Markowitz Mean-variance Model Research Articles

APPLICATION OF QUADRATIC PROGRAMMING ON PORTFOLIO OPTIMIZATION USING WOLFE’S METHOD AND PARTICLE SWARM OPTIMIZATION ALGORITHM

Stock portfolios can be modeled into quadratic programming problems using the Markowitz mean-variance model. Quadratic programming problems can be solved using two methods, namely classical and heuristic methods. In this research, the classical method uses Wolfe’s method, while the heuristic method uses the particle swarm optimization (PSO) algorithm. This research aims to determine optimal results in portfolio problems using two methods, namely Wolfe’s method and the PSO algorithm. The data used in this research is data from 10 stock companies that distribute the highest dividends in the IDX High Dividend 20 category for the 2022 period. The research results discuss the portfolios of PT Astra International Tbk and PT. Indo Tambangraya Megah Tbk. Based on the result, using Wolfe’s method, the ASII and ITMG stock portfolios are obtained, namely the optimal proportion of ASII shares = 0.76401 or 76.401% and ITMG shares = 0.23598 or 23.598%, while the PSO algorithm obtains a portfolio of ASII and ITMG shares, namely ASII shares = 75.02% and ITMG shares = 24.98%. Compared to Wolfe’s method, the PSO algorithm has a smaller Z value 5.7.

Cardinality Constrained Portfolio Optimization via Alternating Direction Method of Multipliers.

Inspired by sparse learning, the Markowitz mean-variance model with a sparse regularization term is popularly used in sparse portfolio optimization. However, in penalty-based portfolio optimization algorithms, the cardinality level of the resultant portfolio relies on the choice of the regularization parameter. This brief formulates the mean-variance model as a cardinality ( l0 -norm) constrained nonconvex optimization problem, in which we can explicitly specify the number of assets in the portfolio. We then use the alternating direction method of multipliers (ADMMs) concept to develop an algorithm to solve the constrained nonconvex problem. Unlike some existing algorithms, the proposed algorithm can explicitly control the portfolio cardinality. In addition, the dynamic behavior of the proposed algorithm is derived. Numerical results on four real-world datasets demonstrate the superiority of our approach over several state-of-the-art algorithms.

Graphical Analysis of the Markowitz Model under Different Constraints

The Markowitz mean-variance model is an important tool in portfolio theory. This study examines the complexity of the model by analyzing its application and performance under different constraints. The study uses Bloomberg data on 10 stocks from 2001 to 2021 to rigorously analyze the impact of limitations on portfolio optimization. The study explores limitations ranging from limiting total allocations and individual weightings to intentional exclusions and long-term strategies to discern the impact on the risk-reward profile. The research uses graphical representations and key metrics such as Sharpe ratios, stock allocation lines, and various portfolio metrics to provide insight into optimal allocation strategies. The results indicate that these constraints have a significant impact on the risk-return profile of a portfolio and that it is essential to take them into account when optimizing a portfolio. The study provides a comprehensive analysis of the Markowitz model and its application under various constraints, which can help investors make informed decisions while optimizing their investment portfolios.

Research on Optimization of Investment Portfolio in the New Energy Vehicle Industry Chain

The urgent environmental problems caused by global climate change have propelled the rise of the new energy vehicle industry. Nations and business are also focusing on the research and promotion of this industry. Due to the fast development, investors face both promised investment opportunities and complicated challenges. Against this backdrop, a vital issue, which is how to choose the optimal investment portfolio to achieve the maximum possible return while experience the lowest possible risk, arises. This paper collects the closing price of stocks from 5 companies in different sectors of the new energy vehicle industry, with the period from 19 August 2022 to 18 August 2023 and then computes the variance of closing price and average return of the stocks, finally uses the COVAR function in excel to obtain the covariance matrix. After processing the data, the paper applies the Markowitz mean-variance model to obtain the optimal portfolio formation. Results show that this industry may not be a good choice for investors currently since all three portfolios show negative returns, while the negativity do not completely negate the long-term potential of this industry as the development of the industry can be influenced by various factors. It is therefore to conduct deeper research to better understand the industry dynamics and future trend.

Uncertain mean-CVaR model for portfolio selection with transaction cost and investors’ preferences

Portfolio selection is a common practice among investors, scholars often rely on probability statistics to construct portfolios based on the Markowitz mean–variance model. However, due to the complexity of the stock market and the limitations of historical data, it may not be possible to fully predict the future market. In such situations, it is necessary to incorporate expert knowledge and judgments to obtain estimates of security return rates. This paper proposes a class of portfolio models suitable for uncertain environments. We employ the uncertainty theory and Arbitrage Pricing Theory (APT) to measure tail risk and construct a new uncertain mean-Conditional Value-at-Risk (CVaR) model. Additionally, to better match investors’ preferences, this paper takes into account transaction costs and liquidity needs. To solve this problem, we design a hybrid algorithm that incorporates these factors. Finally, we present a numerical experiment to illustrate the performance of the proposed model. In summary, our study offers a novel approach to portfolio selection that considers uncertainty theory, tail risk, and investors’ preferences. The results demonstrate that the proposed uncertain mean-CVaR model with hybrid algorithm optimization can improve portfolio performance in uncertain market conditions.

Portfolio Analysis and Investment Value Based on US Stock Market

An investment portfolio can contain a variety of assets, including cash, stocks, bonds, financial derivatives, precious metals, and cash. You shouldn't invest all of your money in the same thing, similar to the adage "don't put all your eggs in one basket." Put your eggs in a variety of baskets so that even if one breaks, they will remain safe. In this study, five equities—Eli Lilly, Amazon, FedEx, J.P. Morgan Chase Bank, and Pfizer—are constructed using the Markowitz Mean-Variance Model and Effective Frontier. The portfolio is built using data from these five stocks during the previous three years. Given that stocks can be shorted, the portfolio has a Sharpe Ratio of 9.07%, a yield of 2.99%, and a ceiling of negative 1 for each stock. The risk of this best answer, which was determined by solving combinations, is 9.63%. The usual 10-year Treasury bond's average return is 2.12%, which is less than the ideal yield.

Effectiveness and Limitation of Markowitz Mean-variance Model: Evidence from Hang Seng Index

As China's economy has expanded rapidly, its financial system has gradually improved, new financial businesses have evolved, and new theories and technologies have also been developed. The Markowitz mean-variance model, the cornerstone of asset pricing theory, is utilized as an example in this paper to demonstrate how the Markowitz portfolio theory may be applied to assess a portfolio of five stocks in the Hang Seng data, a significant indicator of the Hong Kong stock market. Empirically, the optimal portfolios with the highest Sharpe ratios and lowest variances are identified. Their expected returns, standard deviations, and Sharpe ratios are then evaluated by comparing them to equal-weight portfolios and giving the effective frontier. The author further demonstrates the guiding significance of Markowitz's portfolio theory in the Chinese investment market through the assessment of the findings. Finally, in the context of the Chinese securities market, identify and analyze the model's constraints and offer suggestions.

Markowitz-based Shariah compliant portfolio model with stochastic purification and probabilistic compliance screening constraints

PurposeOne important study in the portfolio investment is the study of the optimal asset allocations. Markowitz is the pioneer of modern portfolio theory that analyses the performance of portfolio based on the mean (reward) and variance (risk). Motivated by the Markowitz's mean variance model, the purpose of this paper is to propose a new portfolio optimization model that takes into consideration both processes of purification and screening, which are key to constructing a Shariah-compliant portfolio. In practice, this paper introduces a stochastic purification variable and a probabilistic screening constraint into a portfolio model.Design/methodology/approachFirst, the authors study the stochastic nature of purification variable and apply it to both investment and dividend purification. Second, recognizing that the importance of on-going screening could adversely affect the portfolio strategy, the authors impose probabilistic constraints to control the risk of compliance change. They evaluate the proposed model by formulating the screening constraints at both asset and portfolio levels, together with three different financial screening divisors that are broadly used by the international Shariah boards. The authors also conduct an extensive empirical study using a sample of Shariah-compliant public companies listed on the Indonesia Stock Exchange.FindingsBased on the empirical example presented in this paper, the authors found that the purification variable in the proposed model is closer to the practice in the Sharia capital market in terms of the nature of the non-constant data, and this variable reduces the total income of portfolio which has not been captured in the previous literature. The authors also have successfully derived the portfolio screening constraint to mitigate the risk of the asset change to be non-compliant in the future.Originality/valueBased on the authors’ knowledge, this is the first paper that proposed the stochastic purification and the dynamic of screening processes into the Shariah portfolio model. This paper also examines the impact of non-short-selling, purification and screening policies to the performance of Shariah portfolio.

Optimization of Asset Allocation Strategies in Major Categories—Theories, Indicators, Assets and Timing

Due to the defects of Merrill Lynch Clock, this paper aims to put forward Pringle Clock for theoretical improvement. In addition, strategic optimization for Pringle from perspectives including indicators, assets and timing is made, and finally its effectiveness in domestic market is tested. The results show as follows. 1) Stages of the Pringle cycle divided by three indexes (leading, consistent and lagging) can accurately grasp allocation opportunities of assets in different categories. 2) Researches and investments in the subdivided industries of the equity market are conducive to improving portfolio returns, and Markowitz mean-variance model can be used for portfolio optimization. 3) Selecting appropriate leading interest rate indicators (by using wavelet cross analysis) and predicting the characteristics of the next stage in advance (by using VAR model) are of great help to improve the flexible timing ability of the asset allocation strategies.

Portfolio Optimization under Informationally Asymmetric Markets

Asymmetric information propagation frequently results in distorted financial markets and is generally a feature of informationally inefficient markets. We developed a model of optimal asset allocation using the martingale method to assist an investor in selecting an asset that performs better under the conditions of a market information cascade. In order to confirm that the model satisfies the required conditions, we applied the verification theorem and ascertained that the results produced were optimal. The model outperformed the famous Markowitz mean-variance type model and was shown to produce stable and consistent solutions under such market conditions.

Markowitz Mean-Variance Portfolio Optimization with Predictive Stock Selection Using Machine Learning

With the advances in time-series prediction, several recent developments in machine learning have shown that integrating prediction methods into portfolio selection is a great opportunity. In this paper, we propose a novel approach to portfolio formation strategy based on a hybrid machine learning model that combines convolutional neural network (CNN) and bidirectional long short-term memory (BiLSTM) with robust input features obtained from Huber’s location for stock prediction and the Markowitz mean-variance (MV) model for optimal portfolio construction. Specifically, this study first applies a prediction method for stock preselection to ensure high-quality stock inputs for portfolio formation. Then, the predicted results are integrated into the MV model. To comprehensively demonstrate the superiority of the proposed model, we used two portfolio models, the MV model and the equal-weight portfolio (1/N) model, with LSTM, BiLSTM, and CNN-BiLSTM, and employed them as benchmarks. Between January 2015 and December 2020, historical data from the Stock Exchange of Thailand 50 Index (SET50) were collected for the study. The experiment shows that integrating preselection of stocks can improve MV performance, and the results of the proposed method show that they outperform comparison models in terms of Sharpe ratio, mean return, and risk.

Mean-variance portfolio selection with estimation risk and transaction costs

ABSTRACT There are many approaches that have been proposed to improve the empirical performance of the Markowitz mean-variance model. Designed to mitigate the impact of parameter uncertainty and estimation error, these approaches have delivered substantially better out-of-sample performance. In this paper, we consider the portfolio optimization problem for a single-period investor facing different types of transaction costs. By reformulating the rebalancing problem into a linear regression framework, we show analytically that considering different transaction costs is equivalent to imposing additional constraints on the portfolio weights, thus providing desired properties such as sparsity and stability in the trading strategy.

Research On Finding Optimal Portfolios Based on Markowitz Mean-Variance Model -- Constructing Efficient Frontier and Portfolio with Highest Sharpe Ratio Using 4 Assets in Chinese Market

Markowitz mean-variance model is the foundation of modern investment science, and how to apply this model to construct optimal portfolios is always of interest. This paper uses the Markowitz mean-variance model and four typical assets in Chinese market to construct efficient frontier with highest expected return rate at each risk level and lowest risk at each expected return rate level, and the portfolios with the highest Sharpe ratio. There are three main results in this paper. Firstly, the efficient frontier has the U shape and V shape rotated clockwise in the case of excluding and including risk-free asset respectively. Secondly, the theoretical efficient frontier obtained from mathematical formulas approximately coincide with those from the simulation experiments. Thirdly, the portfolio with the highest Sharpe ratio always occurs in the intersection point of the efficient frontier and its tangent line that passes through the risk-free asset. The results from this paper provide a convenient method of using mathematical formula for investor to construct optimal portfolios in real practice.

A Swarm Intelligence Optimization Algorithm for Cryptocurrency Portfolio Optimization

In recent years, cryptocurrency has been widely adopted and seen as an alternative investment tool for investors. However, which cryptocurrency to invest in and how much to invest becomes a problem. Since there is a conflict of multiple criteria, portfolio optimization (PO) is needed to solve the problem. In this study, an Artificial Bee Colony (ABC) algorithm has been developed based on Markowitz's mean-variance model (M-MVM). With this method, the portfolio of cryptocurrencies has been tried to be optimized. Hourly data of 12 cryptocurrencies between 01.09.2020 and 01.04.2021 were used as data. It has been observed that the ABC algorithm achieves good results in the solution of the problem in a reasonable time. In addition, the method was tested with different parameter values and different risk-averse coefficient values (λ).

An Empirical Analysis on the Stable Return of Resident Funds

This paper mainly studies how investors invest in funds to obtain high returns while avoiding risks. Firstly, from the perspective of portfolio investment, this paper introduces the traditional Markowitz mean-variance model and capital asset pricing model (CAPM), then selects four funds from different industries by MATLAB program in Sina Finance and Economics Network for application analysis from which the optimal portfolio point can be obtained under the combination of efficient frontier and capital allocation line. Subsequently, by analyzing the returns of long-term holdings and short-term operations of Noan Growth Hybrid Fund, it is confirmed that long-term holding funds can better cope with the changing market so as to obtain more stable returns. Finally, this paper discusses the dynamic adjustments of asset portfolio. Resident investors are supposed to take into account the market situation and the changes of the fund itself to adjust the holding fund portfolio. Based on the research in this paper, resident investors ought to combine investment funds to diversify risk allocation and make long-term holding plans according to their risk tolerance. At the same time, they should also make appropriate dynamic adjustments when the external environment changes to ensure long-term benefits.

OPTIMAL ALLOCATION OF BANK CREDITS TO APPLICANTS IN AGRICULTURAL SECTORS

Credit portfolio management is one of the fundamental aspects of banking that can lead to the loss of bank revenue if not properly managed. The expected return and risk in the choice of portfolio cannot be accurately predicted. Considering this impossibility and given the limitations faced by the banking system, this article uses the concept of interval numbers in the Fuzzy Set Theory to extend the Markowitz mean variance model to a non-linear interval multi-objective model. Three strategies were presented in this model, including optimistic, pessimistic, and mixed strategies, and the Genetic algorithm was used to solve the model. This model was ultimately examined at Keshavarzi Bank to determine the optimal credit portfolioCredit portfolio management is one of the fundamental aspects of banking that can lead to the loss of bank revenue if not properly managed. The expected return and risk in the choice of portfolio cannot be accurately predicted. Considering this impossibility and given the limitations faced by the banking system, this article uses the concept of interval numbers in the Fuzzy Set Theory to extend the Markowitz mean variance model to a non-linear interval multi-objective model. Three strategies were presented in this model, including optimistic, pessimistic, and mixed strategies, and the Genetic algorithm was used to solve the model. This model was ultimately examined at Keshavarzi Bank to determine the optimal credit portfolio. The results showed that this bank’s risk, thus leading to the proper management of loans.

Analysis of Risk Measures in Portfolio Optimization for the Uganda Securities Exchange

For the most recent years, risk has become one of the essential parameters in portfolio optimization problems. Today most practitioners and researchers in portfolio optimization have used variance as a standard risk measure. This approach has been found subjective. The Markowitz (1952) mean-variance model considered variance as an adequate portfolio risk measure, and asset returns are multivariate normally distributed and that investors have a quadratic utility function which is subjective too. Other risk measures have been suggested to overcome the limitations of the mean-variance model. This paper analyzes which portfolio optimization models can better explain the optimal portfolio performance (high return, low risk) for the Uganda Security Exchange (USE). We compare Mean-Variance (MV), Mean Absolute Deviation (MAD), Robust Portfolios and Covariance Estimation Models (The Shrinked Mean-Variance (SMV) Models & Alternative Covariance Estimator (ACE) Models) and Mean-Conditional Value-at-Risk (Mean-CVaR) models in terms of the risk and performance. For the computed monthly returns and price data (February 2010 to January 2021) for USE selected stocks, we considered the results to show that Mean-CVaR and ACE portfolios have the highest performance ratio compared to other models. We find that VaR is the best risk measure for portfolio optimization for the USE since it has lower values across all models than other risk measures. It is vital to consider all the available risk measures for a regulator or practitioner to make a good decision since using one can be subjective; as seen in our results, different risk measures yield different results.

Best-case scenario robust portfolio for energy stock market

Based on Markowitz mean-variance theoretical model (MV), the energy portfolio optimization problem has been extensively studied to obtain the optimal strategies of energy resource allocations and achieve the efficient usages and productions of energy. However, MV leads to the optimal energy portfolios infeasible without consideration of uncertainties. Meanwhile, dealing with the uncertain input parameters in the model, robust mean-variance model (RMV-worst) can overcome this shortcoming, but the optimal energy portfolio performances are considerably inferior. Therefore, contrary to RMV-worst, this paper analytically constructs an alternative robust portfolio model (RMV-best). Furthermore, from the energy stock market of China the data containing two motion cycles is divided into three movement statuses to verify the overall performances of the optimal energy portfolios. Finally, the comparison results add to the existing researches on energy portfolio optimization by: (i) RMV-best can validly improve the energy portfolio performances while ensuring the optimal energy portfolios feasible. (ii) The different movement statuses significantly influence on the energy portfolio performances, subsequently giving the favorable decisions of energy portfolios. (iii) The optimal energy portfolios of RMV-best are very reliable, as further indicates that RMV-best can bring about the convincing energy portfolios.

Portfolio selection using R

In this paper, we consider the Markowitz mean-variance model to minimize the risk on two assets and develop the program in R software to improve the performance of the model for two real stocks data with various combinations of the portfolios. We have taken two real stocks data up to 4514 each from yahoo database finance using our R program to show how fast our calculations are.

Investment apportionments among participants of PPP rental retirement villages

Purpose The purpose of this paper is to examine public–private partnership (PPP) approaches for the construction of rental retirement villages in Australia and to allocate the investment proportions under a certain project return rate among three investors which are the government, private sectors and pension funds. The apportionment will achieve a minimum overall investment risk for the project. Design/methodology/approach Capital structure, particularly determination of investment apportionment proportions, is one of the key factors affecting the success of PPP rental retirement villages. Markowitz mean-variance model was applied to examine the investment allocations with minimum project investment risks under a certain projected return rate among the PPP partners for the construction of rental retirement villages. Findings The research findings validate the feasibility of the inclusion of pension funds in the construction of PPP rental retirement villages and demonstrate the existence of relationships between the project return rate and the investment allocation proportions. Originality/value This paper provides a quantitative approach for determination of the investment proportions among PPP partners to enrich the theory of PPP in relation to the construction of rental retirement villages. This has implications for PPP partners and can help these stakeholders make vital contributions in developing intellectual wealth in the PPP investment area while providing them with a detailed guide to decision making and negotiation in relation to investment in PPP rental retirement villages.