Maximum Sharpe Ratio Research Articles

Comparison of Markowitz Model and Index Model in Capital Markets

We are searching for an optimal portfolio that plays a significant role in portfolio management by maximizing the expected return subject to a constant risk or minimizing the risk for a constant expected return. In this work, we first calculate the basic statistical information of our risky instruments, the probability density functions, and the Q-Q plot to compare the daily and monthly data for ten stocks and one broad equity index. We conclude that the monthly returns data is much closer to a normal distribution. Second, when calculating the correlation coefficients, we find that the stocks of the same industry are often highly correlated. Third, through the plotting of the feasible portfolio regions using the Markowitz Model (MM) and the Index Model (IM) consisting of various portfolios under different constraints, calculating two essential points on the efficient frontier, and analyzing the CAL, we generalize that the contrast between the MM model and IM model have similar results whether there is weighted SPX. Compared with the IM model, the MM minimal variance portfolio and maximum Sharpe Ratio the olio the MM model is more desirable than the IM model. The introduction of the generic index SPX affects the results of both models to a certain extent. Finally, we use the Monte Carlo method to simulate that the generated points are all within the feasible region, which indicates that the sample results are reasonable. Our research not only further supplementary the empirical research of the MM model and IM model, but we provide investors with some investment suggestions for constructing portfolios.

Optimal Investment Portfolio Analysis Using The Markowitz Model For Stock In Each Sector In The Indonesia Stock Market During Covid 19 (2020-2021)

The COVID 19 pandemic in early March 2020 starting from Wuhan had a very large impact on the global economy and the Indonesian economy, the COVID 19 pandemic forced the government to establish a PPKM policy (Implementation of Restrictions on Community Activities) to suppress the spread of Covid 19 in Indonesia. Indonesia's State Gross Domestic Product fell in the second quarter 2021 amounting to -5.32% and also having an impact on the stock market in Indonesia at January 02 2020 the JCI was recorded at 6283 fell to 3937 in March 24 2020 (minus 36.77%) in March 2020. The results of this study using 22 of the stocks representing 11 sectors in the stock market in Indonesia obtained a maximum Sharpe ratio calculation of 31.57% with a weekly yield of 1.48% and a standard deviation of 4.39% and a maximum yield with a Sharpe ratio of 31.29% and a yield weekly yield of 1.37% and a standard deviation of 4.08%, the result of the minimum standard deviation with a Sharpe ratio of 5.92% with a weekly yield of 0.24% and a standard deviation of 2.51% and the results of Portfolio in the efficient frontier namely portfolio 6 with a Sharpe ratio of 30.94% and weekly yield of 1.3% and a standard deviation of 3.9%. For investors who want to optimize their portfolio, they can choose stocks with optimal Sharpe ratios that already pay attention to risk-adjusted return.

Portfolio Optimization for Five Influencing Companies of Technology Industry in the Hong Kong Stock Market

Nowadays, as a such big number of countries pay more attention to the scientific research strength, The importance of high and new technology is more and more recognized, the proportion in the securities market is increasing, technology stocks in the eyes of investors. This paper selects 5 Chinese technology growth stocks in Hang Seng Index as the research object and establish the dataset which contains the monthly time series of price in Hang Seng index. Fama experiment is used to well diversify the idiosyncratic risk and make sure that the portfolio is affected by the system risk. Through the mean-standard deviation plot, it can check the independence of the data we collect and check the normality. The portfolio can be divided into two situations: one includes risk-free assets and non risk-free assets. Finally, the performances of the portfolios are accessed including return volatility and weight of assets. The results show that, first, based on the Fama experiment, at least 5 stocks must be chosen to deal with idiosyncratic risk. Second, according to the mean-standard deviation plot,all the assets data are i.i.d. Third, the result show that both maximum return portfolios have the high return, and the portfolio contains risk-free assets is higher than portfolios without risk-free assets in the maximum return portfolio, but lower in the maximum Sharpe ratio portfolio. The findings may be useful to stimulate investors pay attention to invest in the technology stocks and create efficient portfolio. Meanwhile, this paper can suggest people how to rationally allocate stocks from multiple dimensions, build an effective combination, and try to obtain higher returns as far as possible in the condition of low risk.

Portfolio Construction Based on Optimization Model and Combination of Various Assets

Since the fifties of the last century, the concept of portfolio management is proposed to enrich the portfolio theory by Markowitz et al., as well as the improvement of portfolio theory by later generations, forming a modern portfolio management theory. This paper uses Markowitz's mean variance portfolio theory to perform a portfolio return maximization analysis on selected assets with assumptions that investors are risk-averse according to mean variance theory. Based on mean variance portfolio theory, as well as Python computational simulation modeling, Monte Carlo simulation is used to find the effective set and effective frontier of the portfolio, and the optimal solution of the portfolio is filtered according to the two constraints of maximum Sharpe ratio and minimum volatility. According to the analysis, the portfolio return of the maximum Sharpe ratio is relatively high, and the maximum Sharpe ratio combination is more worthwhile than the minimum volatility combination. Overall, these results provide enlightenment for further exploration and implementation of portfolio theory.

Portfolio Optimization for Five Representative Companies in Different Industry

This report examines the asset allocation analysis of a portfolio in the context of assets across multiple sectors. Due to the volatile global economic situation and the significant inter-industry effects, allocating and combining assets across different sectors is essential. This research use the capital asset pricing model (CAPM) and the Fama-French three-factor model to determine, for a portfolio of five sectors, the proportion of investments in each sector at maximum Sharpe ratio and minimal variance. These five sectors include energy, pharmaceuticals, automotive, retail and technology. Under both models, the technology and pharmaceutical sectors should be allocated a more significant proportion of the portfolio at the lowest variance, i.e., when volatility is relatively low, while the retail sector should not be included in this portfolio. On the other hand, the retail and automotive sectors are allocated a smaller proportion of the portfolio when the Sharpe ratio is the largest. The results of this report may be helpful for investors in the relevant sectors of the financial markets.

Portfolio Optimization Analysis in American Industry

Portfolio optimization, as a process of reorganizing investment and dispersing risks by considering the established target return and risk tolerance, is widely used in the financial field. This paper analyzes the asset allocation of six kinds of assets. It uses three methods, namely, mean-variance analysis, CAPM, and the FF3F model, to optimize the investment portfolio. At the same time, the proportion of assets in the portfolio should be considered under the conditions of maximizing the return or minimizing the risk at a specific risk level. The results show that in the mean-variance model, the AEP and Gold ETF have the most considerable weight in the combination of maximum Sharpe ratio and minimum variance, respectively. In the FF3F model, AT&T and Gold ETF have the most prominent weight in the combination of maximum Sharpe ratio and minimum variance, while in CAPM, Google and Gold ETF have the most significant weight in the combination of maximum Sharpe ratio and minimum variance respectively. This research may help potential investors interested in power, communication, science and technology, gold, and automobile industries.

Portfolio Optimization for Six Companies in Different Industries

Portfolio optimization is an essential step in the process of asset management. Studying portfolio can help people gain greater benefits after investing their assets. This paper makes a subjective analysis of the stocks in the American stock market, and finally selects six stocks from different fields, including health care, finance, public utilities, Internet software and services, non-energy minerals, and industry for portfolio analysis. This paper uses mean-variance analysis, CAPM model and Fama-French model to get the best portfolios, and analyses portfolio performance under different methods. The results show that, in the CAPM model, "GS" gets the largest weight in the maximum Sharpe ratio portfolio and "AWK" gains the largest weights in the minimum variance portfolio. At the same time, in the Fama-French model, "GS" and "AWK" still get the largest weight in the maximum Sharpe ratio portfolio and minimum variance portfolio, respectively. This paper will be helpful to investors who pay attention to the six areas involved in this paper.

Application of Fama-French Three-Factor Model in Firefighter Investment Strategy

Using some models to make the portfolio optimization is a widely used approach nowadays. This paper studies how to choose the right portfolio to diversify for the firefighter who is about to retire. This allows customer to avoid risks while obtaining appropriate benefits. This paper selected five stocks from different sectors that performed better and used two main approaches. It uses the Mean-Variance analysis to analyze how to make these two mutually restricted goals, i.e., minimum variance portfolio and the maximum Sharpe ratio portfolio. At the same time, the FF3F model is used to analyze the investment weight of the selected portfolio, so that the funds can be reasonably invested. The results show that all the stocks are positively correlated. In the FF3F model, the Sharpe ratio of the non-buyout case is higher than that of the buyout case. The results in this paper show that the option with higher Sharpe ratio can obtain more return in per unit risk and is more suitable for firefighters.

Portfolio Optimization for Junior Investors under Different Industries

Portfolio optimization has long been considered as an integral procedure of the financial markets. However, optimizing the portfolio may be difficult for junior investors. Therefore, this paper conducts a portfolio containing five diversified assets covering the e-commerce, entertainment industry, finance and insurance, and energy industries, and explores the optimal portfolio by maximizing the Sharpe ratio and minimizing the variance for each of these five assets through three models which are mean-variance analysis, CAPM and FF3F model. The results show that under both the FF3F and CAPM models, DIS has the maximum investment weight in maximum Sharpe ratio portfolio, while GLD has the maximum investment weight in minimum variance portfolio. We then added a risk-free asset to the existing portfolio, and the results display that adding a risk-free asset can further optimize the portfolio's return and reduce its risk. This research can be useful for potential investors who are into investments in related industries.

How does investment portfolio change in pre and post epidemic era?--experience from Chinese medical and pharmaceutical industry

The exogenesis shock, the Covid-19 epidemic, is considered as a big shock in the financial market. The paper discussed how the investment portfolio comprising of the top ten medical and pharmaceutical stocks, changes before and after the break of epidemic. Three constraints are taken into consideration to provide more information to investors. Also, the Medical and Pharmaceutical Index instead of the market return ratio is considered as standard, allowing it much closer to the reality. The research finds that the investors have greater confidence on medical and pharmaceutical industry in the post-epidemic era than in the pre-epidemic era, presented by higher annualized average return and lower Sharpe ratio. The research of this paper will provide some portfolio-construction experience under the global negative shock. At the same time, it is also worth noting that this paper mainly focused on the changes of portfolios with the aim of creating the maximum Sharpe ratio and the minimum standard deviation under certain constraints, whose results showed that the market are having growing confidence in the medical and pharmaceutical industry in the post-epidemic era and more capital is flowing to the corporations with out-standing performance in the anti-epidemic period.

Application of Maximum Sharpe Ratio and Minimum Variance Portfolio Optimization for Industries

Since the start of 2022, expectations regarding the continuous raising of interest rates by the Fed to curb the 40-year-high inflation has been negatively impacting the US stock market, leading to volatility spikes. Thus, portfolio optimization plays an important role to risk-averse investors. This paper investigated an optimal portfolio strategy that aims to maximize the Sharpe ratio to outperform a common benchmark, the S&P500. Eleven US stocks were selected, one from each of the eleven market sectors, based on market capitalization. Then, mean-variance portfolio optimization was conducted to obtain an optimal distribution of stocks weighing in Maximum Sharpe Ratio Portfolio (MSRP) and Global Minimum Variance Portfolio (GMVP), and backtesting was adopted to construct portfolio performance for MSRP, GMVP and Equal-Weight Portfolio (1/N) strategies by using historical data from the first eight months of 2022. The Sharpe ratio was calculated to compare the performance between the three strategies---MSRP, GMVP and 1/N---and the S&P500. Empirical results, supported by a robustness test, suggested that MSRP strategy outperformed S&P500 with the highest Sharpe ratio, which indicated that MSRP achieved a higher return per unit of risk regardless of market volatility presented in different time intervals. Therefore, this research provides insights into portfolio investment decision-making for risk-averse investors.

Portfolio Management for Multi-industry

In the financial field, portfolio management is an important measure in the direction of investment or hedging. This paper mainly focuses on the optimization for the portfolio composed of assets from five industries, which is education, banking, automobile manufacturing, parts industry and e-commerce, and considers the allocation of assets to optimize the returns. In this paper, five representative assets from these five industries are selected. The Markowitz efficient frontier is plotted by Monte-Carlo method, using the return data of assets. Then the portfolio is optimized by mean-variance analysis and the maximum Sharpe ratio portfolio as well as minimum variance portfolio can be calculated. Finally, this paper analyzes the performance of the two portfolios, considering the influence of individual assets on the portfolio weight, and uses the Fama-French three factor model to analyze the performance of the portfolio. The results show that PTAIY and PSO from parts manufacturing and education occupy a large proportion in the maximum Sharpe ratio portfolio as well as the minimum variance portfolio. The findings could help investors interested in these five areas.

Research On Portfolio Construction for Information Technology and Communication Service Industries Based on The Monte Carlo Simulation

Attention is paid to the portfolio construction of the information technology and the communication services industries affected by the Covid-19. Firstly, the representative stocks which cover the most varieties of different market values are selected and the preliminary analysis for return performance is performed. Then, the event-study methodology is used to explore the effect of Covid-19 on the stocks chosen by this paper. The Monte Carlo simulation is also used to do the portfolio optimization. In the process of research, the Monte Carlo simulation and event study method are mainly used. Through the former one, the efficient frontier is obtained. Besides, this research also get the minimum volatility portfolio, where AT&T has the largest share of 16.33%, and the maximum Sharpe ratio portfolio, where ZOOM has the largest share of 18.79%. Then through the results of event-study, it is found that most companies generated negative abnormal returns on event date and had negative cumulative returns during the post-event window. Finally, the back test is done by comparing our portfolio with the equal weighted portfolio and NASDAQ index, and our work performs better both in the return and the risk. The results in this paper benefit the investors in the technology and communication service industries, which is especially helpful for them to do invest decision after COVID-19.

Decision-making support system for managing portfolios of energy saving projects at energy-intensive enterprises

Purpose. Development of a software complex based on decision-making methods for managing a portfolio of energy-saving projects at energy-intensive enterprises. Methodology. To solve the problem of managing project portfolios, Markowitz's portfolio theory of financial investments was chosen, which allows for the most profitable distribution of portfolio risk and performing income assessment using optimization methods. In combination with this theory, it was determined to use the methods of finding the maximum Sharpe ratio, as well as the minimum volatility based on a data package of randomly generated portfolios. Findings. As a result of the work performed, a software system was developed, which has in its functionality the automatic download of a data package of selected shares for the specified period of time from the electronic resource, generates a random portfolio and performs its optimization by maximizing the Sharpe ratio and minimizing the volatility of the portfolio. Also, the program has the ability to display the results of optimization of the generated portfolio in the form of tables and graphs. The decision support system for managing portfolios of energy-saving projects was considered through its generalization to methods of optimizing investment portfolios, but taking into account the specifics of the subject area. The software complex was tested on a data set of share prices in energy-intensive enterprises. Graphical data and tables obtained as a result of system operation allow the program user to evaluate fully the created energy saving project portfolio. Originality. The developed software system combines right away several methods, namely: methods of optimizing an investment portfolio according to Markowitz's portfolio theory, methods of finding the maximum Sharpe ratio and methods of finding minimum volatility. This solution allows you to use the system to solve a wide range of tasks. Practical value. The completed development makes it possible to optimize conveniently the investment portfolios for various assets, which makes it possible to use the development of energy saving project portfolio management in energy-intensive enterprises. Also, the system can serve as a basis for such developments.

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.

Two-Stage Portfolio Optimization Integrating Optimal Sharp Ratio Measure and Ensemble Learning

The traditional portfolio theory has relied heavily on historical asset returns while ignoring future information. Based on ensemble learning and maximum Sharpe ratio portfolio theory, this paper proposes a two-stage portfolio optimization method by considering asset forecast information, aiming to improve the performance and robustness of a portfolio. In the first stage, concerning the underlying asset selection, we integrate six individual prediction models using the ensemble learning method to forecast the future return of assets where the assets with higher potential returns are selected for portfolio optimization. In the second stage, we propose a novel investment strategy by combining the forecasted returns of selected assets with the maximum Sharpe ratio portfolio model. In the empirical analysis, we employ the constituent stocks of the China Securities Index 300 (CSI 300) to test the out-of-sample performance of the proposed strategy with several traditional portfolio strategies, including minimum variance portfolio strategy, traditional maximum Sharpe ratio portfolio strategy, 1/N portfolio strategy, and CSI 300 index. Our analytical results show that (1) compared to individual forecasting models, the ensemble learning method is more accurate in forecasting stock returns, and (2) the proposed portfolio strategy largely outperforms most of its competitors in terms of the Sharpe ratio, Sortino ratio, Omega ratio, and Calmar ratio. This indicates that the proposed two-stage portfolio optimization method is of potential to construct a promising investment strategy due to its trade-off between historical and future information of assets.

Robust Markowitz: Comprehensively maximizing Sharpe ratio by parametric-quadratic programming

<p style='text-indent:20px;'>Markowitz formulates portfolio selection and calls the optimal solutions as an efficient frontier. Sharpe initiates Sharpe ratio for frontier portfolios' reward to variability. Finance textbooks assume that there exists a line which passes through a risk-free rate and is tangent to an efficient frontier. The tangent portfolio enjoys the maximum Sharpe ratio.</p><p style='text-indent:20px;'>However, the assumption is over-simplistic because we prove that other situations exist. For example, Sharpe ratio itself may not be even well-defined. We comprehensively maximize Sharpe ratio. In such an area, this paper contributes to the literature. Specifically, we identify the other situations by parametric-quadratic programming which renders complete efficient frontiers by piecewise-hyperbola structure. Researchers traditionally view efficient frontiers by just isolated points. We accomplish handy formulae, so investors can even manually process them.</p><p style='text-indent:20px;'>The COVID-19 pandemic is unleashing crises. Unfortunately, there is quite limited research of portfolio selection for COVID. In such an area, this paper contributes to the practice. Specifically, we originate a counter-COVID measure for stocks and integrate it as a constraint into portfolio-selection models. The maximum-Sharpe-ratio portfolio outperforms stock-market indexes in sample. We launch the models for Dow Jones Industrial Average and discover outperformance out of sample.</p>

Real-Time Portfolio Management System Utilizing Machine Learning Techniques

There are 1641 companies listed on the National Stock Exchange of India. It is undoubtedly infeasible for a retail investor to invest in all the stocks. It is a well-known fact that the portfolio’s return is an average return of all its constituent stocks, and risk will be less than or equal to the maximum risk of all the portfolio components. This paper is unique as it elaborates on the entire portfolio selection, optimization, and management process. Portfolio selection is accomplished through the K-Means algorithm. Optimization is achieved utilizing the genetic algorithm, and a sliding window is applied for portfolio management. Four different ways of portfolio calculation, namely, equally-weighted portfolio, global minimum variance portfolio, market cap-weighted portfolio, and maximum Sharpe ratio portfolio, are applied. The results depict that all three optimized portfolios outperform the Nifty index. The dataset for the study is obtained from globaldatafeeds.in.

Portfolio Analysis for the Retired Population

Based on the realistic needs of retirees, this paper examines the optimal investment portfolio through diversification. Allows retirees to maximize their returns while taking less risk. Stocks include technology, real estate, biopharmaceuticals, education and other industries. In this study, monthly closing prices from October 2017 to October 2020 were selected as data, and the mean-variance model, CAPM model, and FF3F model were used to calculate the maximum Sharpe ratio and the percentage of each stock, respectively. In the mean-variance model, the maximum Sharpe ratio is about 0.35, of which Vanke accounts for 0 and AAPL accounts for the largest share, about 0.5; in the CAPM model, the maximum Sharpe ratio is about 0.11, of which Heng Rui-like accounts for 0 and CSL accounts for the largest share, about 0.353; in the FF3F model, the maximum Sharpe ratio is about 0.11, of which Heng Rui-like accounts for 0 and CSL accounted for the largest ratio of about 0.45. Meanwhile, this paper calculates the covariance and correlation coefficient between each asset. The correlation coefficient of each asset is obtained close to 0, and the correlation degree is low. Heng Rui Pharma is negatively correlated with Vanke, then this use is that the inclusion of AB in the portfolio at the same time will reduce the risk of the portfolio.

Portfolio Construction Based on Markowitz Model and Index Model for Multiple Assets

Asset allocation has a long history, and is of vital importance. In retrospect, big events (e.g., the World War) gave rise to various shocks to the financial markets and brought large fluctuations. Contemporarily, COVID-19 has been greatly affected the daily life of human beings as well as the stock market for 3 years. On this basis, the research topic is about portfolio construction for multiple assets using Markowitz Model and Index Model in order to gain stable and risk-hedge return from the volatile market. The paper includes a deep analysis of 3-year data of 8 stocks from 3 types of companies in USA. Then it calculates the Minimal Variance Point, Maximum Sharpe Ratio, together with the efficient and inefficient portfolio construction with regard to 3 constraints. Based on the evaluations, this study provides an idea and method of asset allocation in a certain situation, and is appliable in various situations if is flexibly used. These results shed light on guiding further exploration of portfolio construction.