Markowitz Model Research Articles

Analysis of Portfolio Optimization Performance: Markowitz Model and Index Model in Capital Markets

In the post-pandemic era, marked by economic uncertainty and stock market volatility, investors are turning to Modern Portfolio Theory (MPT) to guide their investment decisions. This study aims to develop a robust mathematical framework for portfolio construction using the Markowitz Model (MM) and the Index Model (IM) with added constraints. The objectives are threefold: (1) to create a portfolio framework that reflects investor preferences using MM and IM with additional constraints, (2) to compare these models against the Gaussian Distribution using Python and Excel, (3) to compare the statistical data and correlation tests of daily logarithmic returns in Python with monthly excess returns in Excel, and (4) to evaluate their performance relative to the traditional Markowitz approach through Monte Carlo simulations.The methodology involves incorporating five additional constraints into the MM and IM models. The analysis uses 20 years of historical daily return data for ten stocks from various sectors, one equity index (S&P 500) as a risk-free rate proxy (1-month Fed Funds rate). Daily logarithmic returns are analyzed using Python, while Excel Solver and Solver Table are employed for monthly excess return data.

Further Research in the Chinese Mid-cap Stock Market by Using the Markowitz Model, Capital Asset Pricing Model, and Fama-French Model

This article aims to identify the optimal portfolio of 10 mid-cap stocks in the Chinese stock market. Markowitz model is used to analyze the data from January 1, 2024, to July 1, 2024, including 117 trading days in total, and give some advice on portfolio selection. Markowitz’s model uses “Solver” in Excel to generate different portfolios and gets the optimal portfolio when the Sharpe ratio becomes the largest. In the Capital Asset Pricing Model (CAPM) and the Fama-French model, they can judge whether the stock is worth investing by the result given by linear regression in Excel. It turns out that the optimal portfolio of Markowitz has a Sharpe ratio of 2.14. Although the CAPM and Fama-French Model don’t give an exact percentage of each stock, they can take more conditions and factors into consideration to give a better judgment of the amount of the profit of each certain stock. The research fulfills the blank of using these models in the Chinese mid-cap stock market finding some supporting ideas from CAPM and Fama-French Model.

Comparative Analysis of the Markowitz Model and the Kraljic Matrix Model in Portfolio Optimization and Procurement Management

This research studied two important models of portfolio management: the Markowitz model and the Kraljic Matrix Model. The Markowitz model is the basis of modern portfolio theory and is designed to optimise asset allocation by minimising risk while maximising returns. This paper provides a system to build a balanced portfolio by utilising diversity. On the other hand, the Kraljic Matrix Model classifies products based on supply risk and profit impact and provides a strategic tool for purchasing management. This model categorises products into four categories: noncritical, leverage, strategy, and bottleneck to support informed purchasing decisions. Despite its usefulness, the Kraljic matrix has been criticised for not taking into account the supplier’s perspective and for not providing guidelines for managing the movement of goods within the matrix. This paper studies the application and limitation of the two models, emphasises the need to adapt to the strategy in the portfolio and procurement management, and adjust according to the market dynamics.

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.

The Research on the Investment Portfolio of New Energy Sector Based on Markowitz Model and the Index Model

Abstract: New energy sector stocks in the Chinese market continue to grow at a high rate for two years in 2020 and 2021, but start to retrace in 2022. In order to investigate whether the new energy sector is still worth investing in and to find the optimal portfolio for the new energy industry, this paper analyzes fifteen stocks in the new energy sector using the Markowitz model and the index model. The following conclusions are drawn: 1. Under the constraint that shorting is not allowed in China's stock market, the index model is still advantageous. 2.Investors are more inclined to invest in the Shanghai Composite Index when seeking minimum risk. 3. Under the condition of maximum Sharpe ratio, investors are more willing to invest in the BYD Company Limited, Contemporary Amperex Technology, and EVE Energy. There are many methods of portfolio model construction at this stage, but this paper only analyzes only the Markowitz model and the index model in depth. In the future, other models can be compared and analyzed in depth to get the most suitable portfolio model for the new energy industry.

The Construction of Investment Portfolios under the Minimization of VarianceTaking the Hong Kong Insurance Market as an Example

Abstract: In the context of a decline in the Hang Sheng Index, this paper intended to study the different effect between using Markowitz Model and Index Model to invest insurance industrys stock in Hongkong, especially for those who are risk-averse. A recent ten years of adj close for 9 typical insurance stocks from Hongkong as well as the Heng sheng index has been chosen as the target data. The result illustrates that there is no significant difference between these two models. This study intends to give some reference for those who focus on Hong Kong insurance industrys investment and hate taking risk. This study find that the constraints minimal variance is the smallest at 16.832(The index model of constraint 2) and the constraints highest sharp ratio is around 0.26(The index model of constraint 4). The findings of this paper provide the investors empirical evidence on how to construct optimal investment portfolio in Hong Kong insurance market.

The Influence of ESG Factors on Portfolio Performance Based on the Perspective of Markowitz Portfolio Theory

Abstract: In this paper, the inclusion of Environmental, Social, and Governance (ESG) factors in portfolios is investigated to determine their impact on portfolio performance and its mechanism. Based on the data collected by Bloomberg for 10 stocks from 2003-2023 and Markowitz's portfolio model, it is found that: (1) the inclusion of ESG constraints negatively affects portfolio performance; (2) the inclusion of ESG constraints shifts the GMVP to the right and reduces the convexity of the efficient frontier, thus lowering the portfolio's performance. This study enriches the literature on the factors affecting portfolio performance as well as responsible investment and ESG investment, and is of value to investors or organizations in making investment strategy choices.

Comparative Analysis on the Application of Markowitz Model and Index Model in Portfolios

This article presents a comparison between the Markowitz model and the index model, focusing on their applications in portfolio management. The Markowitz model, also known as the mean-variance model, revolutionized portfolio theory by introducing a quantitative method for balancing risk and return. This model constructs optimal portfolios that maximize expected return for a given level of risk or minimize risk for a given expected return, using a covariance matrix to assess relationships between asset returns. In contrast, index models popularized by William Sharpe offer a simplified approach focused on the relationship between individual asset returns and a common benchmark (usually a market portfolio). The article explores the theoretical foundations of the two models, highlighting their mathematical formulations and assumptions. It also discusses the computational methodologies involved in implementing these models and examines the challenges and advances in optimization techniques. It evaluates how these technological innovations have enhanced portfolio optimization, enabling the handling of larger datasets and more complex market dynamics. In addition to comparing these two models, the article delves deeper into the concepts of efficient frontier, inefficient frontier and minimum variance frontier. The efficient frontier is the portfolios that offer the highest expected return for target risk, while the inefficient frontier includes portfolios that do not offer the best return for the level of risk. Minimum variance frontier focuses on portfolios that minimize risk for target expected return, emphasizing the importance of risk management in investment decisions.

ANALYSIS OF PORTFOLIO FORMATION ON THE LQ45 STOCKS INDEX, USING THE MARKOWITZ AND SINGLE INDEX MODELS

In an investment, there will always be a return and risk, especially in the capital market in the form of stocks. The risk in an investment can be minimized by diversifying assets into several stocks to form a portfolio formation. Several models, such as the Single Index and Markowitz, can evaluate optimal portfolio formation. In this study we provide additional information and discourse on capital market studies and as the input for investors in making investment decisions in the form of stocks. The study shows that based on 25 companies, the Markowitz model gives 12 companies as the optimal portfolio with the largest proportion of funds owned by PT Bank Central Asia Tbk (BBCA), 82.22%. The portfolio of those 12 stocks can provide an expected return of 44.8% where its risk is about 13.77%. The Single Index model provides a formation based on 9 companies as the optimal portfolio with the largest proportion of funds owned by -again- PT Bank Central Asia Tbk (BBCA) which is 66.23%. The portfolio of these nine stocks can provide the expected return of 1.68% and its risk is 0.43%. The ratio of risk and return from each model justifies that the Single Index model gives better portfolio formation. This result should be further compared with other stock indexes, nationally and globally, and also needs to be compared with the period after the pandemic.

Markowitz Model and Index Model: A Comparative Study of Constructing Optimal Portfolios

In the field of investment, how to strike a balance between high returns and low risks has always been a challenge for investors. With the rise of modern portfolio theory (MPT) and index models, investors have more options for constructing optimal portfolios. This paper takes the US stock market as the research object, selects the S&P 500 index and six stocks representing different industries, uses the Markowitz model and the index model to optimize, and analyzes the optimal portfolio allocation, return, risk and Sharpe ratio of the two models under different constraints. It is found that the Markowitz model is more advantageous in risk diversification, while the index model relies more on the allocation of a single stock, especially the S&P 500 index. Both models perform similarly in terms of risk-adjusted returns, but the Markowitz model is slightly superior in terms of Sharpe ratio. In addition, there are differences in the portfolio allocation and risk-return characteristics of the two models under different constraints. The results of this study can help investors better understand the advantages and disadvantages of the two portfolio optimization models, and choose the appropriate model according to their own risk preferences and market environment to construct the optimal portfolio and achieve their investment objectives.

Analisis Markowitz dan Model Indeks Tunggal dalam Pembentukan Portofolio Optimal Saham Jakarta Islamic Index Periode 2019-2023

This research is motivated by the increasing number of sharia investors each year and the uncertainty of stock prices incorporated in the Jakarta Islamic Index in 2019-2023 so there is a needed to plan optimal portfolio to reduce the risk. Sampling in this study using purposive sampling method that meets the sample criteria as many as 15 stocks. The analysis technique used is descriptive analysis and hypothesis testing is done using the Independent Sample T-Test. The results showed that there were 3 stocks incorporated into the optimal portfolio of the Markowitz model, namely ADRO, ANTM, and BRPT, with an expected portfolio return of 0.0238 and a portfolio risk of 0.1066. And there are 4 stocks that are incorporated into the optimal portfolio of the Single Index Model, namely ADRO, BRPT, ANTM, and INCO, with an expected return of 0.0215 and a portfolio risk of 0.1035. Therefore, Markowitz portfolio is better to use than the Single Index Model portfolio because it has a greater expected return than the Single Index Model. However, statistical testing using t-test shows that the expected return and risk of the optimal portfolio of the Markowitz Model and the Single Index Model are not significantly different.

Research on the Optimal Portfolio of New Energy Industry Based on Markowitz Model

Based on Markowitz's portfolio theory, the risks and returns of stocks can be obtained from calculating the historical data, ensuring effective returns with low risk by decentralized investment, which has a considerable degree of practical significance to China's public investment under the current situation. In recent years, the total market capitalization of the new energy industry and the attainable gains from it are growing rapidly, in which case investors need to analyze and evaluate the volatility to determine how to invest. This paper extracts the historical closing price of new energy automobile related industry 7 stocks from June 2018 to March 2024 through the SuperMind database and establishes the mean-variance model, showing the optimal portfolio of new energy industry in the market with short-selling and the market without short-selling and giving a practical investment proposal on weights allocation.

Impact of ESG Risk on Portfolio Optimization and Returns: An Analysis Using the Markowitz Model

This paper explores the integration of Environmental, Social, and Governance (ESG) factors into portfolio optimization using the Markowitz Model, focusing on two groups of ten stocks each from the Technology, Media, and Telecom (TMT) sectors. These stocks are categorized into low and high ESG risk groups according to established ESG rating agencies. Employing historical data, the study computes key financial metrics such as annualized returns, standard deviation, and Sharpe ratios to conduct various portfolio optimizations including the minimal risk frontier, efficient frontier, and inefficient frontier, while also applying five specific operational constraints reflective of real-world investment limits. The analysis distinctly highlights the superior performance of the low ESG risk group, which demonstrated higher returns and better risk-adjusted return profiles, as evidenced by elevated Sharpe ratios. These findings suggest that ESG integration not only aligns with broader societal goals but also enhances financial performance, especially under diverse regulatory and strategic constraints. This research enriches the discourse on sustainable investing by providing empirical evidence on how ESG factors influence traditional portfolio management strategies, potentially guiding future investor decisions and promoting a shift towards more sustainable investment practices.

Comparison of Markowitz Model and Single Index Model with ESG Factors Involved

ESG considerations have become increasingly prominent within the realms of investor and corporate decision-making, underscoring the importance of employing robust methodologies for incorporating ESG factors into portfolio construction. This study aims to leverage the Markowitz Model and Single Index Model to construct portfolios utilizing a selection of 10 stocks, evaluating their applicability across various conditions, particularly investors' risk tolerance levels. Utilizing the solver function within Microsoft Excel, graphical representations will be generated under four distinct constraints, facilitating comparisons based on both graphical depictions and accompanying data analysis. The findings reveal that, under specified conditions, the two models exhibit negligible differences, while highlighting the significant role of ESG constraints in portfolio construction. Nonetheless, given the distinct assumptions and conditions underlying each model's calculations, investors retain the flexibility to choose either approach for portfolio analysis. This research underscores the impact of ESG factors on asset allocation outcomes within both models, offering valuable insights into ESG investing practices and the comparative performances of the Markowitz Model and the Single Index Model.

Comparative Analysis of Portfolio Management Models: Markowitz, CAPM, and Multi-Factor Models

This paper presents a comparative analysis of three foundational portfolio management models: the Markowitz Efficient Frontier, the Capital Asset Pricing Model (CAPM), and Multi-Factor Models. It aims to explore their theoretical foundations, empirical applicability, and practical usage to assess their strengths and limitations in financial portfolio management. The Markowitz model is appreciated for its detailed risk-return optimization framework but criticized for its reliance on historical data and computational demands. The CAPM simplifies risk assessment through market beta, yet its assumptions of market efficiency and a risk-free rate are viewed as impractical under current market conditions. Multi-Factor Models address some limitations of the CAPM by incorporating various risk factors, offering enhanced explanatory power but also adding complexity in factor selection.The study concludes that while no single model is universally superior, the choice of model should depend on the specific needs of the portfolio manager, including risk-return objectives and market environment. The paper suggests a blended or adaptive approach to model selection, highlighting the need for flexibility in response to evolving market dynamics and advances in computational finance.

Research on the Investment Portfolio in Technology and Consumer Goods Industries

This research investigates investment portfolios in the U.S. technology and consumer goods sectors, employing Modern Portfolio Theory (MPT) and the Markowitz Model to analyze and compare their risk-return profiles. The study highlights that the technology sector demonstrates a high-risk and high-return profile, making it attractive for risk-seeking investors aiming for significant gains amidst market volatility. In contrast, the consumer goods sector, with lower volatility, appeals to risk-averse investors who prefer stable and predictable returns. Key findings strongly emphasize the importance of aligning investment choices with individual investor preferences, illustrating how specific industry characteristics can influence investment strategies. The research suggests that investment success is considerably enhanced when portfolios are tailored to match individual risk tolerance and investment goals. This strategic approach provides a robust framework for guiding investors to make informed decisions that reflect their personal preferences and financial objectives, thereby helping them navigate market complexities and enhance portfolio performance.

OPTIMIZATION AND FORECASTING OF A SECURITIES PORTFOLIO BASED ON MACHINE LEARNING METHODS

The article is devoted to the demonstration and analysis of the possibilities of connecting the Markowitz model, which is a classical model for forming a portfolio of securities, and forecasting methods based on machine learning data. The relevance of the chosen topic is justified by the fact that the use of machine learning methods makes it possible to simplify the activities of financial sector workers and the work of professional stock market players, as well as reduce the complexity of interpreting mathematical models and methods of their construction for private investors. The purpose of this work is to use machine learning methods to solve the problem of building an optimal securities portfolio and predicting its behavior. Tasks: - build a Markowitz model based on the selected data; - to build an optimal portfolio based on the proposed optimality criterion; - offer a time series forecast; - to assess the adequacy of the constructed model; - combine the Markowitz model, which belongs to the class of widely known classical models, with the construction of a prediction based on machine learning. Methods and models: machine learning methods are used in the work, the Markowitz model is built based on the selected data, then the Markowitz model is combined with the construction of a forecast based on machine learning. Research results: the optimal portfolio for AXP has been built and its forecast has been fulfilled. The formation of the portfolio was based on the Markowitz model. The data obtained were tested for adequacy and showed fairly good results. A portfolio was built, the optimality criterion of which is the ratio of average profitability and volatility of profitability (maximizing average profitability while minimizing its volatility). The Markowitz model, which belongs to the class of widely known classical models, was combined with the construction of a prediction based on machine learning.

Portofolio Management with Markowitz Model to Determine Optimal Investment Values

Investment is a commitment to a number of funds or other resources made at this time with the aim of obtaining a number of benefits in the future. Investments can be channeled through several instruments, such as deposits, gold, property, stocks, and many more. With the various types of investments that exist today, the difficulty of finding an investment cannot be an obstacle. In investment, the appropriate allocation of funds can be an important factor in obtaining profits. By using the correct method, the risk factors that may occur can be minimized as well as possible. The method that can be used in determining funds in investment activities is using the Markowitz Model. Then, the author initiates a method for optimizing assets using the Markowitz method. In this research, used data from 10 stocks in Indonesia PANI, CLEO, DSSA, UNIC, ADRO, CITA, CAKK, TPIA, MYOR, ANTM. Then, the stocks will be arranged optimally portfolio. The optimal investment weight obtained for stocks from January 1, 2019 to December 31, 2023 using the Markowitz model, each share weighting namely 7,6% PANI, 18,05% CLEO, 8,48% DSSA, 16,902% UNIC, 12,471% ADRO, 10,496% CITA, 7,246% CAKK, 12,946% TPIA, 5,877% MYOR, and 0,464% ANTM company stocks and provide a portfolio ratio of 5.694581 which can also be interpreted that the optimal return ratio profit is 5.694581 times greater than the possible loss or portfolio variance.

Analisis Pembentukan Portofolio Optimal di Bursa Efek Indonesia dengan Menggunakan Model Markowitz

The purpose of this study is to utilize the Markowitz Model to build an optimal portfolio of stocks on the Indonesia Stock Exchange in 2019 to 2023, focusing on stocks in the IDX30 index. Based on information from KSEI, the public premium in capital market speculation continues to increase. On that basis, this study is important to be conducted in order to provide a reference for the public to invest. The IDX30 index was chosen as the subject of the study because it includes stocks with large market capitalization, high liquidity, and stable financial conditions. This study determines the optimal fund allocation for each stock and examines stocks in the IDX30 index from 2019 to 2023 that are worthy of consideration for inclusion in the optimal portfolio. In this test, it produces four stocks that become the optimal portfolio with the most extreme profits, namely ADRO 16.12%, BBCA 65.97%, BBRI 4.13%, and ICBP 13.76% with a return of 1.01% and a risk of 0.22%. In contrast, the minimum risk consists of ADRO of 5.29%, BBCA of 26.14%, CPIN of 13.91%, ICBP of 16.17%, INDF of 8%, KLBF of 0.48%, TLKM of 13.47%, and UNVR of 16.55%, with a risk of 0.1% and an expected portfolio return of 0.11%.

Optimization of Investment Portfolio Structure Using the Markowitz Model

Optimization of Investment Portfolio Structure Using the Markowitz Model