Maximum Sharpe Ratio Research Articles

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.

Connectedness and systemic risk between FinTech and traditional financial stocks: Implications for portfolio diversification

The rapid growth in FinTech is attracting significant investor attention. There are concerns that FinTech stocks may be a source of systemic risk and this has implications for the stability of the financial sector. This study uses a TVP-VAR model to estimate the dynamic connectedness between global FinTech stocks and the stocks of large US banks, regional US banks, US insurance, and global private equity. The findings reveal that FinTech and insurance stocks are net receivers of shocks while large US banks are a major source of shocks. Thus, FinTech stocks are not a source of systemic risk but can be affected by financial contagion and systemic risk originating from large US banks. The highest connectedness was observed at the onset of the COVID-19 lockdowns illustrating the dramatic impact that a health pandemic can have on systemic risk. Systemic risk also increased during the 2023 US bank panic. Connectedness has implications for constructing investment portfolios. The equally weighted, risk parity, and risk parity connectedness portfolios have similar portfolio summary statistics, but lower risk adjusted returns than the maximum Sharpe ratio portfolio which better captures the low correlation between FinTech stocks and traditional financial stocks. These results are robust across various portfolio rebalancing periods (daily, weekly, monthly).

Integrating LSTM Networks with Mean-Variance Optimization for Enhanced Portfolio Construction: An Empirical Study on UK Stock Market

Portfolio optimization has long been a central theme in finance. With ongoing advancements in machine learning, there is a significant opportunity to integrate predictive methods into portfolio optimization. This paper proposes leveraging Long Short-Term Memory (LSTM) networks alongside the established Mean-Variance (MV) optimization framework to construct optimal portfolios. These portfolios aim to help financial investors effectively manage and mitigate risk while maximizing returns. The study meticulously screened the leading stocks of 12 prominent UK companies listed on the London Stock Exchange (LSE), known for their influence and visibility. Initially, the study applies the LSTM networks to predict stock price volatility and integrates these predictions into the MV model to allocate portfolio weights effectively. To underscore the superiority of the proposed approach, the study compares cumulative returns from portfolios optimized for maximum and minimum variance Sharpe ratios with real data against the FTSE100 index over the same period. The results demonstrate that the portfolio optimized with the maximum Sharpe ratio significantly outperforms both the conservative minimum variance portfolio and the FTSE100 index. This empirical evidence underscores the practical value of integrating advanced machine learning techniques with established financial theory, enabling more innovative and efficient investment strategies to meet the evolving needs of financial investors.

Whether ARIMA-based Portfolio Can Beat the Market Index

Portfolio optimization is a long-term topic in the financial field, which can maximize returns while minimizing risks. It is widely used in production and daily life, such as stock investment, production optimization, and engineering models. This article selects data from 10 stocks, namely KO, PG, PEP, CL, MDLZ, STZ, PM, KMB, GIS, and K, from January 24, 2024, to June 14, 2024. Firstly, this article uses the ARIMA model to learn the first 70% of the data and predict the last 30% of the data, and then uses portfolio strategy to evaluate the results. This article obtained the maximum Sharpe ratio model on the Monte Carlo effective boundary. By combining the maximum Sharpe ratio model with the SP 500 index within the same time frame, this article concludes that the market performs better. This article provides different portfolio allocation strategies for risk averse investors seeking stable positive returns in turbulent markets.

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.

Some Results on Bivariate Squared Maximum Sharpe Ratio

The Sharpe ratio is a widely used tool for assessing investment strategy performance. An essential part of investing involves creating an appropriate portfolio by determining the optimal weights for desired assets. Before constructing a portfolio, selecting a set of investment opportunities is crucial. In the absence of a risk-free asset, investment opportunities can be identified based on the Sharpe ratios of risky assets and their correlation. The maximum squared Sharpe ratio serves as a useful metric that summarizes the performance of an investment opportunity in a single value, considering the Sharpe ratios of assets and their correlation coefficients. However, the assumption of a normal distribution in asset returns, as implied by the Sharpe ratio and related metrics, may not always hold in practice. Non-normal returns with a non-linear dependence structure can result in an overestimation or underestimation of these metrics. Copula functions are commonly utilized to address non-normal dependence structures. This study examines the impact of asset dependence on the squared maximum Sharpe ratio using copulas and proposes a copula-based approach to tackle the estimation issue. The performance of the proposed estimator is illustrated through simulation and real-data analysis.

Portfolio Validity Test in the Chinese Market

Modern portfolio theory is one of the most classic theories in financial investment theory. It was first released by a famous economist, Markowitz. As the most important critical model in investment science, it provides investors with scientific investment allocation methods, which are favored by many investors. It has been widely used and researched in the world. Modern portfolio theory analyses the historical returns of investment objects and guides future investment behavior. However, it is still controversial whether this theory is reasonable and adequate in Chinas stock market. China's stock market is more susceptible to fluctuations than those in Europe and the US, and many of these factors stem from China's strategic policies in various areas. Since the end of the epidemic, China's economic development has also slowed down. In this context, this paper will construct the maximum Sharpe ratio strategy, market capitalization strategy, and average weight strategy. Through the performance evaluation indexes of these three strategies' performance comparison, this paper will verify whether the portfolio strategy is real and effective in China's stock market and can bring more than significant market returns to investors.

Application Of Markowitz and Index Models to Real Markets

After Markowitz put forward the portfolio theory in the 1950s, the modern investment theory was developed, and more related theoretical models were created based on it. To find the optimal portfolio in the market, this paper randomly selects 7 stock types, uses three different constraint methods to show the investment characteristics of different group of investors, and uses Index model and Markowitz model to find efficient frontier and the proportion of asset allocation under the condition of maximum Sharpe ratio and minimum variance. The results show that to achieve the maximum Sharpe ratio and find the best combination, it is necessary to purchase AAPL primarily. Secondly, it chooses to purchase assets with less correlation and relatively large return rate, such as MSFT and WMT. The results in this paper shed lights for investor in selecting potential assets and may provide helpful insight for future investments.

Comprehensive Asset Pricing Tests in the Korean Stock Market

AbstractWe examine the empirical performance in the Korean stock market of three new asset pricing factor models: the Stambaugh–Yuan (2017) mispricing factor model, the Daniel et al. (2020) three‐factor model, Barillas‐Shanken (2018) six‐factor model and the Hou et al. (2021) q5‐factor model. We find that all factors in these factor models have significantly positive risk premiums and are not explained by the Fama–French six‐factor model. Compared to other prevalent models, the q5 model shows the highest maximum Sharpe ratio, mainly due to its profitability and expected growth factors. Further, the q5 model exhibits superior performance in explaining the returns of 97 anomaly portfolios in the Korean market.

Research on the Optimal Strategy of Investment Portfolio Based on Markowitz Model

Nowadays, investment is becoming increasingly common. Under the globalization of the economy, investors are given more investment opportunities and choices. Investors need to select excellent assets and allocate the selected asset portfolio on weight during the investment process. The mean-variance model proposed by Markowitz plays an important guiding role in investment and risk management. This model can effectively evaluate investors portfolio risk and return decisions and significantly impact their decision-making choices. This study uses the data of the annual average return and variance from 11 risky assets and 1 risk-free asset in about 20 years to construct an investment portfolio in a fixed group based on the Markowitz Model. The study calculates the changes in the allocation of the maximum Sharpe ratio and the minimum variance portfolios under three different constraints and one condition with the addition of risk-free assets, respectively, and then analyzes changes in the outcome of data. The capital allocation lines are introduced to analyze the outcome of an investment portfolio with risk-free assets. Compared with the changes from three constraints, reasons are explained why these changes happen under three constraints. Then, the above limitations are taken as a premise, and the study proposes recommendations for the optimal investment portfolio selection for different investors according to the investment cycle, the preference of investors based on the situation of different investors, and market constraints. The study guides investors future investment decisions.

Factor Model Comparisons with Conditioning Information

Abstract We develop methods for testing factor models when the weights in portfolios of factors and test assets can vary with lagged information. We derive and evaluate consistent standard errors and finite sample bias adjustments for unconditional maximum squared Sharpe ratios and their differences. Bias adjustment using a second-order approximation performs well. We derive optimal zero-beta rates for models with dynamically trading portfolios. Factor models’ Sharpe ratios are larger but standard test asset portfolios’ maximum Sharpe ratios are larger still when there is dynamic trading. As a result, most of the popular factor models are rejected.

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 Optimization Based on U.S. Stock

In the financial domain, portfolio optimization is of immense significance due to its potential for risk diversification and return enhancement. Particularly in today's society where inflation is on the rise, a well-constructed portfolio can effectively assist investors in maintaining or increasing real assets. This study selected 10 U.S. stocks and analyzed their data for the past decade. Utilizing Monte Carlo simulation, the study identified the efficient frontier and constructed three types of portfolios: equal-weighted (1/N) portfolio, global minimum variance portfolio (hereinafter referred to as GMVP), and maximum Sharpe ratio portfolio. The findings show that Microsoft and Nvidia have the greatest investment weights in the portfolio with the maximum Sharpe ratio. In the GMVP, JNJ and KO have the highest investment weights. By contrasting the three portfolios' combined performance with the S&P 500 index, both the maximum Sharpe ratio and the 1/N portfolios outperformed the benchmark index, while the GMVP performed below the benchmark. The findings of this study may offer insights into portfolio management for investors looking to increase their real assets.

A Python-based Empirical Study of Markowitz's Portfolio Theory in the Chinese Stock Market

Markowitz's portfolio theory serves as a pivotal framework in investment science, offering investors a scientifically robust approach to asset allocation. This paper conducts an empirical analysis of the theory within the context of the Chinese stock market, utilising Python for data manipulation and computation. A selection of five stocks was made based on pre-established criteria, and Python was employed to examine their correlation for portfolio construction viability. Subsequently, Python facilitated the identification of the portfolio with the maximum Sharpe ratio and the minimum variance, as well as the delineation of the efficient frontier. Results from the empirical study confirm the applicability and utility of Markowitz's portfolio theory for Chinese investors, thereby substantiating its significant relevance in China's financial market. Based on the findings, investors are advised to diversify their portfolios following the guidelines of the efficient frontier to optimize returns while managing risks. Moreover, considering the complexities of the Chinese stock market, harnessing computational tools like Python can grant an analytical edge, enabling more informed decision-making. It's also pivotal for investors to routinely review and adjust portfolio compositions in line with market dynamics, ensuring they stay aligned with the principles of the efficient frontier.

Estimation of an efficient benchmark portfolio for the Eastern European market

Purpose: This paper explores the mean-variance inefficiency of cap-weighted indices based on the CECE index as a benchmark. Methodology: For the period from March 2014 to September 2021, several proxies of efficient portfo-lios were estimated: the Global Minimum Variance (GMV) portfolio, the Maximum Sharpe Ratio (MSR) portfolio and the portfolio with equal weights of constituents (EW). Diversification of strategies was also considered by analyzing the performance of a portfolio consisting of GMV and MSR that were weighted equally. Based on monthly data, 90 out-of-sample estimations were made for each strategy in order to com-pare their risk-return characteristics. Furthermore, to confirm the differences in the riskiness and returns of the estimated portfolios, the F-test and the Welch test were performed, respectively. Results: The results show that all analyzed portfolios achieved superior performance compared to the CECE index with the GMV portfolio leading the way. Conclusion: Research findings highlight the importance of market development and liquidity when pursu-ing popular scientific diversification methods.

Portfolio Based on AR Model Using 5 Stocks

An investment portfolio is a collection of stocks, bonds, and financial derivatives held by investors or financial institutions, aimed at diversifying risks and maximizing returns. This article selects stocks of Manulife, BOA, Apple, PLC, and National Pharmaceutical Group from October 21, 2022 to August 9, 2023. This article uses AR model, minimum variance model, and maximum Sharpe's ratio model to predict stock prices, and establishes investment portfolios based on the predicted values. Firstly, based on the first 75% of the data, this article predicts the last 25% of the data. Secondly, based on the prediction, the minimum variance model and the maximum Sharpe ratio model are applied and compared with SP500 within the same time frame. However, the results indicate that the SP500 index performs best in terms of yield. This study suggests that purchasing market index funds is an important investment decision for investors during the volatile US dollar interest rate hike cycle.

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.

Application of Mean-variance Model in Optimizing Stock Portfolio

Constructing an optimized stock portfolio is pivotal in achieving enhanced returns with managed risks. Utilizing data from 2022, the study employed the mean-variance model to determine the optimal allocations for five prominent stocks: Intel (INTC), Johnson & Johnson (JNJ), Coca-Cola (KO), Netflix (NFLX), and Procter & Gamble (PG). In the formulations of both maximum Sharpe ratio and minimum variance portfolios, the stocks with the predominant allocations are NFLX and PG, with respective weights of 47.04% and 45.89% for the former, and 58.05% and 29.61% for the latter. Upon establishing these weightings, the cumulative returns for 2023 were calculated, revealing that the constructed portfolios notably outperformed the broader stock market. This research underscores two key observations: firstly, the NFLX and PG stocks emerge as cornerstones in the optimal portfolio composition; and secondly, these allocations, when evaluated with 2023 data, underscore their efficacy. Robustness checks, which expanded the asset pool, further validated these findings. Ultimately, this study serves as a valuable guide for investors in the financial market, presenting a structured blueprint for effective portfolio assembly.

Portfolio Optimization by Monte Carlo Simulation

In this paper, Monte Carlo simulation is used for constructing Efficient Frontier and optimizing the portfolio. Then the performance of the optimized portfolio had been evaluated and compared to the performance of the whole market, Firstly, this study collected the closing prices of five stocks in different industries that was listed in New York stock exchange between 2023/01/01 and 2023/04/12. Secondly, to testify if the construction of the portfolio can possibly mitigate the volatility, the correlation coefficient between these chosen stocks has been calculated. Then, Monte Carlo simulation has been used to construct the Efficient Frontier and find the weights of Maximum Sharpe Ratio portfolio and Minimum Variance portfolio. Lastly, this study put the market price data between 2023/03/12 and 2023/04/12 into the portfolios which had been built in the last step. The returns were compared to the S&P 500 subsequently. As the results shows, the Maximum Sharpe Ratio portfolio is performed better than S&P 500, Minimum Variance portfolio is performed worse than S&P 500. The results of this paper show the performance of these two portfolios compare to the market, which may help investors to decide which strategy to use when it comes to constructing a portfolio.