Minimum Volatility Research Articles

Portfolio Optimization Based on 9 Chinese Stocks

Geopolitical conflicts and the impact of the pandemic have triggered volatility and downward trends in the Chinese stock market, prompting investors to pay more attention to stabilizing returns and controlling risks through optimizing portfolios. This study selected nine stocks listed on the Shenzhen and Shanghai Stock Exchanges in China and first identified the efficient frontier composed of these nine stocks, then constructed portfolios with maximum Sharpe ratio and minimum volatility. The results indicate that China Yangtze Power Co., Ltd. holds the highest investment weight in all portfolios, followed by Kweichow Moutai Co., Ltd. which also holds significant weights in both portfolio types. By comparing the cumulative returns of the two portfolios with the HS300 index, it was found that the performance of all portfolios outperformed the benchmark index. This result can provide guidance for some investors in managing investments during this particular period of market downturn.

Empirical Analysis of Portfolio Allocation During Market Turbulence Based on Efficient Frontier

The global financial markets have experienced considerable turmoil due to the COVID-19 pandemic, in this context, portfolio management becomes critically important. This paper employs Monte Carlo Simulation to determine Efficient Frontier of a portfolio comprising fourteen US technology stocks in the period of COVID-19 pandemic by python, which also allocates portfolios for Minimum Volatility and Maximum Sharpe Ratio, along with their key parameters. According to this study, Maximum Sharpe Ratio portfolio outperforms Minimum Volatility portfolio in terms of cumulative return. However, its important to note that Maximum Sharpe Ratio portfolio also experiences a greater maximum drawdown. Additionally, this paper visually depicts the optimal allocation of asset weights across different levels of risk aversion using a chart. Furthermore, it identifies NVDA as the optimal choice for investors who have low degree of risk-aversion due to its high volatility and expected return. Conversely, IBM and CSCO emerge as the preferred choices for risk-averse investors, as they effectively mitigate the portfolios entire risk.

Comparison of Portfolio Optimizations under Markowitz Model in Technology Sector and Financial Services Sector

In the period of Covid-19, different sectors received different levels of shocks, which gave investors a degree of caution when investing in various sectors. Therefore, portfolio optimization - using specific model to assign weights of stocks to achieve a higher return while reducing risk – becomes a popular strategy. This paper chooses the Markowitz model to find optimal sector-based portfolios, specifically in technology sector and financial services sector, as well as portfolios that contains stocks in both sectors. The study uses Python to do Monte Carlo simulation, finding two optimal portfolios with maximum Sharpe ratio and minimum volatility for each sector(s), and finally comparing performances to test if the sector-based portfolio works better than the inter-sector portfolio. According to results, the minimum volatility portfolio in combined sectors reaches the same return of 0.11 as the minimum volatility portfolio in technology sector, but with lower volatility. It means the inter-sectors portfolio is better off when seeking minimum volatility. On the other hand, the maximum Sharpe ratio portfolios in technology sector, financial services sector, and combined sectors have values of returns and volatility ordering from highest to lowest. As a result, with current information, without investors’ investment preference, the optimal maximum Sharpe ratio portfolio cannot be determined and needed further exploration.

Portfolio Optimazation Based on 10 US Stocks

The US stock market has recently become volatile because of the increase in interest rates, which arouses investors focus on portfolio optimization. This study selected 10 representative US stocks from different industries listed on NASDAQ and NYSE. This paper applies Monte Carlo simulations to determine the efficient frontier and constructs portfolios with maximum Sharpe Ratio and minimum volatility. The result showed that Lululemon Athletica Inc. possesses the largest proportion of the maximum Sharpe ratio portfolio, and the Coca-Cola Company occupies the greatest weight in the min volatility portfolio. By comparing the cumulative return of the two portfolios with the NASDAQ Composite Index, the max Sharpe ratio portfolio is found to overperform the market benchmark. In the robustness test in which 8 stocks selected from the original group of assets are taken to construct a portfolio, the same result still holds. This result may demonstrate the feasibility of portfolio management for a few investors in that period.

Portfolio Optimization Based on Six Chinese Stocks

China's capital markets started late and there are still many problems with securities trading, adding to the risks for investors. Establishing a portfolio in the A-share market and reducing non-systemic risks through diversification of investment not only reduces the volatility faced by investors, but also stimulates the enthusiasm of investors and enhances the liquidity of the capital market. Therefore, six representative stocks of Yahoo Finance are selected in this paper, and the adjusted closing price of stocks is collected. The mean-variance model is used to find the optimal weight ratio of these six stock portfolios through training sets and test sets. The actual returns are compared with the market to evaluate the outcome of the portfolio. The model results demonstrate that the Sharpe ratio of the portfolio with the highest Sharpe ratio is 68.70%, and the weight of Wuliangye is the highest at 73.55%, while Shenzhen Fountain is only 0.16%. The volatility of the least volatile portfolio is 26.48%, of which YUNNAN BAIYAO has the highest weight (37.78%), and Hithink RoyalFlush has the lowest weight (0.73%). The minimum volatility portfolio yields less than the maximum Sharpe ratio portfolio, but both outperform the market. After excluding the smallest stocks in the portfolio, the portfolio remains stable. The results displays that the mean-variance model can play an effective role in constructing the portfolio of A-share market.

A Novel way to Diversify Portfolio Weights

There is broad agreement among academics and practitioners that, in general, a diversified portfolio delivers more robust out-of-sample performance than a concentrated one. This paper develops a new method to diversify portfolio weights, which does not rely on expected returns or volatilities and is therefore robust to measurement error in these variables. It uses pair-wise regressions to estimate how much variation each asset explains in terms of another asset. The optimization function finds the portfolio weights that maximize the unexplained variation of the portfolio. We benchmark our method against established methods from the literature, such as the minimum volatility and the equal risk contribution portfolios. We demonstrate that our method adheres to established diversification properties and it performs well in empirical tests.

Optimized Portfolio Structured by 5 Stock Indexes

Equity market declines fiercely caused by the current liquidity crisis. Investors pay more attention to optimized portfolio in order to reduce losses. 5 representative indexes were chosen from capital market to construct financial portfolios. The sketch of the efficient frontier was plotted, and portfolios with the 1/N, the maximum sharpe ratio and the minimum volatility were acquired based on 10000 scipy optimization calculations, the FTSE100 accounts for the largest section of the portfolio with the maximum sharpe ratio while the SSE Composite Index possesses the biggest shares in the portfolio with minimum volatility. Comparing three portfolio returns of accumulations, it could be observed that the maximum sharpe ratio portfolios performance surpassed the 1/N and the minimum variance portfolio, several investors could make reasonable decisions refer to this result in the special tough period.

Portfolio Optimization Based on 10 US Stocks

Focusing on the U.S. market, this research selects ten high-capitalization U.S. stocks in different industries and uses stock price forecasting in machine learning as well as Monte Carlo simulation to explore the efficient frontier of assets. Besides, this paper builds a portfolio with equal weight, maximum Sharpe ratio, and minimum volatility criteria, respectively. The results show that the Exxon Mobil Corporation possesses the largest proportion of the maximum Sharpe ratio portfolio, and the UnitedHealth Group Inc. accounts largest weights for the portfolio with the minimum volatility. In addition, this paper also compares the cumulative returns of the three investment portfolios with the important index NASDAQ of the US stock market. The results indicate that that the above mentioned three portfolios are all better than the benchmark index and can obtain a higher return. The results may shed light on some investors' approach to portfolio management during this extraordinary time.

Portfolio Optimization under the Background of Continued Interest Rate Hikes

In the process of investment, the primary investment objectives for investors are undoubtedly risk minimization and return maximization. This paper fo-cuses on the US investment market and, in the context of the Federal Re-serve's continuous interest rate hikes, avoids the currently popular artificial intelligence sectors, and focuses on the analysis of representative stocks in the manufacturing, pharmaceutical, technology, and financial industries. This paper selects 10 stocks from the above-mentioned industries for analy-sis. This paper collects stock prices, financial data (including P/E ratio, BPS, etc.), risk-free rates, market indices, and other data, and uses multiple linear regression models to predict the return data from January 1st, 2023, to March 10th, 2023. Next, the mean-variance framework is employed for the purpose of selecting both the portfolio with the highest Sharpe ratio and the one with the lowest volatility. Once the weights for both groups are ob-tained, this study tests the portfolio's performance using actual stock price data spanning from January 1st, 2023, to March 10th, 2023. After obtaining the performance data of the two groups, this paper further compares the per-formance of the portfolio with the 1/N portfolio and the market performance. The results show that the market performance is the best, followed by the 1/N portfolio and the minimum volatility portfolio, and the maximum Sharpe ratio model is the worst. This result may provide some guidance for portfolio management for some investors in this special period.

Portfolio Optimization for 5 US Stocks

Nowadays, the rose of interest in the US and the changes in the value of the dollar case the public attention of investors on stocks. The US company stock was under a great change in this situation. So, the investors are now focusing on finding the portfolio optimization on the investment allocation. This study directly focuses on the selected five stocks of interest company to find the portfolio optimization using the Monte Carlo simulation and com-pare its return with the actual data. By Monte Carol simulation, the maxi-mum Sharpe ratio and the minimum volatility portfolios would be generat-ed, Netflix is regarded as the largest weight in the maximum Sharpe ratio portfolio, while Sunning is regarded as the largest proportion weight in the minimum volatility portfolio. Besides, after evaluating the results, the max-imum Sharpe ratio and minimum volatility portfolio perform better than the standard 1/N portfolio. Using this portfolio optimization, investors can find how to allocate their investment through several stocks to get the maximum returns with relatively low risk.

Portfolio Optimization Analysis -- Based on Six Stocks from Different Industries in the U.S. Stock Market

As the stock market becomes more and more unstable, investors all over the world pay more attention to risk management. Creating a portfolio is an effective way to make the trade-off between risk and return rate. This paper selects six stocks from the U.S. stock market in different industries, including the real estate industry, high technology, financial services company, pharmaceutical industry, automotive manufacturing industry and gas industry. This paper simulates 1,000,000 different investment portfolios by using the Monte Carlo simulation, then drawing the efficient frontier of the portfolio and figuring out the maximum Sharpe ratio and minimum volatility portfolio. As the results showed, McKesson Corporation accounted for the max proportion in both the maximum Sharpe ratio portfolio and the minimum volatility portfolio, which are 45.7149% and 60.8960% respectively. J.P. Morgan takes up 0.1232%, which is the min proportion in the maximum Sharpe ratio portfolio. However, Amazon accounted for the min proportion in the minimum volatility portfolio, which is 0.4828%. In the last, this paper compared the cumulative return of the three portfolios with the S&P 500 Index, only the return rate of the equal-weight portfolio and minimum volatility portfolio is better than the benchmark. Hence, this result may provide suggestions for picking certain kinds of portfolio in this special period.

Enhancing Portfolio Performances through LSTM and Covariance Shrinkage

Portfolio optimization is a crucial aspect of finance, requiring advanced analytical tools and modeling techniques. This paper proposes a new method for portfolio optimization that combines Long Short-Term Memory (LSTM) forecasting with Covariance Shrinkage and Mean-Variance Optimization (MVO) to construct diversified portfolios that maximize risk-adjusted returns. The study utilizes an LSTM-based model to predict stock prices, evaluating its performance using the RMSE metric. The calculated RMSE of 0.0849 indicates accurate and robust predictions. The portfolio constructed shows different weights each day for different assets based on the minimum variance and maximum Sharpe ratio portfolios. As of January 3rd, 2023, the assets with the largest proportion in the Maximum Sharpe Ratio portfolio and in the Minimum Volatility portfolio, are respectively BA, accounting for 27.64% of the portfolio and PG, accounting for 32.66% of the portfolio. This paper compares the performance of the proposed method and benchmark methods by applying 30 daily portfolio weights to real returns. The portfolio constructed by the proposed method has higher cumulative return with a higher Sharpe ratio and lower maximum drawdown, indicating a better ability to diversify risks and create returns. The proposed method offers a new perspective on portfolio optimization, which can potentially benefit investors and asset managers.

Portfolio Construction Based on Combination of Individual Stocks and LSTM

With the development of the idea of portfolio optimization, it has become one of the important topics in the field of modern finance for achieving the balance between maximizing the return of assets and minimizing the risk. This study selected ten stocks from WIND and used LSTM Neural Network as the fundamental forecasting model. Based on the method of cyclic prediction, we predicted the asset’s return forecast value of the next day by rolling multi-dimensional historical features. Five stocks with the best outcomes were selected for optimization, using both the return component and the volatility, covariance matrix of the stocks’ returns as the covariance matrix to build the efficient frontier and to optimize the weighting. The Monte Carlo Simulation was used to build the maximum Sharpe ratio portfolio and minimum volatility portfolio. The maximum Sharpe ratio portfolio showed that the Midea and Mindray had the potential to profit dramatically at the risk of high volatility. However, relatively high volatility means the possibility of profiting is questionable, so a Minimum Volatility Portfolio was also conducted, which indicated conservative investors usually reduce the risk of their investment as much as possible. Whereas the max Sharpe ratio portfolio showing that risk-seeking investors are more willing to take risks if it can generate more profit. Overall, a hybrid intelligent algorithm based on cyclic prediction, Monte Carlo Simulation and artificial neural network was proposed, and the new applications of machine learning and mathematical methods in asset allocation were promoted.

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.

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.

Is an equally weighted global investment portfolio the outperformer?

The paper builds, in the first part, a benchmark index based on the optimal mix of indices for the global asset classes of equity, fixed-income securities, real estate, commodities, and currencies including cryptocurrencies so as to maximize the ex-post Sharpe ratio. The objective of the first part is to help investors across the globe compare portfolio performance with a uniform benchmark. In the second part, a comparison of portfolio performances is based on five methods of portfolio construction viz; 1) historical returns and variance matrix used along with Markowitz model to discover optimal weights for portfolio components, 2) modification to this approach by using autoregressive integrated moving average (ARIMA) based predicted returns in place of historical returns, 3) global minimum volatility (GMV) portfolio, 4) global market weight portfolio and 5) equal weight portfolio. The objective in the second part is to explore an easy-to-use and at the same time conceptually sound method to build portfolios for any investor worldwide even if such an investor does not have access to or does not wish to rely upon the views and opinions of investment experts. The ex-post performance of portfolios based on these five methods is compared with the ex-post performance of 207 global active and passive funds. This comparison suggests that an equal-weighted portfolio with periodical rebalancing gives the best Sharpe ratio for a global investor.

Portfolio Optimization Based on 10 UK Stocks

The rose of the interest rate caused turbulence in the UK stock market, raising more attention of investors on portfolio optimization. This study selected 10 UK stocks according to their market capitalization. By using the Monte Carlo simulation, this paper found the efficient frontier and constructed the 1/N, the maximum Sharpe ratio and the minimum volatility portfolio. The result showed that the British American Tobacco possesses the largest proportion of the maximum Sharpe ratio portfolio, and the GSK for the portfolio with the minimum variance. Through comparing the cumulative return of the three portfolios with the FTSE 100 Index, all three portfolios are found to outperform the benchmark index. This result may elucidate the portfolio management for some investors in this especial period.

Portfolio Optimization for Real Estate Industry, Food and Beverage Industry, Energy Industry, Medicine Industry, Finance Industry and Retail Industry in Chinese Capital Market

Creating a portfolio is one of the mainstream ways for investors to avoid risks. This paper focuses on Chinese investment market, and selects six different industries in A-shares, which are preferred by Chinese investors, i.e., real estate industry, food and beverage industry, energy industry, medicine industry, finance industry and retail industry. This paper selected six representative assets from these industries for analysis. This paper selects the closing price data of these six assets in the past year, simulates 10,000 different investment portfolios by Monte Carlo simulation, and then uses the mean variance model to select the maximum Sharpe ratio portfolio and the minimum volatility portfolio. After getting the weights of the two groups of assets, this paper used the real income data of nearly two months to test the performance of the portfolio. The results show that: In the maximum Sharpe Ratio portfolio, Poly Development accounted for the max proportion, which is 35.05%, however, Tongrentang accounted for the min proportion, which is only 0.26%. And in the minimum volatility portfolio, the max percentage is Tsingtao Brewery, which is 50.82%, while the min percentage is Chenguang, which is 0.84%. This research results have certain reference value for investors.

The Application of Monte Carlo Simulation and Mean-variance in Portfolio Selection

This paper manages to construct an efficient portfolio that has a better return than the market index. This portfolio is unique because its five assets have been carefully picked from different industries to diversify risk, which is rarely seen in other research. First, this article uses Monte Carlo simulation to generate a possible portfolio and calculate the weight of each asset in different scenarios. Second, it uses the mean-variance model to measure the risk and return of the portfolio. Based on the accessed data, this study finds that the daily return of the minimum volatility portfolio outruns the market index, and it also determines the weight of each stock in the minimum volatility portfolio. The paper provides feasible ways of constructing an efficient portfolio, such as how to select stocks and allocate assets. The results in this paper may benefit the related investors in financial markets and help them find efficient portfolio that outruns the market index.