Portfolio Optimization with Metaheuristics

2017 ◽  
Vol 2 (2) ◽  
Author(s):  
Georgios Mamanis
Keyword(s):  
Portfolio Optimization ◽  
Portfolio Selection ◽  
Value At Risk ◽  
Optimal Allocation ◽  
Optimization Problems ◽  
Objective Functions ◽  
Cardinality Constraints ◽  
Risk Optimization ◽  
Measures Of Risk ◽  
Mean Risk

<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

2017 ◽  
Vol 2 (2) ◽  
Author(s):  
Georgios Mamanis
Keyword(s):  
Portfolio Optimization ◽  
Portfolio Selection ◽  
Value At Risk ◽  
Optimal Allocation ◽  
Optimization Problems ◽  
Objective Functions ◽  
Cardinality Constraints ◽  
Risk Optimization ◽  
Measures Of Risk ◽  
Mean Risk

<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 and Asset Allocation With Metaheuristics

2021 ◽  
pp. 78-96
Author(s):  
Jhuma Ray ◽  
Siddhartha Bhattacharyya ◽  
N. Bhupendro Singh
Keyword(s):  
Portfolio Optimization ◽  
Portfolio Selection ◽  
Asset Allocation ◽  
Value At Risk ◽  
Optimal Allocation ◽  
Short Note ◽  
Objective Functions ◽  
Cardinality Constraints ◽  
Distribution Of Wealth ◽  
Risk Optimization

Portfolio optimization stands to be an issue of finding an optimal allocation of wealth to place within the obtainable assets. Markowitz stated the problem to be structured as dual-objective mean-risk optimization, pointing the best trade-off solutions within a portfolio between risks which is measured by variance and mean. Thus the major intention was nothing else than hunting for optimum distribution of wealth over a specific amount of assets by diminishing risk and maximizing returns of a portfolio. Value-at-risk, expected shortfall, and semi-variance measures prove to be complex for measuring risk, for maximization of skewness, liquidity, dividends by added objective functions, cardinality constraints, quantity constraints, minimum transaction lots, class constraints in real-world constraints all of which are incorporated in modern portfolio selection models, furnish numerous optimization challenges. The emerging portfolio optimization issue turns out to be extremely tough to be handled with exact approaches because it exhibits nonlinearities, discontinuities and high-dimensional, efficient boundaries. Because of these attributes, a number of researchers got motivated in researching the usage of metaheuristics, which stand to be effective measures for finding near optimal solutions for tough optimization issues in an adequate computational time frame. This review report serves as a short note on portfolio optimization field with the usage of Metaheuristics and finally states that how multi-objective metaheuristics prove to be efficient in dealing with portfolio selection problems with complex measures of risk defining non-convex, non-differential objective functions.

Portfolio Optimization and Asset Allocation With Metaheuristics

2019 ◽  
pp. 1-26
Author(s):  
Jhuma Ray ◽  
Siddhartha Bhattacharyya ◽  
N. Bhupendro Singh
Keyword(s):  
Portfolio Optimization ◽  
Portfolio Selection ◽  
Asset Allocation ◽  
Value At Risk ◽  
Optimal Allocation ◽  
Short Note ◽  
Objective Functions ◽  
Cardinality Constraints ◽  
Distribution Of Wealth ◽  
Risk Optimization

Portfolio optimization stands to be an issue of finding an optimal allocation of wealth to place within the obtainable assets. Markowitz stated the problem to be structured as dual-objective mean-risk optimization, pointing the best trade-off solutions within a portfolio between risks which is measured by variance and mean. Thus the major intention was nothing else than hunting for optimum distribution of wealth over a specific amount of assets by diminishing risk and maximizing returns of a portfolio. Value-at-risk, expected shortfall, and semi-variance measures prove to be complex for measuring risk, for maximization of skewness, liquidity, dividends by added objective functions, cardinality constraints, quantity constraints, minimum transaction lots, class constraints in real-world constraints all of which are incorporated in modern portfolio selection models, furnish numerous optimization challenges. The emerging portfolio optimization issue turns out to be extremely tough to be handled with exact approaches because it exhibits nonlinearities, discontinuities and high-dimensional, efficient boundaries. Because of these attributes, a number of researchers got motivated in researching the usage of metaheuristics, which stand to be effective measures for finding near optimal solutions for tough optimization issues in an adequate computational time frame. This review report serves as a short note on portfolio optimization field with the usage of Metaheuristics and finally states that how multi-objective metaheuristics prove to be efficient in dealing with portfolio selection problems with complex measures of risk defining non-convex, non-differential objective functions.

HYPER SENSITIVITY ANALYSIS OF PORTFOLIO OPTIMIZATION PROBLEMS

2004 ◽  
Vol 21 (03) ◽  
pp. 297-317 ◽  
Author(s):  
LEONID CHURILOV ◽  
IMMANUEL M. BOMZE ◽  
MOSHE SNIEDOVICH ◽  
DANIEL RALPH
Keyword(s):  
Sensitivity Analysis ◽  
Portfolio Optimization ◽  
Portfolio Selection ◽  
Optimization Problems ◽  
Selection Problem ◽  
Full Size ◽  
Concave Programming ◽  
Hyper Sensitivity ◽  
Mean Variance Portfolio ◽  
Mean Variance

Hyper Sensitivity Analysis (HSA) is an intuitive generalization of conventional sensitivity analysis, where the term "hyper" indicates that the sensitivity analysis is conducted with respect to functions rather than numeric values. In this paper Composite Concave Programming is used to perform HSA in the area of Portfolio Optimization Problems. The concept of HSA is suited for situations where several candidates for the function quantifying the utility of (mean, variance) pairs are available. We discuss the applications of HSA to two types of mean–variance portfolio optimization problems: the classical one and a discrete knapsack-type portfolio selection problem. It is explained why in both cases the methodology can be applied to full size problems.

scholarly journals RM-CVaR: Regularized Multiple β-CVaR Portfolio

2020 ◽  
Author(s):  
Kei Nakagawa ◽  
Shuhei Noma ◽  
Masaya Abe
Keyword(s):  
Portfolio Optimization ◽  
Value At Risk ◽  
Optimization Problems ◽  
Risk Measures ◽  
Risk Measure ◽  
Superior Performance ◽  
Conditional Value At Risk ◽  
Related Risk ◽  
Mean And Variance ◽  
Portfolio Optimization Problem

The problem of finding the optimal portfolio for investors is called the portfolio optimization problem. Such problem mainly concerns the expectation and variability of return (i.e., mean and variance). Although the variance would be the most fundamental risk measure to be minimized, it has several drawbacks. Conditional Value-at-Risk (CVaR) is a relatively new risk measure that addresses some of the shortcomings of well-known variance-related risk measures, and because of its computational efficiencies, it has gained popularity. CVaR is defined as the expected value of the loss that occurs beyond a certain probability level (β). However, portfolio optimization problems that use CVaR as a risk measure are formulated with a single β and may output significantly different portfolios depending on how the β is selected. We confirm even small changes in β can result in huge changes in the whole portfolio structure. In order to improve this problem, we propose RM-CVaR: Regularized Multiple β-CVaR Portfolio. We perform experiments on well-known benchmarks to evaluate the proposed portfolio. Compared with various portfolios, RM-CVaR demonstrates a superior performance of having both higher risk-adjusted returns and lower maximum drawdown.

scholarly journals Scenario aggregation method for portfolio expectile optimization

2016 ◽  
Vol 33 (1-2) ◽  
Author(s):  
Edgars Jakobsons
Keyword(s):  
Portfolio Optimization ◽  
Value At Risk ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Risk Measures ◽  
Risk Measure ◽  
Conditional Value At Risk ◽  
Aggregation Method ◽  
Portfolio Optimization Problem ◽  
Scenario Aggregation

AbstractThe statistical functional expectile has recently attracted the attention of researchers in the area of risk management, because it is the only risk measure that is both coherent and elicitable. In this article, we consider the portfolio optimization problem with an expectile objective. Portfolio optimization problems corresponding to other risk measures are often solved by formulating a linear program (LP) that is based on a sample of asset returns. We derive three different LP formulations for the portfolio expectile optimization problem, which can be considered as counterparts to the LP formulations for the Conditional Value-at-Risk (CVaR) objective in the works of Rockafellar and Uryasev [

scholarly journals Cardinality Constrained Portfolio Optimization Using Bee Colony Algorithm (Case Study: Tehran Stock Exchange)

2018 ◽  
Author(s):  
Masomeh Mansourinia ◽  
Alireza Momeni
Keyword(s):  
Quadratic Programming ◽  
Portfolio Optimization ◽  
Programming Problem ◽  
Efficient Solution ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Stock Exchange ◽  
Cardinality Constraints ◽  
Bee Colony ◽  
Portfolio Optimization Problem

One of the most studied variant of portfolio optimization problems is with cardinality constraints that transform classical mean-variance model from a convex quadratic programming problem into a mixed integer quadratic programming problem which brings the problem to the class of NP-Complete problems. Therefore, the computational complexity is significantly increased since cardinality constraints have a direct influence on the portfolio size. In order to overcome arising computational difficulties, for solving this problem, researchers have focused on investigating efficient solution algorithms such as metaheuristic algorithms since exact techniques may be inadequate to find an optimal solution in a reasonable time and are computationally ineffective when applied to large-scale problems. In this paper, our purpose is to present an efficient solution approach based on an artificial bee colony algorithm with feasibility enforcement and infeasibility toleration procedures for solving cardinality constrained portfolio optimization problem. Computational results confirm the effectiveness of the solution methodology. In this study, the ABC-I algorithm and the ABC-II algorithm, which are the modern meta-innovative models for solving optimization problems, have been used to optimize the investment portfolio with the goal of increasing returns and reducing risk. Of the 591 companies listed on the Tehran Stock Exchange, 150 companies were selected during the period from 2014 to 2018 using a systematic elimination method with limitation as the final sample. The data from these companies were analyzed using the algorithms used in the research and their performance was compared. The results of the research indicate that the ABC-II algorithm is more efficient than ABC-I for solving the stock portfolio optimization problem.

scholarly journals The Probabilistic Risk Measure VaR as Constraint in Portfolio Optimization Problem

2021 ◽  
Vol 21 (1) ◽  
pp. 19-31
Author(s):  
Todor Stoilov ◽  
Krasimira Stoilova ◽  
Miroslav Vladimirov
Keyword(s):  
Portfolio Optimization ◽  
Value At Risk ◽  
Optimization Problem ◽  
Stock Exchange ◽  
Risk Measure ◽  
Formal Analysis ◽  
Cardinality Constraints ◽  
Algebraic Form ◽  
Portfolio Problem ◽  
Portfolio Optimization Problem

Abstract The paper realizes inclusion of probabilistic measure for risk, VaR (Value at Risk), into a portfolio optimization problem. The formal analysis of the portfolio problem illustrates the evolution of the portfolio theory in sequentially inclusion of different market characteristics into the problem. They make modifications and complications of the portfolio problem by adding various constraints to consider requirements for taxes, boundaries for assets, cardinality constraints, and allocation of the investment resources. All these characteristics and parameters of the investment participate in the portfolio problem by analytical algebraic relations. The VaR definition of the portfolio risk is formalized in a probabilistic manner. The paper applies approximation of such probabilistic constraint in algebraic form. Geometrical interpretation is given for explaining the influence of the VaR constraint to the portfolio solution. Numerical simulation with data of the Bulgarian Stock Exchange illustrates the influence of the VaR constraint into the portfolio optimization problem.

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