Multi-period Portfolio Optimization Research Articles

A Distributed Event-Triggered Approach for Decentralized Multi-Period Portfolio Optimization via the Alternating Direction Method of Multipliers

A Distributed Event-Triggered Approach for Decentralized Multi-Period Portfolio Optimization via the Alternating Direction Method of Multipliers

Multi-period portfolio optimization: A parallel NSGA-III algorithm with real-world constraints

This study introduces an enhanced algorithm that integrates the parallel processing capabilities of PGAs with the multi-objective optimization strengths of NSGA-III, designed for multi-period optimization. We extend optimization objectives to T + 1 by minimizing risk over T periods and maximizing the terminal return, with a practical constraint on portfolio loss. It consistently outperforms the standard NSGA-III algorithm in both risk reduction and return optimization, especially when portfolios are adjusted quarterly. We also pinpoint optimal algorithmic parameters: a population size of 70 and 10 % migration rate. Overall, our research offers invaluable insights into real-world investment scenarios, serving both academic and industry interests.

Multi-period portfolio optimization using a deep reinforcement learning hyper-heuristic approach

Portfolio optimization concerns with periodically allocating the limited funds to invest in a variety of potential assets in order to satisfy investors’ appetites for risk and return goals. Recently, Deep Reinforcement Learning (DRL) has shown its promising capabilities in sequential decision making problems. However, traditional DRL algorithms directly operate in the space of low-level actions, which exhibits poor scalability and becomes intractable in real-world problem instances when the dimensionality of the environment increases. To deal with this, in this work, a novel DRL hyper-heuristic framework is proposed for multi-period portfolio optimization problem. Instead of exploiting the entire action domain, our proposed approach is more effective by searching for low-level well-developed trading strategies. In addition, our proposed approach is data-driven and respects the nature of the problem by taking advantage of expert domain knowledge and posing it multidimensional states to further leverage additional diverse information from alternative views of the environment. The proposed approach is evaluated on five real-world capital market problem instances and numerous experimental results demonstrate our proposed method can achieve notable performance gains compared to state-of-art trading strategies as well as traditional DRL baseline method. The data we used are from five stock indices, covering the period from the 2012 to 2022. Our study can have salient policy implications for investment strategy formulation and effective regulatory frameworks establishment.

Multi-period portfolio optimization based on credibilistic lower and upper VaR ratios

Emerging markets, such as the Chinese financial market, are occasionally subject to extreme risk events that result in investor losses during the investment process. To address the challenge of investment selection amidst market fluctuations, considering the fuzzy uncertainty and tail risk compensation based on the asymmetric perspective, we propose to use the lower VaR ratio and the upper VaR ratio as investment objectives to construct a multi-period credibilistic portfolio selection model. The study reveals that the cumulative returns and terminal wealth of the constructed model surpassed those of the benchmark models, delivering greater social and economic welfare to investors. During extreme events, investors could promptly adjust their portfolio structure to achieve higher investment returns. Investors who prefer the lower VaR ratio tend to make conservative investment decisions and allocate a higher proportion to defensive assets, such as bonds and risk-free assets. Conversely, investors who favor the upper VaR ratio are inclined to adopt aggressive investment strategies and allocate a larger proportion to high-risk stocks. The findings demonstrate that the proposed model offers differentiated investment decisions, and the research conclusions serve as valuable references for investors engaged in multi-period asset allocation and risk management.

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-Period Portfolio Optimization under Cash-In Strategies

Portfolio optimization has been crucial in its applications to finance. Investors allocate capital in terms of various assets and wisely adjust each proportion in quest of higher returns and lower risks. However, common optimization strategies are usually short- sighted, lacking the ability of gaining higher returns over a long period. This paper addresses Multi-Period Portfolio Optimization problem in more applicable settings to provide efficient strategies. Firstly, a summary of conclusions from former works and scholars is given. Since most previous works assume self-financing conditions, this work extends this constraint and considers more complex cash-in and cash-out situations. It also derives the expression of the optimal policy for trading at each period as well as the objective functions. Finally, numerical experiments are done under both self-financing and cash-in situations to prove the validity of conclusions. This work has profound implications in finance because it adopts conditions more consistent with real-world scenarios and provides more farsighted strategies. Moreover, the solution offers a prototype for similar optimization in other fields like electrical engineering and stochastic processes.

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.

Sparse Approximations with Interior Point Methods

Large-scale optimization problems that seek sparse solutions have become ubiquitous. They are routinely solved with various specialized first-order methods. Although such methods are often fast, they usually struggle with not-so-well-conditioned problems. In this paper, specialized variants of an interior point-proximal method of multipliers are proposed and analyzed for problems of this class. Computational experience on a variety of problems, namely, multiperiod portfolio optimization, classification of data coming from functional magnetic resonance imaging, restoration of images corrupted by Poisson noise, and classification via regularized logistic regression, provides substantial evidence that interior point methods, equipped with suitable linear algebra, can offer a noticeable advantage over first-order approaches.

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.

A kernel-based control approach for multi-period assets allocation based on lower partial moments

In quantitative finance, multi-period portfolio optimization can be reformulated as a stochastic optimal control problem, and standard feedback tools can be employed for its analysis. The performance of the trading solutions strongly depend on the quality of the model of the returns. Therefore, data-driven solutions have been recently proposed to optimize simple-linear allocation policies, based only on a set of possible market scenarios. In this work, kernel-based methods are proposed to design more complex and effective control actions, providing better trade-offs in terms of risk and investment performance with respect to linear ones, by preserving convexity. The proposed approach relies on the minimization of the Lower Partial Moments (LPM) risk measure. The effectiveness of the method is shown on a set of real historical financial data.

Multi-period portfolio optimization using model predictive control with mean-variance and risk parity frameworks

We employ model predictive control for a multi-period portfolio optimization problem. In addition to the mean-variance objective, we construct a portfolio whose allocation is given by model predictive control with a risk-parity objective, and provide a successive convex program algorithm that provides 30 times faster and robust solutions in the experiments. We provide a comprehensive comparison of the models in regard of planning horizon, parameter estimation, as well as objective function choice. Computational results on a multi-asset universe show that multi-period models perform better than their single period counterparts in out-of-sample period, 2006–2020, in the presence of market impact costs. The out-of-sample risk-adjusted performance of both mean-variance and risk-parity formulations beat the fix-mix benchmarks, and achieve Sharpe ratio of 0.64 and 0.97, respectively. We also include tests on different asset universes (Fama French industry portfolios) and alternative parameter estimation methods (Bayes-Stein and Black-Litterman) with consistent findings.

Multi-period uncertain portfolio optimization model with minimum transaction lots and dynamic risk preference

An accurate variable description of security returns is necessary to establish a valid portfolio optimization model. It is usually assumed to be a random variable when the historical data of security returns are sufficient. However, when historical data are too limited to estimate its probability distribution, uncertain variables are employed to characterize security returns to be effective. This paper focuses on a multi-period portfolio optimization problem in uncertain environment with the consideration of minimum transaction lots. Different from the previous multi-period work assuming the total available wealth in the end of the investment horizon is consistently in an exponential format, our study provides a simplified additive format of the total wealth, which may make the process of experimental calculation concise, since it is a linear function of decision variables. Besides, we consider the investor’s dynamic risk preference along the whole investment horizon. With these realistic constraints derived from the complex financial markets, we build a multi-period mean-VaR (value-at-risk) model with the objective of maximizing the terminal wealth under the risk control over the whole investment. Genetic algorithm is used to solve the proposed model, and two numerical examples are given to illustrate the effectiveness of the proposed approach.

Black–Litterman and Beyond: The Bayesian Paradigm in Investment Management

The Black–Litterman model is one of the most popular models in quantitative finance, with numerous theoretical and practical achievements. From the standpoint of investment theory, the Black–Litterman model allows seamless incorporation of Bayesian statistics into the portfolio optimization process. From a practical standpoint, it provides portfolio managers with a structured approach to express subjective views, thereby freeing their investment processes from a total reliance on backward-looking historical data. In this article, the authors provide an overview of the original Black–Litterman model and its various extensions and enhancements addressing issues in real-world trading and investment management. <b>TOPICS:</b>Statistical methods, portfolio construction, performance measurement <b>Key Findings</b> ▪ The authors provide an overview of the original Black–Litterman model and its various extensions and enhancements, addressing issues in real-world trading and investment management. ▪ Many important practical considerations in implementing the Black-Litterman model are discussed including choice of priors, view generation, and transaction costs. ▪ Particular emphasis is given to the extensions of the Black-Litterman model of significant practical relevance to today’s investors such as factor models, model misspecification, non-normality, and multiperiod portfolio optimization.

Multi-period Portfolio Optimization using Model Predictive Control with Mean-Variance and Risk Parity Frameworks

We employ model predictive control for a multi-period portfolio optimization problem. In addition to the mean-variance objective, we construct a portfolio whose allocation is given by model predictive control with a risk-parity objective, and provide a successive convex program algorithm that provides 30 times faster and robust solutions in the experiments. Computational results on the multi-asset universe show that multi-period models perform better than their single period counterparts in out-of-sample period, 2006-2020. The out-of-sample risk-adjusted performance of both mean-variance and risk-parity formulations beat the fix-mix benchmark, and achieve Sharpe ratio of 0.64 and 0.97, respectively.

Multiperiod portfolio selection models under uncertain measure and with multiple criteria

This paper explores a multiperiod portfolio optimization problem under uncertain measure involving background risk, liquidity constraints and V-shaped transaction costs. Unlike traditional studies, we establish multiperiod mean-variance portfolio optimization models with multiple criteria in which security returns, background asset returns and turnover rates are assumed to be uncertain variables that can be estimated by experienced experts. When the returns of the securities and background assets follow normal uncertainty distributions, we use the deterministic forms of the multiperiod portfolio optimization model. The uncertain multiperiod portfolio selection models are practical but complicated. Therefore, the models are solved by employing a genetic algorithm. The uncertain multiperiod model with multiple criteria is compared with an uncertain multiperiod model without background risk and an uncertain multiperiod model without liquidity constraint respectively, we discuss how background risk and liquidity affect optimal terminal wealth. Finally, we give two numerical examples to demonstrate the effectiveness of the proposed approach and models.

Effective solving Portfolio Optimization Problems by means of a Multi-Period Diversification model

Abstract A multi-period model for Portfolio optimization problems including a diversification quadratic constraint is considered in this paper. It is designed to minimize the risk, imposing a restriction on the return to be not less than a desired value. An illustrative example with 6 assets, based on data for 131 months historical period is constructed. The formulated optimization problem is solved for 10 different values of desired return by means of the Interior point method in Matlab’s fmincon solver. The experimental results show that the proposed optimization model is effective and successful in solving constrained multi-period portfolio optimization problems.

Econometric Model Used in the Portfolio Optimization over Several Periods

"The classic problem of optimizing a portfolio can be extended to a multi-stage programming problem. The purpose of the multi-period portfolio optimization problem is to determine the optimal portfolio for a certain finite time horizon. In a multi-period model in which investors are allowed to change the composition of the portfolio, it is essential to take into account trading costs, a solution in this regard being the use of tree-type scenarios. The study undertaken by the authors considered the construction of a portfolio optimization model in case there is a certain constraint on returns. ARMA type processes were used to model the conditional mean equation."

Multi-Period Portfolio Optimization with Investor Views under Regime Switching

We propose a novel multi-period trading model that allows portfolio managers to perform optimal portfolio allocation while incorporating their interpretable investment views. This model’s significant advantage is its intuitive and reactive design that incorporates the latest asset return regimes to quantitatively solve managers’ question: how certain should one be that a given investment view is occurring? First, we describe a framework for multi-period portfolio allocation formulated as a convex optimization problem that trades off expected return, risk and transaction costs. Using a framework borrowed from model predictive control introduced by Boyd et al., we employ optimization to plan a sequence of trades using forecasts of future quantities, only the first set being executed. Multi-period trading lends itself to dynamic readjustment of the portfolio when gaining new information. Second, we use the Black-Litterman model to combine investment views specified in a simple linear combination based format with the market portfolio. A data-driven method to adjust the confidence in the manager’s views by comparing them to dynamically updated regime-switching forecasts is proposed. Our contribution is to incorporate both multi-period trading and interpretable investment views into one framework and offer a novel method of using regime-switching to determine each view’s confidence. This method replaces portfolio managers’ need to provide estimated confidence levels for their views, substituting them with a dynamic quantitative approach. The framework is reactive, tractable and tested on 15 years of daily historical data. In a numerical example, this method’s benefits are found to deliver higher excess returns for the same degree of risk in both the case when an investment view proves to be correct, but, more notably, also the case when a view proves to be incorrect. To facilitate ease of use and future research, we also developed an open-source software library that replicates our results.

Multi-period portfolio optimization using coherent fuzzy numbers in a credibilistic environment

In this paper, we use an extension of fuzzy numbers, called coherent fuzzy numbers, to model asset returns and an investor’s perception of the stock market (pessimistic, optimistic, or neutral) simultaneously. Two multi-period multi-objective portfolio optimization models are formulated using mean absolute semi-deviation and Conditional Value-at-Risk (CVaR) as risk measures, respectively. We aim to provide more flexibility to the investor in specifying the risk tolerance and devise optimum investment plans for different investment horizons. The proposed models also incorporate bound, cardinality, and skewness constraints for each investment period to capture various stock market scenarios. A real-coded genetic algorithm is employed to solve the resultant models. Two real-life case studies involving 20 assets of the National Stock Exchange (NSE), India, and another involving 50 assets listed in the S&P 500 and NASDAQ-100 indexes have been provided to illustrate the efficacy and advantages of the models. An in-sample and out-of-sample analysis have been done for both the models to analyze the performance in the real-world scenario. The conclusion drawn from the analysis strongly emphasizes on accurately assessing the current stock market prospects, i.e., adopting the right attitude (pessimistic, optimistic, or neutral), is of paramount importance and must be included in the portfolio optimization problem.

A Case Study in Multiperiod Portfolio Optimization: A Classic Problem Revisited

Conventional wisdom holds that multiperiod portfolio optimization problems are best, if not only, solved by dynamic programming. But dynamic programming suffers from the curse of dimensionality whereby optimization becomes intractable as time horizon and number of assets increase, thereby limiting its practical applications. In this paper I show for a classic multiperiod investment problem that a feed-forward, open-loop procedure, amenable to solution by conventional methods (e.g. calculus of variations) and not subject to the curse of dimensionality, generates `here and now' portfolios identical to those generated by the dynamic programming approach. The analytic results in this paper demonstrate that for this classic problem a feed forward approach is not inferior to the more common backward induction approach, suggesting that an `open-loop with recourse' process is a viable closed-loop approach for some practically useful multiperiod investment problems.