Minimum Lots Research Articles

An uncertain bi-objective mean-entropy model for portfolio selection with realistic factors

In the imprecise investment environment, there are many indeterminate factors impacting security returns. This paper introduces a portfolio optimization problem where cross-entropy is utilized to control portfolio risk within the framework of uncertainty theory and presents an uncertain bi-objective mean-entropy portfolio selection model. To be more realistic, some realistic factors such as minimum transaction lots, dividend factors and tax factors are also considered. By introducing a risk preference coefficient, the bi-objective model is converted into a single-objective model and some equivalents are discussed. Additionally, a hybrid intelligent algorithm integrating a genetic algorithm with uncertain estimation is designed to solve the proposed model. Finally, a case study is executed to confirm the practicability of the model and the performance of the algorithm, and an empirical analysis based on the proposed model and the uncertain mean–variance model is developed to illustrate the advantage of the uncertain mean-entropy model in practical investment.

Portfolio optimization: A multi-period model with dynamic risk preference and minimum lots of transaction

Sufficient description of stock returns is essential to generate an efficient model of portfolio optimization. Security returns are considered to be random variables where there exist sufficient data of historical returns. Nonetheless, uncertain variables may be applied to increase the effectiveness of security returns. The following research entails an optimization objective problem focusing on minimum lots of transaction in uncertain environments of dynamic trading. Also, the changing risk preference of the investor over the horizon of investment has been factored in the model. An average- Value at Risk (VaR) framework has been used to maximize wealth creation using genetic algorithms.

Mean-Variance Programming Framework in Markowitz Modeling

For mathematical frameworks in place, which are applied to portfolio optimization problems, the majority come in the form of risk minimization – relative to the return parameter. When it comes to the quadratic programming framework, in relation to Markowitz, its associated challenges have been countered when considerations are made to recent trends in algorithmic scholarly investigations. In particular, a linear risk function has been introduced, especially in response to the need to address problems of portfolio selection, given real constraints. In this study, the main aim is to address the problem of portfolio selection in relation to minimum transaction lots. Also, the paper focuses on an improved search model that is applied to active constrained, whereby solutions are developed for the integer programming algorithm. The proposed model is that which focuses on the relaxed problem’s solution initially, before establishing solutions that are deemed closer to the continuous solutions..

Multi-period uncertain portfolio optimization model with minimum transaction lots and dynamic risk preference

An accurate variable description of security returns is necessary to establish a valid portfolio optimization model. It is usually assumed to be a random variable when the historical data of security returns are sufficient. However, when historical data are too limited to estimate its probability distribution, uncertain variables are employed to characterize security returns to be effective. This paper focuses on a multi-period portfolio optimization problem in uncertain environment with the consideration of minimum transaction lots. Different from the previous multi-period work assuming the total available wealth in the end of the investment horizon is consistently in an exponential format, our study provides a simplified additive format of the total wealth, which may make the process of experimental calculation concise, since it is a linear function of decision variables. Besides, we consider the investor’s dynamic risk preference along the whole investment horizon. With these realistic constraints derived from the complex financial markets, we build a multi-period mean-VaR (value-at-risk) model with the objective of maximizing the terminal wealth under the risk control over the whole investment. Genetic algorithm is used to solve the proposed model, and two numerical examples are given to illustrate the effectiveness of the proposed approach.

Microstructure invariance in U.S. stock market trades

We examine invariance relationships in tick-by-tick transaction data in the U.S. stock market. Over the period 1993–2001, monthly regression coefficients of the log of the trade arrival rate on the log of trading activity have an almost constant value of 0.666, close to the value of two-thirds predicted by market microstructure invariance. Over the 2001–2014 period, after decimalization and the increasing use of electronic order matching systems and algorithmic trading, the coefficients increase to about 0.79. The evidence suggests that changes in coefficients are due to increasing importance of minimum lots size in a world where algorithmic traders split orders into tiny pieces.

An Approach Based on Active Constraint Strategy for Solving The Portfolio Optimization Problem

The mathematical model of portfolio optimization has been largely written in terms of minimizing the risk, given the return. The difficulty of this model is to deal with the quadratic programming model due to Markowitz. This situation has been overcome by the recent progress in algorithmic research, and the introduction of linear risk function. This paper deals with the portfolio selection problem with minimum transaction lots. A neighbourhood search algorithm based on active constrained strategy is proposed to solve the mixed integer programming model. The algorithm starts from the solution of the relaxed problem to find a solution which is close to the continuous solution.

Model Pengoptimuman Portofolio Mean-Variance dan Perkembangan Praktisnya

Many research about portfolio optimization in Indonesia still uses the ‘original’ mean-variance model as proposed by Markowitz more than 60 years ago. This article reviews the development and modification of the Markowitz’s mean-variance model, especially that dealing with real stock-market features, which could help the investor to create their own portfolio. There were several real-stock market features that implemented in the modification of mean-variance portfolios optimization models, such as the minimum transaction lots, the transaction cost, the cardinality constraint, the weight constraint, and the sectoral constraint. To implement these features, several heuristic methods were used to obtain the optimal portfolio weight, such as genetic algorithm, Tabu search, bee colony algorithm, particle swarm algorithm, and simulated annealing. These methods become alternative to the mathematical programming method.

A novel hybrid heuristic algorithm for a new uncertain mean-variance-skewness portfolio selection model with real constraints

This paper discusses a portfolio selection problem under the mean-variance-skewness framework wherein the security returns are obtained through evaluation of the experts instead of historical data. By treating security returns as the uncertain variables, an uncertain mean-variance-skewness model is proposed for portfolio selection under consideration of the transaction costs, bounds on holdings, cardinality of the portfolio, and minimum transaction lots constraints. To solve the resultant portfolio selection problem, which is an NP-Complete nonlinear integer programming problem, a hybrid solution method termed the FA-GA is developed by combining features of the firefly algorithm (FA) and genetic algorithm (GA). In the proposed method, the crossover and mutation operators of the GA are integrated into the FA to strike an optimal balance between the exploration and exploitation. A numerical example of portfolio selection is given to demonstrate effectiveness of the proposed model and solution algorithm. Furthermore, a detailed performance analysis and comparison are done to establish superiority of the proposed model and solution method.

Off-the-Grid in an On-Grid Nation: Household Energy Choices, Intra-Community Effects, and Attitudes in a Rural Neighborhood in Utah

This research is an investigation of the perceived positive and negative aspects of off grid living in a middle to upper-class neighborhood in rural Utah in which no public utility grid was available for connection. Off-grid living is defined as unconnected to a public utility power grid, water, or sewer system. In the researched community, all individuals lived off-grid on minimum twenty-acre lots of land with single-household dwellings. We used surveys with closed and open-ended questions to qualitatively explore the local social effects (from individual attitudes to group identity to household economics to conservation attitudes) off-grid living had on individuals and households, and daily intra-community life. Our study group was a compelling community in which to ask this question since most of our participants came to live off-grid by chance as much as choice and they lived off-grid for a relatively long time (average of 9 ½ years). Among this group we coded responses into categories based on qualitative conversation analysis, word usage counts, and categorization and found the “independence” of off-grid living perceived as a strong “positive” factor and the cost and time-intensive maintenance as “negatives.” Gendered work also affected attitudes about daily life and energy choices. In addition, living off-grid, particularly the use of solar energy, seemed to enhance a heightened sense of intra-community neighborliness among most residents.

Portfolio Optimization with Metaheuristics

<p>Portfolio optimization is the problem ofsearching foran optimal allocation of wealth to put in the available assets. Since the seminalworkdoneby Markowitz, the problem is codifiedas a two-objective mean-risk optimization problem where the best trade-off solutions (portfolios) between risk (measured by variance) and mean are hunted. Complex measures of risk (e.g., value-at-risk, expected shortfall, semivariance), addedobjective functions (e.g., maximization of skewness, liquidity, dividends) and pragmatic, real-worldconstraints (e.g., cardinality constraints, quantity constraints, minimum transaction lots, class constraints) that are included in recent portfolio selection models, provide many optimization challenges. The resulting portfolio optimizationproblem becomes very hard to be tackledwith exact techniquesas it displaysnonlinearities, discontinuities and high dimensional efficient frontiers. These characteristics prompteda lot ofresearchers to explorethe use of metaheuristics, which are powerful techniquesfor discoveringnear optimal solutions (sometimes the real optimum) for hard optimization problems in acceptable computationaltime. This report provides a briefnoteon the field of portfolio optimization with metaheuristics and concludes that especially Multiobjectivemetaheuristics (MOMHs) provide a natural background for dealing with portfolio selection problems with complex measures of risk (which define non-convex, non-differential objective functions), discrete constraints and multiple objectives.</p>

Portfolio Optimization with Metaheuristics

<p>Portfolio optimization is the problem ofsearching foran optimal allocation of wealth to put in the available assets. Since the seminalworkdoneby Markowitz, the problem is codifiedas a two-objective mean-risk optimization problem where the best trade-off solutions (portfolios) between risk (measured by variance) and mean are hunted. Complex measures of risk (e.g., value-at-risk, expected shortfall, semivariance), addedobjective functions (e.g., maximization of skewness, liquidity, dividends) and pragmatic, real-worldconstraints (e.g., cardinality constraints, quantity constraints, minimum transaction lots, class constraints) that are included in recent portfolio selection models, provide many optimization challenges. The resulting portfolio optimizationproblem becomes very hard to be tackledwith exact techniquesas it displaysnonlinearities, discontinuities and high dimensional efficient frontiers. These characteristics prompteda lot ofresearchers to explorethe use of metaheuristics, which are powerful techniquesfor discoveringnear optimal solutions (sometimes the real optimum) for hard optimization problems in acceptable computationaltime. This report provides a briefnoteon the field of portfolio optimization with metaheuristics and concludes that especially Multiobjectivemetaheuristics (MOMHs) provide a natural background for dealing with portfolio selection problems with complex measures of risk (which define non-convex, non-differential objective functions), discrete constraints and multiple objectives.</p>

Fuzzy portfolio selection model with real features and different decision behaviors

In the ever changing financial markets, investor’s decision behaviors may change from time to time. In this paper, we consider the effect of investor’s different decision behaviors on portfolio selection in fuzzy environment. We present a possibilistic mean-semivariance model for fuzzy portfolio selection by considering some real investment features including proportional transaction cost, fixed transaction cost, cardinality constraint, investment threshold constraints, decision dependency constraints and minimum transaction lots. To describe investor’s different decision behaviors, we characterize the return rates on securities by LR fuzzy numbers with different shape parameters in the left- and right-hand reference functions. Then, we design a novel hybrid differential evolution algorithm to solve the proposed model. Finally, we provide a numerical example to illustrate the application of our model and the effectiveness of the designed algorithm.

Price Discovery of Index Futures across Markets

The trading of foreign index futures by the Singapore Exchange (SGX) offers an ideal opportunity to study price discovery and information of trading across different markets. We examine four popular indices - Nikkei 225 Index, MSCI Taiwan Index, CNX Nifty Index and the FTSE China A50 Index traded in SGX and compare them with their home market trading. In contrary to standard theory and evidence, we show that smaller bid-ask spread, lower minimum lots and cheaper transaction cost do not necessary improve information efficiency. These results may shed some light on the usefulness of the role of an international financial centre on the price discovery of foreign indices.

Uncertain portfolio selection model considering transaction costs and minimum transaction lots requirement

Uncertain portfolio selection model considering transaction costs and minimum transaction lots requirement

Solving portfolio selection problems with minimum transaction lots based on conditional-value-at-risk

Portfolio selection problems conventionally means ‘minimizing the risk, given the certain level of returns’ from some financial assets. This problem is frequently solved with quadratic or linear programming methods, depending on the risk measure that used in the objective function. However, the solutions obtained by these method are in real numbers, which may give some problem in real application because each asset usually has its minimum transaction lots. In the classical approach considering minimum transaction lots were developed based on linear Mean Absolute Deviation (MAD), variance (like Markowitz’s model), and semi-variance as risk measure. In this paper we investigated the portfolio selection methods with minimum transaction lots with conditional value at risk (CVaR) as risk measure. The mean-CVaR methodology only involves the part of the tail of the distribution that contributed to high losses. This approach looks better when we work with non-symmetric return probability distribution. Solution of this method can be found with Genetic Algorithm (GA) methods. We provide real examples using stocks from Indonesia stocks market.

Hedging an option portfolio with minimum transaction lots: A fuzzy goal programming problem

Options are designed to hedge against risks to their underlying assets such as stocks. One method of forming option-hedging portfolios is using stochastic programming models. Stochastic programming models depend heavily on scenario generation, a challenging task. Another method is neutralizing the Greek risks derived from the Black–Scholes formula for pricing options. The formula expresses the option price as a function of the stock price, strike price, volatility, risk-free interest rate, and time to maturity. Greek risks are the derivatives of the option price with respect to these variables. Hedging Greek risks requires no human intervention for generating scenarios. Linear programming models have been proposed for constructing option portfolios with neutralized risks and maximized investment profit. However, problems with these models exist. First, feasible solutions that can perfectly neutralize the Greek risks might not exist. Second, models that involve multiple assets and their derivatives were incorrectly formulated. Finally, these models lack practicability because they consider no minimum transaction lots. Considering minimum transaction lots can exacerbate the infeasibility problem. These problems must be resolved before option hedging models can be applied further. This study presents a revised linear programming model for option portfolios with multiple underlying assets, and extends the model by incorporating it with a fuzzy goal programming method for considering minimum transaction lots. Numerical examples show that current models failed to obtain feasible solutions when minimum transaction lots were considered. By contrast, while the proposed model solved the problems efficiently.

Multi-period fuzzy mean-semi variance portfolio selection problem with transaction cost and minimum transaction lots using genetic algorithm

Multi-period models of portfolio selection have been developed in the literature with respect to certain assumptions. In this study, for the first time, the portfolio selection problem has been modeled based on mean-semi variance with transaction cost and minimum transaction lots considering functional constraints and fuzzy parameters. Functional constraints such as transaction cost and minimum transaction lots were included. In addition, the returns on assets parameters were considered as trapezoidal fuzzy numbers. An efficient genetic algorithm (GA) was designed, results were analyzed using numerical instances and sensitivity analysis were executed. In the numerical study, the problem was solved based on the presence or absence of each mode of constraints including transaction costs and minimum transaction lots. In addition, with the use of sensitivity analysis, the results of the model were presented with the variations of minimum expected rate of programming periods.

Improved Constrained Portfolio Selection Model using Particle Swarm Optimization

Objective: The main objective of this study is to improve the extended Markowitz mean-variance portfolio selection model by introducing a new constraint known as expert opinion practicable for portfolio selection in real-life situation. Methods: This new extended model consists of four constraints namely: bounds on holdings, cardinality, minimum transaction lots, and expert opinion. The first three constraints have been presented in other researches in literature. The fourth constraint introduced in this study is an essential parameter in making and guiding a realistic portfolio selection. To solve this new extended model an efficient heuristic method of Particle Swarm Optimization (PSO) was engaged with existing benchmark data in the literature. Results: The outcome of the computational results obtained in this study with the new extended Markowitz mean-variance portfolio selection model proposed in this study and solved with PSO showed an improved performance over existing algorithm in particular GA in different instances of the data set used. Conclusion: The study evolves a new extended portfolio selection model and the findings demonstrate the superiority of PSO performance in solving portfolio selection problem in comparison with GA algorithm.

Portfolio selection problem using generalized differential evolution 3

This Portfolio selection Problem (PSP) remains an intractable research problem in finance and economics and often regarded as NP-hard problem in optimization and computational intelligence. This paper solved the extended Markowitz mean- variance portfolio selection model with an efficient Metaheuristics method of Generalized Differential Evolution 3 (GDE3). The extended Markowitz mean- variance portfolio selection model consists of four constraints: bounds on holdings, cardinality, minimum transaction lots, and expert opinion. There is no research in literature that had ever engaged the set of four constraints with GDE3 to solve PSP. This paper is the first to conduct the study in this direction. The first three sets of constraints have been presented in other researches in literatures. This paper introduced expert opinion constraint to existing portfolio selection models and solved with GDE3. The computational results obtained in this research study show improved performance when compared with other Metaheuristics methods of Genetic algorithm (GA), Simulated Annealing (SA), Tabu Search (TS) and Particle Swarm Optimization (PSO).

A multi-period fuzzy portfolio optimization model with minimum transaction lots

Abstract In this paper, we consider a multi-period fuzzy portfolio optimization problem with minimum transaction lots. Based on possibility theory, we formulate a mean-semivariance portfolio selection model with the objectives of maximizing the terminal wealth and minimizing the cumulative risk over the whole investment horizon. In the proposed model, we take the return, risk, transaction costs, diversification degree, cardinality constraint and minimum transaction lots into consideration. To reflect investor’s aspiration levels for the two objectives, a fuzzy decision technique is employed to transform the proposed model into a single objective mixed-integer nonlinear programming problem. Then, we design a genetic algorithm for solution. Finally, we give an empirical application in Chinese stock markets to demonstrate the idea of our model and the effectiveness of the designed algorithm.