A mixed integer linear programming formulation of the optimal mean/Value-at-Risk portfolio problem

Benati, Stefano; Rizzi, Roméo

doi:10.1016/j.ejor.2005.07.020

Cited by 131 publications

(77 citation statements)

References 16 publications

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“…Thus, minimax model is used for formulating security measures and half of the mean-average deviation as a stability measure. Benati and Rizzi (2007) have based their model on the Markowitz's, but they have substituted variance as a measure of risk with the value at risk (VaR). Authors have presented that the posed problem can be solved using CPLEX in rational time if the number of observed periods and the number of assets are not too large.…”

Section: Literature Reviewmentioning

confidence: 99%

Efficiency of the minmax portfolio on the european capital market - can we beat the market

Arnaut-Berilo¹,

Zaimović²,

Sikalo³

2017

Pressacademia

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Purpose-This paper presents game theory approach for solving problem of the optimal investment portfolio selection. Methodology-Model was formed on the basis of historical returns on stocks presented as a matrix of payments. The goal is seeking the minimum between the largest potential losses, and therefore it is called minmax model. The main objective is to answer whether the minimax model tool performs better than the stock market index, and to verify the relationship between the established Markowitz meanvariance (MV) efficient portfolios and minmax optimum portfolio. We use data from the European capital market and Euro Stoxx 50 index as a reference index in the period 2004-2015, which we divided into two parts. We compared and analyzed the performance of the portfolios created through minimax model with the performance of market index and MV model in the actual investment period and it proved to be dominant and more successful. Findings-Results speak in favor of minmax portfolio model as effective passive investment strategy. It is possible to maximize returns over even longer periods of up to year without changing portfolio investments, i.e. without frequent trading and not just to gain market return, but to beat the market by this technical investing. Conclusion-Minmax model could be used for asset allocation in portfolio investments and that there is a real possibility to beat the market using minimax model.

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Section: Literature Reviewmentioning

confidence: 99%

Efficiency of the minmax portfolio on the european capital market - can we beat the market

Arnaut-Berilo¹,

Zaimović²,

Sikalo³

2017

Pressacademia

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“…Finally, the decisions that must be made are subject to certain requirements and restrictions of a system which are called constraints (Smith, Taşkın 2008). LP has been widely used in optimizing complex systems, such as those arising in marketing (Stapleton et al 2003), finance (Benati, Rizzi 2007), energy (Xydis, Koroneos 2012), product design (Seibi, Sawaqed 2002), transportation (Luathep et al 2011), production planning and control (Rasmussen 2013;Doganis, Sarimveis 2007), chemistry (Rossi et al 2009), medicine (Mangasarian et al 1994), telecommunications (Sirdey, Maurice 2008), sports (Soleimani-Damaneh et al 2011), and military (Tucker et al 1998). Some attempts have been made to develop linear programming models for optimization problems in construction industry.…”

Section: Literature Reviewmentioning

confidence: 99%

Maximizing the Value of Residential Projects Using Fuzzy Rule Based Linear Programming

Üstündağ

Çevikcan

2016

Journal of Civil Engineering and Management

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Abstract. Optimizing the allocation of residence types has a great impact on efficient management of resources for construction projects. Hence, determining appropriate allocation of residence types provides effective financial activities, especially for large-scaled residential projects. Subjectivity and vagueness in the determination of price per m 2 for residences requires the consideration of fuzzy logic, since the modeling of imprecise and qualitative knowledge, as well as the transmission and handling of uncertainty at various stages are possible through the use of fuzzy sets. This study proposes an approach that integrates Fuzzy Rule Based System (FRBS) with mathematical programming. In the proposed hybrid approach, FRBS is used to set price per square meter and it provides input for Net Present Value (NPV) formulation. Mixed integer linear programming (MILP) model is developed for the maximization of (NPV) of the project. The proposed model is applied to a residential project in Istanbul to demonstrate its performance. The optimal NPVs and allocation results for four types of residences are analyzed depending on the different factor levels of total construction area, sales rate and bank loan interest rate. The results indicate that the optimal NPV and allocation of residences are significantly influenced by the factor of construction area.

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“…For general returns distributions, problem (3.72) is non-convex. A mixed integer LP (MILP) formulation of problems (3.72) and (3.73) can be achieved as follows ( [7] and [91]). Let r L be a lower bound on returns in the market and consider T scenarios, for which at each scenario t, a binary variable y t is 1 if ∑ n j=1 x j r jt ≥ r L and 0 otherwise.…”

Section: Value-at-risk Modelmentioning

confidence: 99%

Mean-Variance Portfolio Optimization : Eigendecomposition-Based Methods

Mayambala¹

2015

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Modern portfolio theory is about determining how to distribute capital among available securities such that, for a given level of risk, the expected return is maximized, or for a given level of return, the associated risk is minimized. In the pioneering work of Markowitz in 1952, variance was used as a measure of risk, which gave rise to the wellknown mean-variance portfolio optimization model. Although other mean-risk models have been proposed in the literature, the mean-variance model continues to be the backbone of modern portfolio theory and it is still commonly applied. The scope of this thesis is a solution technique for the mean-variance model in which eigendecomposition of the covariance matrix is performed.The first part of the thesis is a review of the mean-risk models that have been suggested in the literature. For each of them, the properties of the model are discussed and the solution methods are presented, as well as some insight into possible areas of future research.The second part of the thesis is two research papers. In the first of these, a solution technique for solving the mean-variance problem is proposed. This technique involves making an eigendecomposition of the covariance matrix and solving an approximate problem that includes only relatively few eigenvalues and corresponding eigenvectors. The method gives strong bounds on the exact solution in a reasonable amount of computing time, and can thus be used to solve large-scale mean-variance problems.The second paper studies the mean-variance model with cardinality constraints, that is, with a restricted number of securities included in the portfolio, and the solution technique from the first paper is extended to solve such problems. Near-optimal solutions to large-scale cardinality constrained mean-variance portfolio optimization problems are obtained within a reasonable amount of computing time, compared to the time required by a commercial general-purpose solver.v Populärvetenskaplig sammanfattningFör den som har kapital att investera kan det vara svårt att avgöra vilka investeringar som är mest fördelaktiga. Till stöd för beslutet kan matematiska modeller användas och denna avhandling handlar om hur man kan beräkna lösningar till sådana modeller. De investeringsalternativ som betraktas är finansiella instrument som är föremål för daglig handel, som aktier och obligationer.En investerare placerar kapital i finansiella instrument eftersom de förväntas ge en god avkastning över tiden. Samtidigt är sådana placeringar alltid förknippade med risktagande. Förväntad avkastning och risk varierar kraftigt mellan olika instrument. Till exempel ger placeringar i statsobligationer typiskt mycket låg avkastning till mycket låg risk, medan placeringar i aktier i nystartade bolag som utvecklar nya läkemedel kan ge mycket hög avkastning samtidigt som risken är mycket hög.Att investera kan ses som en avvägning mellan den förväntade avkastningen och den risk som investeringen innebär, och typiskt är hög förväntad avkastning också associerade med e...

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A mixed integer linear programming formulation of the optimal mean/Value-at-Risk portfolio problem

Cited by 131 publications

References 16 publications

Efficiency of the minmax portfolio on the european capital market - can we beat the market

Efficiency of the minmax portfolio on the european capital market - can we beat the market

Maximizing the Value of Residential Projects Using Fuzzy Rule Based Linear Programming

Mean-Variance Portfolio Optimization : Eigendecomposition-Based Methods

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