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.

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 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 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.

MEAN-SEMIVARIANCE MODELS FOR PORTFOLIO OPTIMIZATION PROBLEM WITH MIXED UNCERTAINTY OF FUZZINESS AND RANDOMNESS

2013 ◽  
Vol 21 (supp01) ◽  
pp. 127-139 ◽  
Author(s):  
ZHONGFENG QIN ◽  
DAVID Z. W. WANG ◽  
XIANG LI
Keyword(s):  
Portfolio Optimization ◽  
Optimization Problem ◽  
Risk Measure ◽  
Fuzzy Variable ◽  
Expected Returns ◽  
Random Fuzzy Variable ◽  
Fuzzy Variables ◽  
The Mean ◽  
Security Returns ◽  
Portfolio Optimization Problem

In practice, security returns cannot be accurately predicted due to lack of historical data. Therefore, statistical methods and experts' experience are always integrated to estimate future security returns, which are hereinafter regarded as random fuzzy variables. Random fuzzy variable is a powerful tool to deal with the portfolio optimization problem including stochastic parameters with ambiguous expected returns. In this paper, we first define the semivariance of random fuzzy variable and prove its several properties. By considering the semivariance as a risk measure, we establish the mean-semivariance models for portfolio optimization problem with random fuzzy returns. We design a hybrid algorithm with random fuzzy simulation to solve the proposed models in general cases. Finally, we present a numerical example and compare the results to illustrate the mean-semivariance model and the effectiveness of the algorithm.

scholarly journals Kelly's Criterion in Portfolio Optimization: A Decoupled Problem

2017 ◽  
Author(s):  
Zachariah Peterson
Keyword(s):  
Differential Evolution ◽  
Portfolio Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Stock Exchange ◽  
Differential Evolution Algorithm ◽  
Monte Carlo Calculations ◽  
Evolution Algorithm ◽  
Portfolio Optimization Problem ◽  
Single Objective

Kelly's Criterion is well known among gamblers and investors as a method for maximizing the returns one would expect to observe over long periods of betting or investing. These ideas are conspicuously absent from portfolio optimization problems in the financial and automation literature. This paper will show how Kelly's Criterion can be incorporated into standard portfolio optimization models. The model developed here combines risk and return into a single objective function by incorporating a risk parameter. This model is then solved for a portfolio of 10 stocks from a major stock exchange using a differential evolution algorithm. Monte Carlo calculations are used to verify the accuracy of the results obtained from differential evolution. The results show that evolutionary algorithms can be successfully applied to solve a portfolio optimization problem where returns are calculated by applying Kelly's Criterion to each of the assets in the portfolio.

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