Portfolio Optimization Model Research Articles

Improving Portfolio Selection by Balancing Liquidity-Risk-Return: Evidence from Stock Markets

The Modern Portfolio Theory was mathematically structured on the basis of the risk-return tradeoff: in other words, the riskier the investment, the greater the required potential return. Traditional portfolio optimization models, however, implicitly consider that all assets can be traded at any time and in any quantity, which is unrealistic. The aim was to propose a two-stage method that includes the prior classification of liquidity based on the bid-ask spread and a mathematical optimization model that uses liquidity as a defined participation constraint. Simulations were carried out using twenty years of data from the American (NYSE) and Brazilian (B3) stock exchanges. The results showed that the method developed offers a broader range of the alternatives that comprise the MV model with a more realistic approach to liquidity. The proposed method can form portfolios that respect the risk-return rules once the investor’s risk profile has been defined, making it a useful recommendation tool for institutional investors. From a conservative point of view, the developed method also showed the potential for reducing uncertain sales by 10.3% on average.

Efficient one asset replacement scheme for an optimized portfolio

<abstract><p>The traditional mean-variance portfolio optimization models in practice have suffered from complexity and heavy computation loads in the process of selecting the best assets for constructing a portfolio. If not, they are considerably departed from the theoretically optimized values. In this work, we develop the optimized portfolio investment strategy in which only one asset substitution occurs when re-balancing a portfolio. To do this, we briefly look into a quadratically constrained quadratic programming (QCQP), which has been well-studied for the non-negative solution. Based on the quadratic programming, an efficient scheme is presented for solving the large-scale inverse problem. We more precisely update the rank of an inverse matrix, so that the optimal solution can be easily and quickly obtained by our proposed scheme.</p> <p>Various numerical and practical experiments are presented to demonstrate the validity and reliability of our scheme. Our empirical application to the U.S. and South Korea stock markets is tested and highlighted. Moreover, comparisons of a random allocation strategy and our proposed scheme reveal the better performance in the lower risks and higher expected returns obtained by our scheme.</p></abstract>

A new bond portfolio optimization model as two-stage stochastic programming problems in U.S. market

We formulate a new bond portfolio optimization model as a two-stage stochastic programming problem in which a decision maker can optimize the cost of bond portfolio selection while deciding which bonds to sell, which bonds to hold, and which bonds to buy from the market, as well as determine the quantity of additional cash in period t under different scenarios and varying assumptions, The model proved its efficiency by finding the optimal values and giving an investment plan that, it will reduce the cost of the portfolio.

Bayesian Imputation with Optimal Look-Ahead-Bias and Variance Tradeoff

Missing time-series data is a prevalent problem in finance. Imputation methods for time-series data are usually applied to the full panel data with the purpose of training a model for a downstream out-of-sample task. For example, the imputation of missing returns may be applied prior to estimating a portfolio optimization model. However, this practice can result in a look-ahead-bias in the future performance of the downstream task. There is an inherent trade-off between the look-ahead-bias of using the full data set for imputation and the larger variance in the imputation from using only the training data. By connecting layers of information revealed in time, we propose a Bayesian consensus posterior that fuses an arbitrary number of posteriors to optimally control the variance and look-ahead-bias trade-off in the imputation. We derive tractable two-step optimization procedures for finding the optimal consensus posterior, with Kullback-Leibler divergence and Wasserstein distance as the measure of dissimilarity between posterior distributions. We demonstrate in simulations and an empirical study the benefit of our imputation mechanism for portfolio optimization with missing returns.

Capital asset pricing model under distribution uncertainty

<p style='text-indent:20px;'>In this paper, we investigate and demonstrate the capital asset pricing model (CAPM) based on distribution uncertainty (or ambiguity, defined as uncertainty about unknown probability).</p><p style='text-indent:20px;'>We first achieve directly capital asset pricing model based on spectral risk measures (abbreviated as SCAPM) in the case of normal distributions; Then we can characterize SCAPM under the condition of uncertain distributions of returns by solving a robust optimal portfolio model based on spectral measures. Specifically, we do it in the following two folds: 1) Completing first the corresponding effective frontier fitting; 2) Getting the valuation of the market portfolio return <inline-formula><tex-math id="M1">\begin{document}$ r_m $\end{document}</tex-math></inline-formula> and the risk parameters of <inline-formula><tex-math id="M2">\begin{document}$ \beta_\phi $\end{document}</tex-math></inline-formula> in use of the kernel density estimation under the distribution uncertainty of returns.</p><p style='text-indent:20px;'>Finally, by selecting 10 stocks from the constituent stocks of the HS300 Index, and comparing the valuation results from the SCAPM formula with the actual yield in the market, we verify the model proposed in the present paper is reasonable and effective.</p>

A Hybrid Model for Portfolio Optimization Based on Stock Price Forecasting with LSTM Recurrent Neural Network using Cardinality Constraints and Multi-Criteria Decision Making Methods (Case study of Tehran Stock Exchange)

پیش‌بینی قیمت سهام به دلیل ماهیت نوسانی بازار و پویایی روند حرکت قیمت، نقش مهمی در ایجاد یک استراتژی کارآمد با بازدهی بالا دارد، همچنین نتایج حاصل از پیش‌بینی، پیش‌نیاز ایجاد سبد سهام با ساختاری بهینه است. لذا هدف از انجام این پژوهش ارائه مدلی ترکیبی است تا به سرمایه‌گذاران در انتخاب سبد سهام بهینه کمک نماید. بنابراین، با استفاده از فرآیند تحلیل سلسله مراتبی بهبود‌یافته از میان صنایع فعال در بورس اوراق بهادار تهران، ده صنعت برتر براساس معیارهای مؤثر بر ارزش صنایع انتخاب می‌شوند. سپس با کمک شبکه عصبی بازگشتی حافظه کوتاه مدت ماندگار قیمت سهام شرکت‌های فعال طی بازه زمانی ابتدای خرداد 1395 تا ابتدای خرداد 1400، در افق‌های زمانی مورد نظر، پیش‌بینی می‌گردد. در گام بعد با روش راه‌حل سازشی ترکیبی، سه سبد سهام با افق زمانی کوتاه‌مدت، میان‌مدت و بلند‌مدت انتخاب می‌شود و در نهایت براساس مدل دارایی محدود مارکویتز با استفاده از روش برنامه‌ریزی غیرخطی عدد صحیح مختلط با الگوریتم شاخه و برش، اوزان بهینه مشخص و مرز کارا رسم می‌گردد. نتایج پژوهش نشان می‌دهد، مدل ارائه شده، بازدهی بیشتری را باتوجه به ریسک در تشکیل سبدهای سهام با افق‌های زمانی مشخص نسبت به روش‌های سنتی نصیب سرمایه‌گذاران می‌نماید.

Stock Price Prediction Methods based on FCM and DNN Algorithms

With the rapid economic development and the continuous expansion of investment scale, the stock market has produced increasing amounts of transaction data and market public opinion information, making it further difficult for investors to distinguish effective investment information. With the continuous enrichment of artificial intelligence achievements, the status and influence of artificial intelligence researchers in academia and society have been greatly improved. Expert system, as an important part of artificial intelligence, has made breakthrough progress at this stage. Expert system is based on a large amount of professional knowledge and experience for a specific field. Computers of this system can be used to simulate the decision-making process of experts to provide a decision-making basis for solving some complex problems. This research mainly discusses stock price prediction methods on the basis of artificial intelligence (AI) algorithms. Fuzzy clustering is a data mining tool that has been developed in recent years and is widely used. Using this method to process super large-scale databases with various data attributes has the characteristics of high efficiency and small amount of information loss. Theoretically speaking, the use of fuzzy clustering technology and related index method can effectively reduce the massive financial fundamentals of listed companies. By analyzing the influencing factors of stock value investment, we specifically select from the financial statements of listed companies the five aspects that can reflect their profitability, development ability, shareholder profitability, solvency, and operating ability. The full text runs through a variety of AI methods that is the characteristic of the research method used in this article, which pays special attention to verifying the theoretical method model. Doing so ensures its effectiveness in practical applications. In stock value portfolio research, a portfolio optimization model, which integrates the dual objectives of portfolio risk and returns into the risk-adjusted return of capital single objective constraints and solves the portfolio, is established. The accuracy and recall of the FCM model are relatively stable, with accuracies of 0.884 and 0.001, respectively. This research can help improve the number and quality of listed companies.

Two-stage flexible power sales optimization for electricity retailers considering demand response strategies of multi-type users

Since the electricity market is opening up in China, it is necessary for power retailers to participate in the market and find a way to gain benefits. In this context, this paper constructs a two-stage flexible power sales optimization model with multi-type demand response strategies. First, the demand response strategies of different types of users are analyzed. Second, two-stage optimization is conducted: In the first stage, the fuzzy K-means clustering method is used to divide a day into peaks, flats, and valleys, and then, a multi-objective time-of-use pricing model is constructed with the aims of minimizing the peak–valley load ratio and maximizing the response revenue rate of users. A flexible power retailing portfolio optimization model is built considering multiple types of users in the second stage and the model is solved by the chaotic particle swarm optimization algorithm. Finally, a case study with four scenarios is conducted, where the demand response is taken as a changeable factor. The results show that (1) the price-based demand response can shave peaks and fill valleys, whilst also reducing the electricity cost, and optimization for industrial users has the optimal effect, followed by that of commercial users and agricultural users; (2) different types of demand responses have different emphases on peak shaving and valley filling, and a combination can achieve the best effect; (3) with the demand response, an electricity retailer can effectively reduce the deviation assessment cost, and increase the revenue by flexibly allocating electricity sales, without resulting in unsatisfied users. The conclusions verify the effectiveness of the proposed model.

Optimal investment portfolio strategies for power enterprises under multi-policy scenarios of renewable energy

Planning a portfolio that includes different power generation technologies is an important method to ensure expected value and to reduce risks for the project investment of electric-power enterprises. This paper evaluates the optimal investment portfolio strategies implemented by electric power enterprises by using real option and portfolio optimization methods. The real options method is used to generate investment values and their distribution. These serve as the input variables of the portfolio optimization model. The portfolio optimization model is built based on the conditional value at risk. The optimal investment is analyzed by considering four policy scenarios: different expected investment values, the phase-out of subsidies, tightened carbon reduction standards, and different initial renewable energy certificate prices. A case study is conducted to analyze the investment decision of an electric power enterprise in China. The results show the optimal investment portfolio strategy, the investment value, and the conditional value at risk. The optimal decision for ensuring a relatively high expected value while reducing risks is to increase the share of solar PV power generation and wind power generation in current conditions. Tightened carbon reduction standards and higher renewable energy certificates prices are conductive to increase the investment value, reduce the risk of loss and increase the share of renewable energy power generation. In contrast, the phase-out of the subsidies had the opposite effect. The methodology and results can provide a reference for investors to guide the formulation of the optimal investment decision and for the government to optimize the policy effect.

Analyzing the Performance of a Two-Tail-Measures-Utility Multi-objective Portfolio Optimization Model

Analyzing the Performance of a Two-Tail-Measures-Utility Multi-objective Portfolio Optimization Model

Optimal Portfolio Formation with Combination of LQ45 Stocks and Corporate Bonds

The objective of investors to invest their money was to maximize return, although they were subject to constraints, primarily risk, so this study aims to provide an alternative to the formation of portfolios and corporate bonds to obtain optimal returns with acceptable risk. The alternative model is to combine Graham's stock selection model with the formation of an optimal portfolio model, namely the Markowitz model. The results of the selection using the Graham model of defensive investors and aggressive investors are 9 and 13 stocks, respectively, of the 45 stocks listed on the LQ45 index. From the selected stocks, the optimal portfolio is formed using the Markowitz model. The results show that the Markowitz model optimizing portfolio provides better performance (reward to variability ratio) than the LQ45 portfolio index with a yield difference of 13.68 – 20.24% per year. Furthermore, the selection of corporate bonds for the optimal portfolio resulted in 8 corporate bonds with a portion of each bond, and this portfolio can generate rates of 8.88% per annum.JEL: G10, G11, G12

A Self-Learning Based Preference Model for Portfolio Optimization

An investment in a portfolio can not only guarantee returns but can also effectively control risk factors. Portfolio optimization is a multi-objective optimization problem. In order to better assist a decision maker to obtain his/her preferred investment solution, an interactive multi-criterion decision making system (MV-IMCDM) is designed for the Mean-Variance (MV) model of the portfolio optimization problem. Considering the flexibility requirement of a preference model that provides a guiding role in MV-IMCDM, a self-learning based preference model DT-PM (decision tree-preference model) is constructed. Compared with the present function based preference model, the DT-PM fully considers a decision maker’s bounded rationality. It does not require an assumption that the decision maker’s preference structure and preference change are known a priori and can be automatically generated and completely updated by learning from the decision maker’s preference feedback. Experimental results of a comparison show that, in the case that the decision maker’s preference structure and preference change are unknown a priori, the performances of guidance and fitness of the DT-PM are remarkably superior to function based preference models; in the case that the decision maker’s preference structure is known a priori, the performances of guidance and fitness of the DT-PM is approximated to the predefined function based model. It can be concluded that the DT-PM can agree with the preference ambiguity and the variability of a decision maker with bounded rationality and be applied more widely in a real decision system.

A new hybrid risk-averse best-worst method and portfolio optimization to select temporary hospital locations for Covid-19 patients

Choosing the right place to set up temporary hospitals is one of the most important and urgent measures for pandemic response. To solve this problem, we propose a new hybrid approach based on two steps. Firstly, since human health is highly sensitive to the impact of decisions about temporary hospital locations and a mistake may pose severe threat to human lives, we propose a new risk-averse multi-criteria decision-making (MCDM) approach. To choose the alternatives with the fewest possible weaknesses, a comprehensive hierarchal structure of relevant criteria categorized into environmental, social, economic, and infrastructural, along with a new risk-averse best-worst method (BWM), are presented as the two components of the MCDM approach. Secondly, considering the output of risk-averse BWM and the distance between the selected centres for better patient coverage as parameters, a portfolio optimization model is used for the hospital selection locations. Our new approach has been applied to a real case study to select cities in Mazandaran, a northern Iranian province seriously affected by the Coronavirus (COVID-19), as places to build temporary hospitals.

CCMV Portfolio Optimization with Stocks and Options using Forecasted Data

Although the future of a financial market is ambiguous and mysterious, historical data play a key role to forecast the future of the market. Along with all the advantages of these data, they may result to some errors and consequently, some losses. In this paper, we consider the cardinality constraints mean-variance (CCMV) portfolio optimization model in the presence of short selling, risk-neutral interest rate and transaction costs. We insure the investment using options against unfavorable outcomes. The Geometric Brownian Motion model is utilized to forecast the stocks prices. Also, to improve the results, we calibrate its parameters using historical data by the maximum likelihood estimation method. We perform numerical experiments using historical and forecasted data on the S&P 500 index, to assess the efficiency of the GBM model in forecasting stocks prices. Also, to examine the effect of options in the portfolio, we compare the portfolio with stocks only versus the portfolio with stocks and options using historical and forecasted data in terms of returns and Sharpe ratios.

Portfolio Optimization with a Mean-Absolute Deviation-Entropy Multi-Objective Model.

Investors wish to obtain the best trade-off between the return and risk. In portfolio optimization, the mean-absolute deviation model has been used to achieve the target rate of return and minimize the risk. However, the maximization of entropy is not considered in the mean-absolute deviation model according to past studies. In fact, higher entropy values give higher portfolio diversifications, which can reduce portfolio risk. Therefore, this paper aims to propose a multi-objective optimization model, namely a mean-absolute deviation-entropy model for portfolio optimization by incorporating the maximization of entropy. In addition, the proposed model incorporates the optimal value of each objective function using a goal-programming approach. The objective functions of the proposed model are to maximize the mean return, minimize the absolute deviation and maximize the entropy of the portfolio. The proposed model is illustrated using returns of stocks of the Dow Jones Industrial Average that are listed in the New York Stock Exchange. This study will be of significant impact to investors because the results show that the proposed model outperforms the mean-absolute deviation model and the naive diversification strategy by giving higher a performance ratio. Furthermore, the proposed model generates higher portfolio mean returns than the MAD model and the naive diversification strategy. Investors will be able to generate a well-diversified portfolio in order to minimize unsystematic risk with the proposed model.

A rapidly converging artificial bee colony algorithm for portfolio optimization

A survey of the relevant literature shows that there have been many studies of the portfolio optimization problem, and that the number of these studies that have been based on heuristic techniques is quite high. We present a heuristic approach to the portfolio optimization problem using the artificial bee colony technique. As a test dataset, we use weekly prices from March 1992 to September 1997 from the following indices: Hang Seng in Hong Kong, DAX 100 in Germany, FTSE 100 in the UK, S&P 100 in the USA and Nikkei in Japan. This test dataset also includes daily prices from May 2013 to April 2016 from the XU030 and XU100 indices in Turkey. In this study, the cardinality-constrained mean–variance portfolio optimization model is treated as a mixed quadratic and integer programming problem, for which heuristic approaches are appropriate. The results of this study are compared with those of genetic algorithms, tabu search, simulated annealing, particle swarm optimization, a differential evaluation algorithm, a greedy randomized adaptive search procedure, an artificial bee colony, ant colony optimization, and a variable neighborhood search algorithm. The purpose of this paper is to present a relatively efficient and effective heuristic method to the portfolio optimization problem. The results show that the proposed artificial bee colony approach achieves these aims.

Reducing forecasting error by optimally pooling wind energy generation sources through portfolio optimization

Generation variability is generally accepted as one of the key challenges in enabling wider penetration of renewable energy sources in general, and wind energy in particular. It is widely documented that it is often possible to reduce the severity of generation intermittency by pooling together generation from geographically (or technologically) diverse sources. This paper aims at evaluating the potential for a similar approach targeted at addressing the related issue of limited predictability of wind energy generation. Specifically, a portfolio optimization model for intelligently constructing a wind energy portfolio for a given harvesting region with the goal of reducing the prediction error is proposed. The mathematical model, based on Conditional Value-at-Risk (CVaR) optimization methodology, is used to evaluate potential improvement in (day ahead) generation predictability for a collection of locations in the USA. The study concludes that pooling indeed can significantly reduce wind energy generation forecasting error, with the effect largely dependent on the size of the harvesting region. Further, if advanced optimization techniques are used, it is possible to balance this reduction with average generation output. Consequently, the results imply that the positive effect of pooling diverse wind resources can be an important factor in planning for generation expansion projects.

An automatic trading system for fuzzy portfolio optimization problem with sell orders

This paper deals with a portfolio optimization problem with sell orders, in which the investor will immediately sell the risky assets once their prices reach the preset sell thresholds. Departing from the traditional portfolio models, the investor needs to determine not only an investment proportion but also a sell threshold for each risky asset. We formulate the portfolio problem as a sequential decision problem and propose an automatic trading system with three stages to determine the investment strategy at the beginning of each period. In Stage 1, we formulate the return of an investment strategy as an LR-power fuzzy number based on the historical data and propose a fuzzy mean–semi-variance portfolio optimization model with sell orders. In Stage 2, we design a multi-objective genetic algorithm to solve the proposed model. In Stage 3, we select an optimal investment strategy among the efficient solutions based on the fuzzy Value-at-Risk ratio. Moreover, we conduct two case studies in the real stock market to illustrate the effectiveness and practicability of the proposed model and algorithm. The comparison results show that the proposed trading system has a better out-of-sample performance than the other ones.

Providing an Optimal Robust Portfolio Model with Mean- CVaR Approach

The portfolio selection problem is one of the main investment management prob-lems. In the portfolio selection problem, robustness is sought against uncertainty or variability in the value of the parameters of the problem. This paper has been conducted for Robust portfolio optimization based on the mean-cvar approach. And introduces the linear mean-cvar model as a criterion for calculating risk and provides an optimal Robust mean-cvar model. Robust approach used in this research is the Bertsimas and Sim. In this approach, Robust counterpart presented for a linear programming model remains linear, maintaining the advantages of the linear programming model in the optimal model. The model developed in this research is randomly selected by real data of 20 stocks of the S&P 500 index for three years, this development help portfolio selection problem to consider uncertainty. Interval optimization is modeling approach to consider parameters uncertainty in this paper. Considering uncertainty make model more realistic. The results of model show that this approach has computational efficiency and on the other hand proposed model produce better solution in risk and portfolio rate of return point of view

A novel mathematical approach for fuzzy multi-period multi-objective portfolio optimization problem under uncertain environment and practical constraints

Investment portfolio optimization (IPO) is one of the most important problems in the financial area. Also, one of the most important features of financial markets is their embedded uncertainty. Thus, it is essential to propose a novel IPO model that can be employed in the presence of uncertain data. Accordingly, the main goal of this paper is to propose a novel fuzzy multi-period multi-objective portfolio optimization (FMPMOPO) model that is capable to be used under data ambiguity and practical constraints including budget constraint, cardinality constraint, and bound constraint. It should be noted that three objectives including terminal wealth, risk, and liquidity as well as practical constraints are considered in proposed FMPMOPO model. Also, the alpha-cut method is employed to deal with fuzzy data. Finally, the proposed fuzzy multi-period wealth-risk-liquidity (FMPWRL) model is implemented in real-world case study from Tehran stock exchange (TSE). The experimental results show the applicability and efficacy of the proposed FMPWRL model for fuzzy multi-period multi-objective investment portfolio optimization problem under fuzzy environment.