Markowitz Theory Research Articles

Portfolio Optimization Strategies for the Common Investor

Abstract: Financial Analytics is a key field to making investment decisions and has been developed only recently. It involves analytical thinking, computational knowledge and creative thinking about investment strategies. There are many ways to invest money. Some people invest them in Gold, some in real estate, some create a fixed deposit, some in the stock market. Some people diversify their money into different sectors of the market and invest to get an optimal profit by understanding the market. This kind of investment is called portfolio management. Unlike gambling, understanding of the portfolio and its management can actively minimize the risks associated with investment. In the proposed research we tried to study the different strategies of investing in the different sectors and building a portfolio, with the express aim of creating optimal diversified portfolios. Our methods include optimizing the weights of different investment instruments in different sectors, with implementations carried out in Python and using time-series Python libraries. We have focussed on three different investment strategies in particular: (1) Genetic algorithms help us to divide the portfolio (chromosome) into the genes (sectors) and understand it in a better way. Exploiting the existing algorithms for optimizing fitness functions in genetic algorithms, we have implemented one strategy for optimizing portfolios; (2) Efficient frontier analysis from Markowitz theory helps in investing and creating our own portfolio. We developed some of the strategies that help in displaying portfolio allocation and efficient frontier graphs; (3) We have also implemented a new criterion in vogue in the financial markets today, the “Kelly Criterion” preferred by many investors all over the world. We used real time financial stock data to validate and test our functions. All the strategies developed are modular and we also show a proof-of-concept web interface for one of the developed strategies. It is hoped that our work enables investors in making better decisions about where to park their money and converting their wealth into high-yield portfolios.

Simulation of decision-making processes regarding the formation of an invest-ment portfolio using IT

Significant changes observed in the global economy and in particular in Ukraine in recent years have significantly increased interest in the problems of investment theory. An example of this is the intensification of trading in shares of large and medium-sized international companies and cryptocurrencies, which causes a rapid increase in their values. It is known that in the theory of investments, the task of optimizing the set of components of investment portfolios is considered as a special case. As you know, the issue of decision-making regarding the formation and optimization of an investment portfolio is in the field of attention both for large investment companies and for private investors, since when choosing among possible alternatives for the distribution of capital investments within the market of financial assets, the investor will receive different results. As a result, it is necessary to understand the amount of income received during the period of ownership of the investment portfolio. It is known, according to Gary Markowitz's theory of investment risk, that the optimal distribution of the filling of the investment portfolio should provide the best income while maintaining the lowest risks. At the same time, the decision regarding the structure of capital distribution is often made in conditions of uncertainty, and the profitability of investing capital in investment objects is of a random nature. Since uncertainty creates additional risks, the investment of capital and the task of optimizing the investment portfolio must be considered and solved in the presence of risk. At the same time, effective investment activities require the use of special mathematical methods and informational tools to support decision-making. In the article, using the Ruby programming language, a model is proposed that can be used in the decision-making process when forming a set of components of a portfolio of securities, which allows potential investors to independently assess the effectiveness of a set of investment portfolios by comparing the growth dynamics of shares available on the financial market. It is known that most of the information an investor encounters is in a tabular format, and according to the methodology of scientific knowledge, a person better perceives visualized ways of presenting information. The model proposed in the work uses visualization tools built into the software product, which presents available tabulated information in a structured graphic form.

Presenting a two-echelon multi-objective supply chain model considering the expiration date of products and solving it by applying MODM

The supply chain (SC) as the most significant factor influencing competitive advantage has a great impact on the organization's life and progress. Considering the expiration date of products in supply chain modeling is essential for ensuring operational efficiency, reducing waste, maintaining product quality, and ultimately driving business success. Therefore, this paper provides a two-level supply chain including manufacturer and distributor then chain modeling with considered conditions and applying the concept of Markowitz's theory. Finally, drawing the optimal cost curve of producer and distributor as an efficient frontier. For this purpose, the main contribution of the paper is determining the optimal cost of each level of the chain if the cost of another level is known and increasing the power of analysis. The proposed model applied in Darupakhsh Manufacturing Company and Mahya Daroo Distribution Company, a two-echelon supply chain design, including a manufacturer and a distributor is developed. At first, this chain is modeled, and then, implementing the concept of Markowitz theory, the optimal cost curve of producer and distributor is drawn as an efficient frontier. Findings show it is found that the optimal cost of the two echelons of the chain is inversely correlated and decreases with the increase of another one. Furthermore, it is found that the producer warehouse limit is redundant and has no effect on the final response. Also, with the increase in the cost of the manufacturer, the number of deliveries decreases, and instead, the number of products in each delivery increases, which results in a reduction in the costs of the distributor.

Optimization investment portfolio of ESG capital market in Indonesia: An investigation of Polynomial Goal Programming based on higher moments

The development of capital market investors in Indonesia has experienced rapid growth, leading to increasingly volatile movements in the domestic market. Companies or investment managers must form asset portfolios with optimal expected returns and measurable risks to address this issue. This study aims to analyze the potential combinations that can be formed using ESG Capital Market Indonesia 2022 and safe-haven instruments, utilizing the Markowitz theory and Polynomial Goal Programming (PGP) method. This research uses secondary data, and the research variables used are ESG Capital Market Indonesia 2022 and Gold from January 2007 to December 2022. Based on the previous research, the formation of portfolio combinations using safe-haven instruments, employing the Markowitz theory and Polynomial Goal Programming (PGP) method can provide better investment portfolio combinations during crises. Furthermore, the performance of each formed combination is measured using the Sharpe Ratio. The findings indicate that Markowitz's theory can generate better performance than the PGP method. However, it exhibits suboptimal skewness and kurtosis values compared to the PGP method.

Comprehensive Benefit Assessment of the Middle Route of South-to-North Water Diversion Project Based on Markowitz Theory

Comprehensive Benefit Assessment of the Middle Route of South-to-North Water Diversion Project Based on Markowitz Theory

The Net Zero Emissions Decision Model of the Sustainable Path of Chinese Business Parks

Business parks account for 30% of China’s total carbon emissions. Exploring emissions reduction approaches for business parks is crucial to achieve a net-zero emissions target, as well as for achieving a representative example for all types of emissions entities. Business parks mainly adopt two types of emissions reduction approaches: energy-saving renovations and purchasing carbon reduction products. However, there are limited studies focusing on the optimal combinations of the two approaches for reaching net-zero emissions and evaluating the cost effectiveness. To find a feasible and quantified way to build net-zero business park, a comprehensive path decision model is proposed. The problem is broken down into two parts: the optimal carbon reduction portfolio and the optimal electricity saving were researched. For the optimal product portfolio, the Markowitz theory is employed to balance the risk of carbon reduction products with the expected cost. In the part of optimal electricity saving, considering a ten-year life cycle, the total cost includes renovation investment, carbon reduction products cost, and cost saving of electricity consumption reduction. Based on the energy consumption, technical, and price data, the combination of energy-saving renovations and carbon reduction products is optimized. The model suggests a business park can save 24% of energy consumption through renovation investment and purchase CCER as 66% of the carbon reduction product portfolio. Taking only purchasing carbon reduction products as a benchmark to assess economic efficiency, implementing an optimized level of energy-saving renovation is found to save 16% of the comprehensive cost for the life cycle required to achieve zero carbon emissions. This model provides a new comprehensive optimization idea that will help future parks make decisions to achieve zero-carbon emission targets.

An Empirical Study on the Markowitz portfolio

Markowitz's portfolio model laid the foundation of the modern portfolio theory (MPT). As an intuitive and effective quantitative method, the Markowitz model has long been considered one of the most successful approaches in financial modeling. This paper tries to illustrate the process of Markowitz modeling and demonstrate the usefulness of the Markowitz theory empirically. Three high-tech companies, Apple Inc. (AAPL), Alphabet Inc. (GOOG), and Microsoft Corporation (MSFT) investigated to build the Markowitz model. We first retrieve the dataset from the website of yahoo finance and provide the descriptive statistics for the three companies, respectively. Then, the global minimum variance (GMV) portfolio is constructed to identify the boundary point of the efficient frontier. The optimized portfolio model at the given risk level is constructed according to the Markowitz theory. Also, the random portfolio weights under the budget constraint are generated for comparison. To evaluate the performance, we provide the Sharpe ratio for the constructed Markowitz portfolio.

Investment portfolios construction under the industrial chains of new-energy vehicles

New-energy vehicles are getting increasingly prevailing all around the world. Driven by the booming market, the whole industrial chains of new-energy are thriving. This essay combines the finance of a specific industry with the machine learning. It puts forward new suggestions and ideas for controlling the risks and expends the returns of the investment portfolio. This essay focuses on several new-energy leading enterprises in China and constructs a portfolio based on the Markowitz theory and gives the prediction to stock prices in one year based on Monte-Carlo Method to offer individual investors reasonable investment suggestions. It selects the daily stock prices of Tinci, Tianqi Lithium Corporation, Huayou Cobalt, CATL and BYD as the raw data including its opening price, closing price, highest possible price, lowest price, volume as well as the trading amount from 11st Jun 2018 to 28th Sep 2022. The experiment research shows that this method is effective in expanding returns and bringing risks down.

Maximizing Returns and Minimizing Risk: A Data-Driven Portfolio Optimization Analysis Using Markowitz's Theory and Sharpe Ratio

The implementation of new technologies in the financial sphere is expanding as the era of big data arrives. This study uses Python tools to choose four representative stocks from 11 distinct industries for portfolio analysis, based on Markowitz's portfolio theory. The best portfolio solution is discovered through empirical research: Maximum Sharpe ratio of one; The anticipated return, standard deviation, and Sharpe ratio were compared and examined, and the effective frontier of the asset portfolio was calculated using Monte Carlo simulation. In addition, as a simple trading method, build two different simple moving averages. Backtesting reveals that the ideal portfolio's return rate is close to 20% using this strategy.

Design of Quantitative Investment Strategy Based on Domestic Chip Industry

Select 59 concept stocks in the chip industry for quantitative analysis, use principal component analysis method and k-means clustering to process our financial indicators; use historical simulation method, variance-covariance method and Monte Carlo simulation method to calculate the VaR value of each stock for effective risk management. Based on Markowitz theory, the effective frontier of five stocks is constructed, combined with the utility of investors in different risk aversion levels, the best portfolio is selected to obtain the best portfolio of concept stocks in the chip field, using the Sharp ratio and CV ratio for performance evaluation, and the corresponding investment suggestions are given.

Analysis of Financial Investment Strategy of Manufacturing Enterprises under ESG System

At present, China is in the context of achieving the goal of "carbon peaking and carbon neutrality". From the perspectives of ESG responsible investment and value investment, this article aims at the investment efficiency of Chinese manufacturing enterprises. The 2018-2022 listed company market data is tested empirically. An efficient frontier is constructed based on Markowitz's theory, and the KMV model is used to measure the credit risk of a portfolio. The research found that: First, the value investment based on the ESG concept has much higher investment benefits than the CSI 300 Index over the same period. Second, corporate social responsibility can be recognized by the capital market, and the credit risk is therefore lower than the market average. The research conclusion of this paper proves that ESG value investment can promote the high-quality development of manufacturing industry. It provides an important policy inspiration for the Chinese government to implement the concept of sustainable development, which will convey the image of a responsible big country to the world.

Portfolio optimization based on self-organizing maps clustering and genetics algorithm

In this modern era, gaining additional income is necessary to fulfill daily needs since inflation is unavoidable. Investing in stocks can give passive income to help people deal with the increasing prices of necessities. However, selecting stocks and constructing a portfolio is the major problem in investing. This research will illustrate the stock selection method and the optimization method for optimizing the portfolio. Stock selection is carried out by clustering using Self-organizing Maps (SOM). Clustering will show the best stocks formed for a portfolio to be optimized. The best stocks that have the best performance are selected from each cluster for the portfolio. The best performance of the stock can be determined using the Sharpe Ratio. Optimization will be carried out using a Genetic Algorithm. The optimization is carried out using software R i386 3.6.1. The optimization results are then compared to the Markowitz Theory to show which method is better. The expected return on the portfolio generated using Genetic Algorithm and Markowitz Theory are 3.348458 and 3.347559975, respectively. While, the value of the Sharpe Ratio is 0.1393076 and 0.13929785, respectively. Based on the results, the best performance of the portfolio is the portfolio produced using Genetic Algorithm with the greater value of the Sharpe Ratio. Furthermore, the Genetics Algorithm optimization is more optimal than the Markowitz Theory.

Agent-based retail competition and portfolio optimization in liberalized electricity markets: A study involving real-world consumers

The liberalization of energy markets brought full competition to the electric power industry. In the wholesale sector, producers and retailers submit bids to day-ahead markets, where prices are uncertain, or alternatively, they sign bilateral contracts to hedge against pool price volatility. In the retail sector, retailers compete to sign bilateral contracts with end-use customers. Typically, such contracts are subject to a high-risk premium—that is, retailers request a high premium to consumers to cover their potential risk of trading energy in wholesale markets. Accordingly, consumers pay a price for energy typically higher than the wholesale market price. This article addresses the optimization of the portfolios of retailers, which are composed of end-use customers. To this end, it makes use of a risk-return optimization model based on the Markowitz theory. The article presents a simulation-based study conducted with the help of the MATREM system, involving 6 retailer agents, with different risk preferences, and 312 real-world consumers. The retailers select a pricing strategy and compute a tariff to offer to target consumers, optimize their portfolio of consumers using data from the Iberian market, sign bilateral contracts with consumers, and compute their target return during contract duration. The results support the conclusion that retail markets are more favourable to risk-seeking retailers, since substantial variations in return lead to small variations in risk. However, for a given target return, risk-averse retailers consider lower risk portfolios, meaning that they may obtain higher returns in both favourable and unfavourable situations.

Silver in Equity Portfolio Risk Optimization: Polish Investor Perspective

Purpose: The study aims to verify whether silver can help reduce the risk of the equity portfolio for a Polish investor without diminishing its return. What are optimal shares of silver and equity in such a portfolio, and does it also improve skewness and kurtosis of the portfolio return distribution compared with a stock portfolio? Do optimal shares change depend on the situation on the silver market? Design/Methodology/Approach: The author calculates descriptive statistics for silver and equity to decide if the former can diversify assets for the latter. As equity, the WIG20 Total Return index is used. Equity-silver portfolio optimization is conducted in the light of the Markowitz theory. The analysis is done for the period between January 2005 and April 2021. Findings: The research shows that including silver in an equity portfolio lets both decrease its risk and increase the return during the silver bull market and an extended period, which take part in a growing silver market trend. Conclusions do not change when the short sale is allowed. It is indicated that during silver bear markets 100% equity portfolio is not an efficient portfolio in the light of the Harry Markowitz theory. Simultaneously, the author suggests that although the portfolio diversification conducted in the study results in diminishing risk understood as variance or standard deviation, the results for skewness and kurtosis of created optimum portfolios are various. Practical Implications: The research may be interesting for institutional and individual Polish investors seeking different diversifying instruments in various market conditions. Originality/Value: The research contributes to the existing international literature by confirming that silver can be a diversifying asset and indicates its optimal shares in the silver-equity portfolio in different market conditions for a Polish investor endangered with USD/PLN currency rate risk.

Has the Composition of the Greek Banking Sector Investment Portfolio Contributed to the Greek Economy Financial Crisis?

The banking sector in Greece met a large growth and provided the Greek economy with a vital push after the credit release. The galloping increase of private, business, and public loans reinforced business activity and offered high incomes for a few years. However, this push that the Greek economy experienced was based on consumption and not on the development of financial sectors that could constantly produce income for the economy and the state. The research examines the Greek banking investment portfolio from 2003 until 2017 based on the portfolio theory of Markowitz. Furthermore, it evaluates its differentiation and examines whether or not has contributed to the financial crisis that the domestic economy faced the previous decade. The findings point out that the negative portfolio returns during the span of seven out of 15 reviewed years and their covariances highlight that the portfolio diversification was not successful according to Markowitz's theory.

Portfólio E-V eficiente: Bibliometria das evoluções considerando simulação ou métricas do risco com espaço objetivo aumentado

A produção científica e a necessidade de indicadores que a quantifique se fortaleceu e cresceu nas últimas décadas, como também a de ferramentas que auxiliem na sua mensuração e a busca por técnicas para analisar de forma temporal, entre outras, o volume de publicações, autores, citações e citações das referências. A bibliometria é uma importante técnica quantitativa e estatística para medir índices de produção e conhecimento científico utilizando softwares, palavras chaves de interesse e títulos para realizar levantamentos bibliométricos em plataformas de repositórios de artigos científicos, teses e livros. O trabalho objetiva analisar a veracidade de duas suposições sobre as evoluções, até a presente data, do modelo da teoria de portfólio E-V eficiente de Markowitz. A primeira se existe evoluções do modelo, com simulação pelo método de Monte Carlo, que utilizem a simulação como um fim para obter a distribuição de probabilidade empírica de todos os resultados ótimos inerentes à simulação e não, pelo usual método de concentração de dados, sendo apenas um meio para se obter melhores resultados e modelos, para comparação entre modelos ou para análise de resultados dos modelos ou ainda para projeção dos resultados dos modelos em janelas de holdout. A segunda se existe evoluções do modelo utilizando métricas do risco com espaço objetivo aumentado, possibilitando a estimação de um maior número de parâmetros. A partir de softwares para análise bibliométrica se conseguiu chegar à conclusão de que na teoria analisada, e nas suas evoluções até a presente data, as duas suposições não são verdadeiras.

Changes in the Portfolio Management and Construction under the Pandemic Era

This paper focuses on comparing portfolio management and construction before and after the coronavirus. First, this paper presents the importance of building up portfolios for investors to diversify their risks. Theories on portfolio management are discussed in this section to show how they have been developed to help on investing and reduce risk. Then, the paper moves on to show the impact of the pandemic on the financial market and portfolio management. Sample data on tech stock returns are collected to perform a Monte Carlo simulation on portfolio construction to find out the efficient portfolio before and after the COVID-19 outbreak. The efficient portfolio is build based on the Markowitz theory to find the combination. Comparisons between these portfolio constructions are made to find out the changes in portfolio management and construction under the pandemic era. In conclusion, this paper presents how pandemic has changed and impacted the investments and lists recommendations on future portfolio management and construction.

Optimal sizing of battery energy storage system in smart microgrid considering virtual energy storage system and high photovoltaic penetration

In the smart microgrid system, the optimal sizing of battery energy storage system (BESS) considering virtual energy storage system (VESS) can minimize system cost and keep system stable operation. This paper proposes a two-layer BESS optimal sizing strategy considering dispatch of VESS in a smart microgrid with high photovoltaic (PV) penetration. In the first layer, VESS modelling and aggregation are established, and the initial size of BESS is determined by considering VESS participation in demand response program. In the second layer, the optimal sizing of BESS is studied and the optimal energy resources dispatching strategy is formulated via considering various constraints in the system. The mean-variance Markowitz theory is applied to assess the risk of system cost variability due to the presence of PV and load uncertainties. With the ratio of load varies from 70% to 130%, and PV generation ratio from 40% to 100%, sensitivity analysis reveals the optimal size of BESS is less impacted by PV generation change. Also with VaR(95%) the risk of system cost variability can be further reduced through VESS participation.

Stochastic optimization of integrated energy system considering network dynamic characteristics and psychological preference

To improve the flexibility of integrated energy system (IES) and promote the clean energy accommodation, an IES stochastic optimization model considering the network dynamic characteristics and psychological preference is proposed. Firstly, the uncertainty and spatial-temporal correlation between multiple wind farms are dealt by the auto-regressive and moving average (ARMA) time series and Cholesky decomposition, and then typical scenarios are constructed by the scenario method. Secondly, considering the dynamic characteristics of heat and gas networks such as heat network delay, thermal inertia of buildings and gas linepack, the IES model which coordinates the supply side, transmission side and demand side is proposed. Finally, based on the mean-variance Markowitz theory and endowment effect in behavioral psychology, the influence of human psychological preference (such as risk concern and loss aversion) on the IES is reflected. A 52-node electricity-gas-heat IES is used to verify the proposed model. The simulation results reveal that the network dynamic characteristics and demand response (DR) can effectively improve the IES flexibility and wind power accommodation. Meanwhile, the psychological preference and wind power spatial-temporal correlation also have significant influence on the IES optimization.

Oil supply risk and affecting parameters associated with oil supplementation and disruption

The fossil fuel energy carriers significantly affect the energy security. The oil security has turned to one of the main political agenda by considering the two world’s oil crises. In this study, an index of oil supply vulnerability has been developed to compare the world’s top fifteen oil importing South Asian countries. The index includes comprehensive set of indicators like imported oil over GDP ratio, market liquidity, GDP per capita, geopolitical risk, diversification, the ratio of oil importation over consumption, transportation risk, oil price volatility and US $ volatility. Two popular techniques (composite indicator (CI) and the principal component analysis (PCA)) were used to combine all the aforesaid indicators. Although numerous techniques have been used to assess the oil vulnerability index, for example DEA like models and Markowitz theory of portfolio, none of them incorporated the principal component analysis and composite indicator together to develop an oil vulnerability index. Results shows that the South Asian countries have highest economic, supply and overall oil vulnerability risk whereas the second group countries Belgium, Thailand, Spain, Netherlands, Japan, Korea, India and China are in a relatively less risky as compared to South Asian countries. Contrary to this third group of countries are Canada, Singapore, UK, and France, Italy, Germany and US are considered as a least vulnerable country.