Modeling and Assessment of Financial Investments by Portfolio Optimization on Stock Exchange

Stoilov, Todor; Stoilova, Krasimira; Vladimirov, Miroslav

doi:10.1007/978-3-030-55347-0_29

Cited by 3 publications

(6 citation statements)

References 12 publications

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“…The analytical form of the VaR constraint in problem ( 17) becomes 𝐄 T 𝐰 − 1.645√𝐰 T 𝚺𝐰 ≥ −0.3. Solving problems (17) and (18) for different values of the parameter 𝜆 ∈ (0, ∞), points of the corresponding efficient frontier are evaluated. From these sets of portfolio, for comparison reasons, it has been chosen the portfolios from ( 17) and (18), which have maximal Sharpe ratio = Portfolio return/Portfolio risk.…”

Section: Graphical Interpretation Of Var Constraintmentioning

confidence: 99%

“…4. The "Efficient frontier" is the same for problems (17) and (18) To find the reason why problems (17) and (18) have equal solutions here it is graphically presented the influence of the VaR constraint. The form of constraint (16) is quadratic one and it makes and elliptic curve in the space of the assets weights w2(w1).…”

Section: Graphical Interpretation Of Var Constraintmentioning

confidence: 99%

“…The form of constraint (16) is quadratic one and it makes and elliptic curve in the space of the assets weights w2(w1). This elliptic curve restricts the set of points on the line, 𝐰 T |𝟏| = 1, where problem (18) can have a solution. For appropriate value of γ the relation ( 16) can define only one feasible point between ( 16) and 𝐰 T |𝟏| = 1.…”

Section: Graphical Interpretation Of Var Constraintmentioning

confidence: 99%

“…The objective function also is an elliptic curve, which makes a tangent point with 𝐰 T |𝟏| =1. 17) and (18) For the case of problem (18) the objective function is the same as for (17). The VaRα constraint ( 16) restricts the feasible points on line 𝐰 T |𝟏| = 1, but the solution of (17) falls down in this feasible area.…”

Section: Graphical Interpretation Of Var Constraintmentioning

confidence: 99%

“…The portfolio theory progressively evolves and complicates its formal background. This results in continuously increase in the set of parameters and variables, which are considered for the portfolio management, optimization of resources and investments, the definition and solution of portfolio optimization problems [18]. This paper pays general attention to the inclusion of new risk parameter Value at Risk (VaR) [12,20] for the portfolio problem.…”

Section: Introductionmentioning

confidence: 99%

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The Probabilistic Risk Measure VaR as Constraint in Portfolio Optimization Problem

Stoilov

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Vladimirov

2021

Cybernetics and Information Technologies

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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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Section: Graphical Interpretation Of Var Constraintmentioning

confidence: 99%

Section: Graphical Interpretation Of Var Constraintmentioning

confidence: 99%

Section: Graphical Interpretation Of Var Constraintmentioning

confidence: 99%

Section: Graphical Interpretation Of Var Constraintmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The Probabilistic Risk Measure VaR as Constraint in Portfolio Optimization Problem

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Intelligent Approach to Infrastructure Changes in Urban Environment

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Explicit Value at Risk Goal Function in Bi-Level Portfolio Problem for Financial Sustainability

2021

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The mean-variance (MV) portfolio optimization targets higher return for investment period despite the unknown stochastic behavior of the future asset returns. That is why a risk is explicitly considering, quantified by algebraic characteristics of volatilities and co-variances. A new probabilistic definition of portfolio risk is the Value at Risk (VaR). The paper makes explicit inclusion and minimization of VaR as a quantitative measure of financial sustainability of a portfolio problem. Thus, the portfolio weights as problem solutions will respect not only the MV requirements for risk and return, but also the additional minimization of risk defined by VaR level. The portfolio problem is defined in a new, bi-level form. The upper level minimizes and evaluates the VaR value. The lower level evaluates the optimal assets weights by minimizing portfolio risk and maximizing the return in MV form. The bi-level model allows to have extended set of portfolio solutions with the portfolio weights and the value of VaR. Graphical interpretation of this bi-level definition of the portfolio problem explains the differences with the MV portfolio definition. Thus, the bi-level portfolio problem evaluates the optimal weights, which makes maximization of portfolio return and minimization of the risk in its algebraic and probabilistic form of definition.

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Modeling and Assessment of Financial Investments by Portfolio Optimization on Stock Exchange

Cited by 3 publications

References 12 publications

The Probabilistic Risk Measure VaR as Constraint in Portfolio Optimization Problem

The Probabilistic Risk Measure VaR as Constraint in Portfolio Optimization Problem

Intelligent Approach to Infrastructure Changes in Urban Environment

Explicit Value at Risk Goal Function in Bi-Level Portfolio Problem for Financial Sustainability

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