Dynamic Portfolio Optimization Research Articles

Enhancing investment strategies through machine learning: A comprehensive analysis across market sectors

Abstract. This study presents a detailed exploration of the application of machine learning (ML) models to optimize investment strategies across various market sectors, including equity markets, fixed income and derivatives, and the volatile cryptocurrency markets. We evaluate three primary ML models: linear regression, decision trees, and neural networks, based on their predictive accuracy, computational efficiency, and robustness to market volatility. A rigorous process involving backtesting and cross-validation assesses each model's performance. Our framework encompasses data preprocessing, feature engineering, model implementation, and a nuanced approach to risk assessment integrating Value at Risk (VaR) and the Sharpe Ratio. We demonstrate the models' effectiveness in predicting stock prices, interest rates, and cryptocurrency price movements. The application of our ML framework led to the development of dynamic portfolio optimization strategies that significantly outperform traditional methods. This study contributes to the understanding of ML's potential to revolutionize investment strategies, providing a foundation for future research and practical applications in financial markets.

Comprehensive Analysis of Portfolio Optimization Using the Markowitz and Index Models

Harry Markowitz’s 1952 systematic approach to optimizing the trade-off between risk and return, known as Modern Portfolio Theory (MPT), revolutionized investment strategy. The objective of this final project is to apply the Markowitz and index models to provide a comprehensive analysis of portfolio optimization and conduct a comparative examination of the two models. By utilizing 20 years of historical daily total return data for 10 selected stocks within the S&P 500 Index, the study will develop optimal portfolios under various realistic constraints, such as typical leverage limitations and short selling restrictions. Additionally, the study evaluates the performance of these models and demonstrates that while index models offer computational simplicity, there are some drawbacks. In this scenario, a Markowitz model will generally provide a more precise risk-return optimization. Finally, the findings highlight the substantial influence of real-world constraints on portfolio management, which can significantly alter the efficient frontier and the structure of the optimal portfolio. This article, in the chapter on future research, proposes some possible future research directions, including the integration of behavioral finance elements and dynamic portfolio optimization, and furthermore discusses the implications of these research results.

A Global-in-Time Neural Network Approach to Dynamic Portfolio Optimization

ABSTRACT We discuss a neural network approach, which does not rely on dynamic programming techniques, to solve dynamic portfolio optimization problems subject to multiple investment constraints. The approach allows for objectives of a very general form encompassing both time-consistent and time-inconsistent objectives, as well as objectives requiring multi-level optimization. The number of parameters of the neural network remains independent of the number of portfolio rebalancing events. Compared to reinforcement learning, this technique avoids the computation of high-dimensional conditional expectations. The approach remains practical when considering large numbers of underlying assets, long investment time horizons or very frequent rebalancing events. We prove convergence of the numerical solution to the theoretical optimal solution of a large class of problems under fairly general conditions, and present ground truth analyses for a number of popular formulations, including mean-variance, mean-semi-variance, and mean-conditional value-at-risk problems. Numerical experiments show that if the investment objective functional is separable in the sense of dynamic programming, the correct time-consistent optimal investment strategy is recovered, otherwise we obtain the correct pre-commitment (time-inconsistent) investment strategy. This method is agnostic as to the underlying data generating assumptions, and results are illustrated using (i) parametric models for underlying asset returns, (ii) stationary block bootstrap resampling of empirical returns, and (iii) generative adversarial network (GAN)-generated synthetic asset returns.

Portfolio optimization with feedback strategies based on artificial neural networks

Dynamic portfolio optimization has significantly benefited from a wider adoption of deep learning (DL). While existing research has focused on how DL can applied to solving the Hamilton–Jacobi–Bellman (HJB) equation, some very recent developments propose to forego the derivation of HJB in favor of empirical utility maximization over dynamic allocation strategies expressed through artificial neural networks. In addition to simplicity and transparency, this approach is universally applicable, as it is essentially agnostic about market dynamics. We apply it to optimal portfolio allocation between cash account and risky asset following Heston model. The results appear on par with theoretical ones.

Dynamic portfolio optimization with the MARCOS approach under uncertainty

This paper introduces a dynamic portfolio selection approach that integrates the robustness of interval type-2 fuzzy sets (IT2FSs) with the flexibility of the MARCOS (Measurement of Alternatives and Ranking according to COmpromise Solution) method, offering a novel framework for asset evaluation amidst uncertainty. The IT2FSs enhance the adaptability of asset criteria representation, while the innovative application of MARCOS within the IT2FS environment refines the asset selection process. The weighted semi-absolute deviation metric is embraced to capture portfolio risk characteristic, which ingeniously harnesses the utility function values derived from the IT2F-MARCOS framework to delineate the anticipated return profile. On this basis, a dynamic bi-objective portfolio allocation model with realistic constraints and dynamic risk preference is formulated to rebalance portfolio periodically. Empirical evidence demonstrates the robustness and effectiveness of this approach compared to benchmark indexes, different allocation strategies, and the TOPSIS-based selection method, offering significant advancements in portfolio optimization for investors navigating uncertain markets. This study endeavors to contribute to the field of portfolio management, providing a thoughtful approach that enhances both theoretical understanding and practical application.

Portfolio Optimization Based on Rolling Window Using 5 Stocks

This paper aims to explore a method of constructing dynamically adjusted investment portfolios through the combination of rolling windows and mean-variance models. The construction of investment portfolios plays a crucial role in financial markets by effectively diversifying risks and achieving stable investment returns. This study analyzed adjusted closing price data from five stocks (AAPL, JPM, JNJ, XOM, and PG), sourced from Yahoo Finance. The rolling window method was employed to predict future stock prices and construct investment portfolios based on these predictions. This study calculated annualized average return and covariance matrix for each window. The mean-variance model and optimization algorithms were then used to determine the optimal weights for daily portfolio composition. The results demonstrate the high accuracy of the rolling window method in predicting short-term stock prices. Notably, Procter & Gamble (PG) and Johnson & Johnson (JNJ) exhibited the lowest prediction errors. Investment portfolios based on rolling window predictions performed well over a certain period. Nevertheless, the S&P 500 index did not show a substantial disadvantage compared to their long-term performance. This research provides dynamic portfolio optimization methods of practical value for investors in financial markets.

The role of ESG-based assets in generating the dynamic optimal portfolio in Indonesia

The role of ESG-based assets in generating the dynamic optimal portfolio in Indonesia

Bayesian Learning in an Affine GARCH Model with Application to Portfolio Optimization

This paper develops a methodology to accommodate uncertainty in a GARCH model with the goal of improving portfolio decisions via Bayesian learning. Given the abundant evidence of uncertainty in estimating expected returns, we focus our analyses on the single parameter driving expected returns. After deriving an Uncertainty-Implied GARCH (UI-GARCH) model, we investigate how learning about uncertainty affects investments in a dynamic portfolio optimization problem. We consider an investor with constant relative risk aversion (CRRA) utility who wants to maximize her expected utility from terminal wealth under an Affine GARCH(1,1) model. The corresponding stock evolution, and therefore, the wealth process, is treated as a Bayesian information model that learns about the expected return with each period. We explore the one- and two-period cases, demonstrating a significant impact of uncertainty on optimal allocation and wealth-equivalent losses, particularly in the case of a small sample size or large standard errors in the parameter estimation. These analyses are conducted under well-documented parametric choices. The methodology can be adapted to other GARCH models and applications beyond portfolio optimization.

Risk-averse Reinforcement Learning for Portfolio Optimization

This investigation explores Reinforcement Learning (RL) for dynamic portfolio optimization with risk assessment. The challenges include market complexity, uncertain reactions, and regulatory requirements for risk-averse decisions. Our solution leverages Bayesian Neural Network (BNN) to capture uncertainties. We successfully implemented a risk-averse Reinforcement Learning algorithm, achieving 18 percent lower risk. Reinforcement Learning with risk-aversion shows promise for optimizing portfolios for risk-averse investors.

POLYNOMIAL UTILITY

We approximate the utility function by polynomial series and solve the related dynamic portfolio optimization problems. We study the quality of the Taylor and Bernstein series approximation in response to the points and degrees of the expansions and generalize from earlier expansions applied to portfolio optimization. The issue of time inconsistency, arising from a dynamically adapted center of the expansion, is approached by equilibrium theory. We present new ways of constructing polynomial utility functions and study their pitfalls and potentials. In the numerical study, we focus on two specific utility functions: For power utility, access to the optimal portfolio allows for a complete illustration of the approximations; for the S-shaped utility function of prospect theory, the use of equilibrium theory allows for approximating the solution to the (obviously interesting but yet unsolved) case of current wealth as a dynamic reference point.

Central bank asset purchases, banks’ risky security holdings and profitability: Macro and micro evidence from Japan and the U.S.

By focusing exclusively on risky securities and conducting cross-country analyses at both macro and micro levels -- a different approach than those employed in the existing literature -- this paper attempts to shed light on the under-explored yet important issue of banks’ dynamic portfolio optimization in times of unconventional monetary policy. It explores how and why banks adjust their risky security holdings in the context of central bank asset purchases. The macro and micro evidence from Japan and the U.S. suggests that banks may adjust their risky security holdings to optimize their profitability over the post-global financial crisis period. Interesting differences are also found in the pattern of adjustment of risky security holdings between the two countries. These findings provide new insights not only into the risk-taking and portfolio-rebalancing channels of unconventional monetary policy, but also into the link between unconventional monetary policy and bank profitability.

Meta-heuristics for portfolio optimization

AbstractPortfolio optimization has been studied extensively by researchers in computer science and finance, with new and novel work frequently published. Traditional methods, such as quadratic programming, are not computationally effective for solving complex portfolio models. For example, portfolio models with constraints that introduce nonlinearity and non-convexity (such as boundary constraints and cardinality constraints) are NP-Hard. As a result, researchers often use meta-heuristic approaches to approximate optimal solutions in an efficient manner. This paper conducts a comprehensive review of over 140 papers that have applied evolutionary and swarm intelligence algorithms to the portfolio optimization problem. These papers are categorized by the type of portfolio optimization problem considered, i.e., unconstrained or constrained, and are further categorized by single-objective and multi-objective approaches. Furthermore, the various portfolio models used, as well as the constraints, objectives, and properties in which they differ, are also discussed in a detailed analysis. Based on the findings of the reviewed work, guidance for future research in portfolio optimization is given. Possible areas for future work include dynamic portfolio optimization, predictive pricing, the further investigation of multi-objective approaches.

Multi-period power utility optimization under stock return predictability

In this paper, we derive an analytical solution to the dynamic optimal portfolio choice problem in the case of an investor equipped with a power utility function of wealth. The results are established by solving the Bellman backward recursion under the assumption that the vector of asset returns follows a vector-autoregressive process with predictable variables. In an empirical study, the performance of the derived solution is compared with the one obtained by applying the numerical method. The comparison is performed in terms of the final wealth and its expected utility. It is documented that the application of the analytical solution to the multi-period portfolio choice problem leads to higher values of both the final wealth and the expected utility.

Optimal investment strategies and profit shares distributions: A stochastic control approach

With the advent of Solvency II regulations in 2016, European insurance companies are tasked with calculating technical provisions by either using a standard formula given by regulators or developing their own internal model. This paper first reviews a model adapted to Solvency II regulations for an insurance company’s participating contracts, which was proposed by Hainaut [1]. The objective of the insurer is to optimize profit shares distributions and asset allocation strategies. In this setting, a stochastic control approach is used to formulate a dynamic portfolio optimization problem. The insurer invests in an account or bond that is risk-free, she also invests in a risky asset that is based on the Black-Scholes model. A closed form solution to the problem under a power utility function on future profit shares and the insurer’s future economic wealth is calculated. The paper ends with a numerical example, where Tesla and Apple share prices are used as the insurer’s risky asset, in order to test the usability of the model in industry.

Distorted probability operator for dynamic portfolio optimization in times of socio-economic crisis

A robust optimal control of discrete time Markov chains with finite terminal T and bounded costs or wealth using probability distortion is studied. The time inconsistency of these distortion operators and hence its lack of dynamic programming are discussed. Due to that, dynamic versions of these operators are introduced, and its availability for dynamic programming is demonstrated. Based on dynamic programming algorithm, existence of the optimal policy is justified and an application of the theory to portfolio optimization along with a numerical study is also presented.

Dynamic portfolio optimization with inverse covariance clustering

Market conditions change continuously. However, in portfolio investment strategies, it is hard to account for this intrinsic non-stationarity. In this paper, we propose to address this issue by using the Inverse Covariance Clustering (ICC) method to identify inherent market states and then integrate such states into a dynamic portfolio optimization process. Extensive experiments across three different markets, NASDAQ, FTSE and HS300, over a period of ten years, demonstrate the advantages of our proposed algorithm, termed Inverse Covariance Clustering-Portfolio Optimization (ICC-PO). The core of the ICC-PO methodology concerns the identification and clustering of market states from the analytics of past data and the forecasting of the future market state. It is therefore agnostic to the specific portfolio optimization method of choice. By applying the same portfolio optimization technique on a ICC temporal cluster, instead of the whole train period, we show that one can generate portfolios with substantially higher Sharpe Ratios, which are statistically more robust and resilient with great reductions in the maximum loss in extreme situations. This is shown to be consistent across markets, periods, optimization methods and selection of portfolio assets.

Dynamic optimal mean-variance portfolio selection with stochastic volatility and stochastic interest rate

Dynamic optimal mean-variance portfolio selection with stochastic volatility and stochastic interest rate

Dynamic portfolio optimization using technical analysis‐based clustering

An accurate prediction of asset prices is perhaps the biggest challenge of any study in portfolio optimization. Asset prices are affected by several random and nonrandom factors, which makes them difficult to forecast. This paper proposes a two-phase dynamic portfolio optimization approach. In the first phase, assets are clustered into buy, sell, and hold groups using technical indicators. We provide a methodology to integrate the investor attitude (optimistic, pessimistic, or neutral) during the clustering phase. In the second phase, we input the clustered groups into a portfolio optimization model to obtain the optimum asset allocations. We use coherent fuzzy numbers to model the asset returns to integrate the investor attitude in this phase. The optimization model is solved using a genetic algorithm. The portfolios are rebalanced at regular intervals as new data becomes available. We illustrate the proposed methodology on a 100-asset problem of the US stock market. We analyze the real-world performance of the obtained portfolios. We compare the performance of the proposed approach with the mean–variance model, and other portfolios, such as the naïve portfolio and the NASDAQ-100 index.

Optimal Dynamic Momentum Strategies

Path Dependence of Optimal Dynamic Momentum Strategies The momentum effect has been studied by a tremendous number of papers, but surprisingly, there is little research on optimal momentum strategies. In “Optimal Dynamic Momentum Strategies,” Li and Liu explicitly solve the optimal dynamic portfolio problem when a risky asset has momentum. They show that, to optimally exploit momentum, one needs to account for path dependence, as well as momentum. In contrast, the momentum strategies discussed in most papers exploit only momentum. The optimal portfolio weight also significantly differs from that in the classic framework of Merton. Due to their path dependence, optimal portfolio weights have a wide distribution for a given level of momentum; for example, investors may short the risky asset if it has rebound price paths but leverage if it has hump-shaped price paths. This effect tends to be the most significant after large price swings. Path dependence is described through explicit formulas as well as heuristic statistics.

Dynamic portfolio optimization with real datasets using quantum processors and quantum-inspired tensor networks

In this paper we tackle the problem of dynamic portfolio optimization, i.e., determining the optimal trading trajectory for an investment portfolio of assets over a period of time, taking into account transaction costs and other possible constraints. This problem is central to quantitative finance. After a detailed introduction to the problem, we implement a number of quantum and quantum-inspired algorithms on different hardware platforms to solve its discrete formulation using real data from daily prices over 8 years of 52 assets, and do a detailed comparison of the obtained Sharpe ratios, profits, and computing times. In particular, we implement classical solvers (Gekko, exhaustive), D-wave hybrid quantum annealing, two different approaches based on variational quantum eigensolvers on IBM-Q (one of them brand-new and tailored to the problem), and for the first time in this context also a quantum-inspired optimizer based on tensor networks. In order to fit the data into each specific hardware platform, we also consider doing a preprocessing based on clustering of assets. From our comparison, we conclude that D-wave hybrid and tensor networks are able to handle the largest systems, where we do calculations up to 1272 fully-connected qubits for demonstrative purposes. Finally, we also discuss how to mathematically implement other possible real-life constraints, as well as several ideas to further improve the performance of the studied methods.