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Both were very dark, and this, in connection with the shrugs and stealthy glances that accompanied their palpable intriguing, lent still greater force to the similarity. He felt in no mood for conversation, and as he sipped his absinth he let his mind run rather sorrowfully over the past few weeks of his life. Time and again he had wondered if he had acted wisely in renouncing his birthright to a man to whom he owed nothing. More accurately, she had given me a hint, a strong one, and I wanted to confirm it. Now that I know him, or her, the rest should be easy.

Analysis of new approaches used in portfolio optimization: a systematic literature review. The paper presents a useful discussion on aspects of portfolio optimization, both for researchers and investors and for finance professionals. A point of attention should be given to the input data of optimization models. Robust optimization, Fuzzy logic, and prediction are examples of techniques used to reduce estimation errors.

At the end of the article are pointed out trends and some gaps for future work. Portfolio Optimization consists of determining a set of assets, and their respective portfolio participation weights, which satisfy the investor concerning the combination of risk-return binomial. In the model, the expected return is given by the average of the historical data of the stock's return, and the risk is calculated by the variance of these returns. The main idea of the MV model is to deal with the returns of individual assets as random variables and to adopt the value of expected return and variance in order to quantify the return and investment risk, respectively Zhang et al.

If the customer wants to minimize the risk for a given value of fixed return, then the mathematical model that will select the stocks is given by for a given level of risk, maximizing returns is also its equivalent model :. Merton approaches the portfolio optimization problem from the perspective of how to systematically build and analyze optimal dynamic models of continuous-time under uncertainty.

According to the author, the main advantage of the continuous-time model comparing to models that consider the discrete-time is the fact that it contemplates only two types of stochastic processes: functions of Brownian movements and Poisson processes. Thus, the number of parameters in the problem is reduced, which allows taking full advantage of the huge amount of written literature about these processes. In Uryasev , Conditional-Value-at-Risk CVaR is proposed as a risk measure of the portfolio, and therefore optimization would be on top of that metric.

Another approach to the portfolio problem is robust optimization, which, according to Fabozzi et al. DeMiguel et al. Sparse and stable optimization is an important advance for mean-variance portfolio selection.

In general, DeMiguel et al. The idea is to stabilize the weights of the assets to reduce the estimation error using the Mean-Variance model with the addition of the restriction that the norm of the portfolio weight vector is less than a certain limit.

The sum of the weights can be less than or equal to 1 1-norm. In addition, the model consists of admitting negative values Short , but normalization brings them to the positive side.

Furthermore, the threshold of the sum of the weights can be greater than or equal to 1. This simple change brought better results in terms of Sharpe than strategies present in the literature.

Some authors reviewed the Portfolio optimization methods. For example: Hu et al. Given the importance of the portfolio optimization theme and the scope of related matters, this study has as purpose to identify, by means of a Systematic Literature Review SLR , the main methods, tools and techniques of portfolio optimization, real-world constraints, and to analyze how the applications of this set were changing over the years.

This article is organized as follows: Section 2 presents the method through which state of the art was sought in the literature on portfolio optimization; in Section 3, the results are presented; in Section 4, the results are discussed, and the research questions are answered. Moreover, the conclusions are shown in Section 5. This study is categorized as a configurative review, as it explored the theme defined with qualitative data and data gathered from more heterogeneous primary studies.

The Research Questions in Table 1 guided the authors on the aspects that should be observed in reading the compiled articles. The papers selected were those published in journals in the period between and Other than this criterion, Figure 1 has the inclusion or exclusion filters for the papers.

Search strings are defined in Table 1. The papers were selected according to their approach regarding the Portfolio optimization theme and their potential relevance to solving the research questions shown in Table 1.

Inclusion of analysis on the data used to test the algorithms or models whether they were real or of instances ;. Inclusion of VosViewer software for macro analysis of the articles found and their references to classical authors. The following is a macro view of the results of the search for papers on the portfolio optimization theme.

With these papers, some analyzes were performed with the aid of VosViewer software. A survey of the main words used in the titles of the articles was performed, whose mapping can be seen in Figure 2.

Note in Figure 2 , the presence of terms such as transaction costs, risk management, dynamic programming, and robust optimization. Besides, the terms related to portfolio optimization have also been identified: genetic algorithms, multi-objective optimization, and stochastic optimization. These terms give clues about the lines of research explored by the articles found. In Figure 3 , the main countries where the papers were published are shown.

China and the USA appear as the two countries that publish the most on the topic under study. Followed by Germany, France, Canada, and England. Brazil appears on the map with a considerable number of publications on the subject. In Figure 4 , the mapping of the most cited authors in the studies researched is shown. The author is identified on the map, along with the year of publication of the aforementioned work and the place of publication. Markowitz appears as the most cited author, evidencing that the Medium Variance model is still widely discussed in the financial market and the universe of portfolio optimization.

In addition to Markowitz, authors such as Zadeh , DeMiguel et al. Table 2 shows the journals where the analyzed papers were published.

Table 2 data show that the selected papers come from excellent journals. Table 3 presents the list of papers that used exact methods to solve the portfolio optimization problem, evidencing the strong participation of these methods for the selection of the best assets stocks.

Most of the studies presented in Table 4 , which use heuristics, addressed multi-period, and multi-objective problems. According to Table 4 , among the articles that use heuristics, Figure 5 shows the papers' distribution according to the year of publication. Which key methods, tools, or optimization techniques are used in the portfolio optimization problem? In 18 studies, the authors use exact techniques to solve the portfolio optimization problem starting from the MV Model, or by adapting it inserting new parameters instead of the mean and variance what some authors call the extension of Markowitz model Ali et al.

Regardless of the degree of difficulty of modeling or computational spending that will be required, exact techniques always return to the optimal solution, so they are so attractive, especially for conservative investors. The number of published studies that used heuristics to solve the portfolio optimization problem demonstrates the strong participation of these methods Babaei et al. In Figure 6 , the distribution of the resolution techniques for the Portfolio optimization problem is shown.

It is possible to notice the strong participation of heuristics solutions, although the exact techniques have an extensive presence. One of the justifications for the use of metaheuristics is the fact that they find a solution closer to optimal with a lower computational expense than if it were exact methods. Furthermore, depending on the degree of complexity of the model, these techniques converge to the optimal solution faster than the exact ones. Another advantage of heuristics is the ease of working with multi-objective problems and with several restrictions.

Multi-objective problems are solved either by a combination that transforms them into the mono objective or taking as an objective function only one objective and turning others into constraints. The main goal of hybridization is to unite the advantages of two or more each algorithm and to build a robust model. With Fuzzy, it is possible to solve Multi-objective problems by transforming the problem single-objective.

About GP, the great advantage of this model is the fact that it allows the management of a stock portfolio in an automatic way, without requiring the help of financial market specialists, without having to make constant adjustments in the model Berutich et al.

The choice of method to solve the optimization problem depends primarily on what the researcher wants to obtain concerning the expected results:.

The complexity of the model, because the difficult model is commonly solved by heuristics;. The time spent to get a solution more powerful methods like the exact ones spend more time and deliver optimal solutions, and heuristic methods spend less time but deliver an approximate solution that can be considered feasible.

Constraints make the model more complex to be solved; however, they make the portfolio optimization process much easier. Table 5 shows the constraints, the authors who cited them, and the method used by the authors to solve the problems.

The non-negativity constraints and the total value available must be fully invested, have not entered the count, because they are considered trivial in portfolio optimization models.

There is an extension to comment on the databases that the authors used to test their algorithms in this section. In some studies, the OR-Library instance was used that allows free access to the data. The data sources are well diversified, and among the papers, only one used data from Brazil through the Thomson-Reuters Datastream platform Macedo et al. With several studies that succeeded in the model proposed by Markowitz , some constraints were proposed, among them the cardinality constraints and minimum purchase limits constraints.

Below there is the description of the meaning of each constraint of Table 5 :. Transaction costs: in the financial markets, there are transaction costs arising from the process of purchasing and selling bonds and investment portfolio review;. Transaction lots - rounds: is a minimum transaction unit required to invest in an asset;. Cardinality constraint : restricts the number of bonds that will compose the investment portfolio;.

Investment threshold constraints : these constraints define upper limits of the ratio-amount of each asset held in the portfolio;. Decision dependency constraints : decision dependency requirements that are common in financial transactions;. Quantity constraint: the quantity constraint is used to limit the position size by placing maximum and minimum values. The lower limit avoids virtually insignificant positions for the portfolio performance, and the upper limit averts too much exposure or weight for any stock;.

Long-only constraint : means that the realization of selling short operations is not permitted, i. What type of analysis is done regarding the stock: fundamental, technical, or mixed fundamental and technical? There are few studies using fundamental analysis Ackermann et al. The technical analysis for being simpler, since it analyzes few variables, has an advantage regarding the fundamental type in terms of the analysis speed in daily operations, for example.

Most papers use technical analysis Al Janabi, ; Ali et al. In addition, investors who use this data want to get rapid gains in daily, weekly, or monthly operations, identifying through simpler analyses and fewer variables, the opportunities offered by the market.

In Figure 7 presents the distribution of the types of analysis in the selected papers. Silva et al. In the points below, the financial indices that enable the company's fundamental analysis in terms of profitability, liquidity, debt, and growth are mentioned Silva et al.

Net Return ROE : measures financial performance in the case of generating profits using company assets;. Profit Margin Index PM : assess the company profitability by calculating the percentage of retained earnings after paying the operational, administrative and financial costs, in addition to taxes;.

Revenue growth percentage GR : is an economic indicator that shows the business evolution;. Positive Trend of net profit NI : shows the increase in profits, and aims to show the companies with the highest growth;.

Portfolio optimization is the process of selecting the best portfolio asset distribution , out of the set of all portfolios being considered, according to some objective. The objective typically maximizes factors such as expected return , and minimizes costs like financial risk. Factors being considered may range from tangible such as assets , liabilities , earnings or other fundamentals to intangible such as selective divestment. Modern portfolio theory was introduced in a doctoral thesis by Harry Markowitz ; [1] [2] see Markowitz model. It assumes that an investor wants to maximize a portfolio's expected return contingent on any given amount of risk.

Portfolio construction is one of the most critical problems in financial markets. In this paper, a new two-phase robust portfolio selection and optimization approach is proposed to deal with the uncertainty of the data, increasing the robustness of investment process against uncertainty, decreasing computational complexity, and comprehensive assessments of stocks from different financial aspects and criteria are provided. Then in the second phase, by applying robust mean-semi variance-liquidity RMSVL and robust mean-absolute deviation-liquidity RMADL models, the amount of investment in each qualified stock is determined. Finally, the proposed approach is implemented in a real case study of the Tehran stock exchange TSE. Additionally, a sensitivity analysis of all robust models of this study is examined. Illustrative results show that the proposed approach is effective for portfolio selection and optimization in the presence of uncertain data. The portfolio selection and optimization problems are two of the main branches of studies in investment management.

This content was uploaded by our users and we assume good faith they have the permission to share this book. If you own the copyright to this book and it is wrongfully on our website, we offer a simple DMCA procedure to remove your content from our site. Start by pressing the button below! Grant and James A. Crabbe and Frank J. Peterson and Frank J. Fabozzi, Steven V.

Portfolio construction is one of the most critical problems in financial markets. In this paper, a new two-phase robust portfolio selection and optimization approach is proposed to deal with the uncertainty of the data, increasing the robustness of investment process against uncertainty, decreasing computational complexity, and comprehensive assessments of stocks from different financial aspects and criteria are provided. Then in the second phase, by applying robust mean-semi variance-liquidity RMSVL and robust mean-absolute deviation-liquidity RMADL models, the amount of investment in each qualified stock is determined. Finally, the proposed approach is implemented in a real case study of the Tehran stock exchange TSE.

Handbook of Portfolio Construction pp Cite as. Outliers in asset returns factors are a frequently occurring phenomenon across all asset classes and can have an adverse influence on the performance of mean—variance optimized MVO portfolios. This occurs by virtue of the unbounded influence that outliers can have on the mean returns and covariance matrix estimates alternatively, correlations and variances estimates that are inputs are optimizer inputs.

Analysis of new approaches used in portfolio optimization: a systematic literature review. The paper presents a useful discussion on aspects of portfolio optimization, both for researchers and investors and for finance professionals. A point of attention should be given to the input data of optimization models. Robust optimization, Fuzzy logic, and prediction are examples of techniques used to reduce estimation errors.

The system can't perform the operation now. Try again later. Citations per year. Duplicate citations. The following articles are merged in Scholar.

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Enferno, - извиняясь, сказал Беккер. - Я плохо себя чувствую. - Он знал, что должен буквально вдавиться в пол.

*Тело же его было бледно-желтого цвета - кроме крохотного красноватого кровоподтека прямо над сердцем. Скорее всего от искусственного дыхания и массажа сердца, - подумал Беккер. - Жаль, что бедняге это не помогло.*

Вчера вечером я скачал файл Танкадо и провел у принтера несколько часов, ожидая, когда ТРАНСТЕКСТ его расколет. На рассвете я усмирил свою гордыню и позвонил директору - и, уверяю тебя, это был бы тот еще разговорчик. Доброе утро, сэр.

* - Бринкерхофф рассеянно кивнул, стараясь не смотреть на лиф ее платья. - Когда знаменатель равняется нулю, - объясняла Мидж, - результат уходит в бесконечность.*

She held her head very high, but she was conscious of an odd feeling of regret.

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