to predict the ESG-valued returns. We develop a symmetric alternating direction method of multipliers to solve the regularized optimization model. Additionally, some other sparsity-driven penalty functions are discussed which results in a general framework of multi-period portfolio optimization. Finally, numerical experiments on several real datasets from both in-sample and out-of-sample demonstrate the positive effect of ESG in multi-period portfolio optimization.

Multi-criteria fuzzy portfolio selection based on three-way decisions and cumulative prospect theory

Portfolio selection is one of the hottest issue in decision-making and management engineering. But due to the capital market natural complexity and investors’ irrational behaviors, it is not easy for investors to achieve their predefined goals. In this study, we propose a novel three-way decisions model based on cumulative prospect theory and outranking relations. Compared with traditional two-way decisions, the introduction of a boundary region into the three-way decisions theory makes it possible to reduce decision risk. By constructing an outranked set for each alternative and a hybrid multi-criteria decision-making matrix, three strategies are proposed by us to design the three-way decisions model. In order to test the effectiveness of the proposed model, we introduce it into a fuzzy multi-period portfolio selection case and design an improved particle swarm optimization as the solution algorithm. Finally, the effectiveness of the algorithm is validated by some test functions. And an experiment based on real market data validates the proposed multi-period portfolio selection model outperforms other compared models in terms of return, risk and risk-adjusted criteria.

An Approach for a Multi-Period Portfolio Selection Problem by considering Transaction Costs and Prediction on the Stock Market

This paper addresses a method to solve a multi-period portfolio selection on the stock market. The portfolio problem seeks an investor to trade stocks with a finite budget and a given integer number of stocks to hold in a portfolio. The trade must be performed through a stockbroker that charges its respective transaction cost and has its minimum required trade amount. A mathematical model has been proposed to deal with the constrained problem. The objective function is to find the best risk-return rate; thus, Sharpe Ratio and Treynor Ratio are used as objective functions. The returns are the same for these ratios, but the risks are not Sharpe considering covariance and Treynor systematical risk. The returns are predicted using a Neural Net with Long-Short-Term Memory (LSTM). This neural net is compared with simple forecasting methods through Mean Absolute Percentage Error (MAPE). Computational experiments show the quality prediction performed by LSTM. The heteroskedastic risk is estimated by Generalized Autoregressive Conditional Heteroskedasticity (GARCH), adjusting the variance for every period; this risk measure is used in Sharpe Ratio. The experiment contemplates a weekly portfolio selection with 5 and 10 stocks in 122 weekly periods for each Chilean market ratio. The best portfolio is Sharpe Ratio with ten stocks, performing a 62.28% real return beating the market, represented by the Selective Stock Price Index (IPSA). Even the worst portfolio, Treynor Ratio, overcomes the IPSA cumulative yield with ten stocks.

Distributionally robust multi-period portfolio selection subject to bankruptcy constraints

<p style='text-indent:20px;'>An optimization problem with moments information which suffers from distributional uncertainty can be handled through distributionally robust optimization. In this paper, we will consider distributionally robust multi-period portfolio selection since only moment information of portfolios can be gathered in practice. We will consider two different scenarios. One is that moments information can be obtained exactly and the other one is that the moments information is also uncertain. For the two scenarios, we will show how to transform the corresponding distributionally robust optimization problem into a second order cone problem (SOCP) which can be easily solved by existing methods. Some numerical experiments are presented to demonstrate the effectiveness of our proposed method.</p>

Distributionally robust optimization with Wasserstein metric for multi-period portfolio selection under uncertainty

The mean-variance model formulated by Markowitz for a single period serves as a fundamental method of modern portfolio selection. In this study, we consider a multi-period case with uncertainty that better matches the reality of the financial market. Using the Wasserstein metric to characterize the uncertainty of returns in each period, a new distributionally robust mean-variance model is proposed to solve multi-period portfolio selection problem. We further transform the developed model into a tractable convex problem using duality theory. We also apply a nonparametric bootstrap method and provide a specific algorithm to estimate the radius of the Wasserstein ball. The effects of the parameters on the corresponding strategy and evaluation criteria of portfolios are analyzed using in-sample data. The analysis indicate that the return and risk of our portfolio selections are relatively immune to parameter values. Finally, a series of out-of-sample experiments demonstrate that the proposed model is superior to some other models in terms of final wealth, standard deviation, and Sharpe ratio.

An event-triggered iteratively reweighted convex optimization approach to multi-period portfolio selection

This paper addresses multi-period portfolio selection driven by events. We define an event-triggering function to mimic fund managers to activate sequential portfolio rebalancing and maximize Sharpe and Sortino ratios in the Markowitz’s return–risk framework. At first, the multi-period portfolio selection problem is formulated with a variable weight as a series of biconvex optimization problems with a surrogated objective function to maximize the Sharpe ratio or Sortino ratio. In each period, the portfolio optimization problem is further reformulated as an iteratively reweighted convex quadratic optimization problem. The multi-period portfolio selection problem is then solved sequentially based on a defined event-trigger function and a quadratic optimizer. The experiments are done on eight world stock markets datasets to show the capabilities of the proposed approach in calculating market indices and equal-weighted portfolios in terms of Sharpe and Sortino ratios.

Multi-period portfolio selection based on uncertainty theory with bankruptcy control and liquidity

Due to the impact of uncertain events, such as the 2008 financial crisis and the outburst of COVID-19 pandemic, the experts’ evaluations information is becoming increasingly important. This paper considers a multi-period portfolio optimization problem under uncertain circumstance, and the return rates of risky securities are regarded as uncertain variables, where the uncertainty theory is used to deal with experts’ evaluations. In light of the complexity of financial markets, we formulate an uncertain multi-period mean-entropy-variance model, where bankruptcy, liquidity, diversification and self-financing are considered as realistic constraints. Furthermore, the maximum return and the minimum risk are both achieved in a single-objective model through the normalization method. Then the equivalent deterministic forms of two secondary models for main model are provided. In addition, we develop a modified root system growth algorithm, which is more suitable for the proposed model. Finally, the effectiveness of the proposed model and designed algorithm is confirmed by numerical simulations.

Multi-period uncertain portfolio selection model with prospect utility function.

In this paper, we discuss a multi-period portfolio optimization problem based on uncertainty theory and prospect theory. We propose an uncertain multi-period portfolio selection model, in which the return utility and risk of investment are measured by prospect theory utility function and uncertain semivariance. More realistically, the influence of transaction costs and bankruptcy of investor are also considered. Moreover, to solve the portfolio model, this paper designs a new artificial bee colony algorithm by combining sine cosine search method. Finally, a numerical experiment is presented to demonstrate the proposed model and the effectiveness of the designed algorithm.

Multiagent-based deep reinforcement learning for risk-shifting portfolio management

The growing popularity of quantitative trading in pursuit of a systematic and algorithmic approach to investment has drawn considerable attention among traders and investment firms. Consequently, an effective computational method for evaluating potential risk factors and returns is crucial for the development of algorithmic trading strategies. In traditional finance and financial engineering research, statistical approaches have been widely applied to quantitative analysis. Meanwhile, investor demand for quantitative hedge funds has surged worldwide. In the current study, the multiperiod portfolio selection problem was considered in terms of the realistic transaction cost model, which is a major concern for quantitative hedge fund managers. We developed a dedicated multiagent-based deep reinforcement learning framework with a two-level nested agent structure to determine effective portfolio management methods with different objectives. In addition, we proposed a specially-designed reward function for investment performance evaluation and a novel policy network structure for trading decision-making. To efficiently identify specific asset attributes in a portfolio, each agent is equipped with a refined deep policy network and a special training method that enables the proposed reinforcement learning agent to learn risk transfer behaviors. The results revealed the effectiveness of our proposed framework, which outperformed several established or representative portfolio selection strategies.

An Event-Triggered Iteratively Reweighted Convex Optimization Approach to Multi-Period Portfolio Selection

An Event-Triggered Iteratively Reweighted Convex Optimization Approach to Multi-Period Portfolio Selection

Multi-period portfolio selection under the coherent fuzzy environment with dynamic risk-tolerance and expected-return levels

We discuss the portfolio selection problems in which the uncertainty of future returns and the heterogeneity of investor attitudes towards the stock market (optimistic–pessimistic–neutral) are captured by coherent fuzzy numbers. Two coherent fuzzy multi-period portfolio selection models are developed from the perspectives of wealth maximization and risk minimization. Given that the constraint levels regarding risk and return of the current period tend to be influenced by the outcome of the previous period, the dynamic risk-tolerance and expected-return levels are integrated into the portfolio modeling. Practical constraints and transaction costs are also taken into account, which enables the models more effective and lifelike in simulating the real-world trading of the stock market. The empirical studies based on two large data sets are presented to illustrate the applicability of the proposed models. To survey the models’ performance, several portfolio evaluation criteria are used to conduct out-of-sample analysis. The results show outstanding performance of the presented models with dynamic strategies over conventional ways (static risk-tolerance and expected-return levels) on most of the indicators. This research offers references for investors with different attitudes to make long-term investment decisions, and is an effective supplement to behavioral portfolio selection research based on bounded rationality under uncertainty.

A new approach to the bi-criteria multi-period fuzzy portfolio selection

The proposed approach to the bi-criteria multi-period fuzzy portfolio selection is based on the observation that the treating the variance as a measure of portfolio risk provides sometimes questionable results. Therefore, the simple criteria of portfolio risk and return are proposed. Based on them and three popular methods for local criteria aggregation, a new fuzzy portfolio selection one-period model has been developed. It is shown that this model provides reasonable results coinciding with common sense. Based on this model, a new two-stage bi-criteria optimization approach to portfolio selection has been developed, tested and used as a main component of proposed multi-period portfolio selection model. A method for obtaining fuzzy distributions of stocks returns based on real market data is developed and used for the optimal portfolio selection. In some cases, to make the presentation of developed methods features more transparent, the problem simplification, when all market decisions (Buy, Sell and Hold) were considered as right ones was used. But finally, the real-world market decisions which are generated using the stock trading expert system based on the real market data were used for the portfolio selection. To do this, the known stock trading expert system has been applied, which was adapted for the conditions of the considered stock markets (NYSE and NASDAQ) providing best results after optimization. Using the real-world examples, it is shown that incorporating the stock signals (decisions) Buy, Sell and Hold in the multi-period portfolio selection models improves strongly the models results making them closer to reality.

An analytic solution for multi-period uncertain portfolio selection problem

An analytic solution for multi-period uncertain portfolio selection problem

Dynamic multi-period sparse portfolio selection model with asymmetric investors’ sentiments

Asymmetric investors’ sentiments on returns and risks play an important role in updating the portfolio strategies in multi-period portfolio selection problems. By introducing the Prospect Theory to measure the asymmetric investors’ sentiments, a dynamic sentiment-adjusted model (DSAM) is proposed to sparse portfolio selection problem over multiple periods, in which the objective is to minimize the risk of the portfolio. As we focus on the sparse portfolio, a l0 constraint is added to our model. The l0 constraint represents that we can only purchase at most k securities from N candidate securities, in which k is a small number compared to N. Since the objective function of the sparse portfolio with l0 constraint is NP-hard, and could not be solved by the Deep Learning algorithms. The stochastic neural networks algorithm with re-parametrisation trick (SNNrP) is introduced to solve the DSAM. The back-testing framework of our paper includes a multi-period portfolio selection model, in which asymmetric investors’ sentiments are modeled to iterate investors’ expected return level each period. In the back-testing framework, we conduct the experiments for different investment periods with different investors’ sentiments. The experimental results for the Nasdaq and CSI 300 data sets show that, on average, compared with the traditional Mean–variance model, the terminal return and risk obtained by the DSAM model outperforms by 9% and 11.75%.