Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 13

Portfolio Optimization Related Abstracts

13 Mathematical Programming Models for Portfolio Optimization Problem: A Review

Authors: DAUD MOHAMAD, Adibah Shuib, Mazura Mokhtar


Portfolio optimization problem has received a lot of attention from both researchers and practitioners over the last six decades. This paper provides an overview of the current state of research in portfolio optimization with the support of mathematical programming techniques. On top of that, this paper also surveys the solution algorithms for solving portfolio optimization models classifying them according to their nature in heuristic and exact methods. To serve these purposes, 40 related articles appearing in the international journal from 2003 to 2013 have been gathered and analyzed. Based on the literature review, it has been observed that stochastic programming and goal programming constitute the highest number of mathematical programming techniques employed to tackle the portfolio optimization problem. It is hoped that the paper can meet the needs of researchers and practitioners for easy references of portfolio optimization.

Keywords: Mathematical Programming, Portfolio Optimization, multi-objective programming, solution approaches

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12 The Impact of Transaction Costs on Rebalancing an Investment Portfolio in Portfolio Optimization

Authors: B. Marasović, S. Pivac, S. V. Vukasović


Constructing a portfolio of investments is one of the most significant financial decisions facing individuals and institutions. In accordance with the modern portfolio theory maximization of return at minimal risk should be the investment goal of any successful investor. In addition, the costs incurred when setting up a new portfolio or rebalancing an existing portfolio must be included in any realistic analysis. In this paper rebalancing an investment portfolio in the presence of transaction costs on the Croatian capital market is analyzed. The model applied in the paper is an extension of the standard portfolio mean-variance optimization model in which transaction costs are incurred to rebalance an investment portfolio. This model allows different costs for different securities, and different costs for buying and selling. In order to find efficient portfolio, using this model, first, the solution of quadratic programming problem of similar size to the Markowitz model, and then the solution of a linear programming problem have to be found. Furthermore, in the paper the impact of transaction costs on the efficient frontier is investigated. Moreover, it is shown that global minimum variance portfolio on the efficient frontier always has the same level of the risk regardless of the amount of transaction costs. Although efficient frontier position depends of both transaction costs amount and initial portfolio it can be concluded that extreme right portfolio on the efficient frontier always contains only one stock with the highest expected return and the highest risk.

Keywords: Portfolio Optimization, transaction costs, Croatian capital market, Markowitz model, fractional quadratic programming

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11 Portfolio Selection with Active Risk Monitoring

Authors: Marc S. Paolella, Pawel Polak


The paper proposes a framework for large-scale portfolio optimization which accounts for all the major stylized facts of multivariate financial returns, including volatility clustering, dynamics in the dependency structure, asymmetry, heavy tails, and non-ellipticity. It introduces a so-called risk fear portfolio strategy which combines portfolio optimization with active risk monitoring. The former selects optimal portfolio weights. The latter, independently, initiates market exit in case of excessive risks. The strategy agrees with the stylized fact of stock market major sell-offs during the initial stage of market downturns. The advantages of the new framework are illustrated with an extensive empirical study. It leads to superior multivariate density and Value-at-Risk forecasting, and better portfolio performance. The proposed risk fear portfolio strategy outperforms various competing types of optimal portfolios, even in the presence of conservative transaction costs and frequent rebalancing. The risk monitoring of the optimal portfolio can serve as an early warning system against large market risks. In particular, the new strategy avoids all the losses during the 2008 financial crisis, and it profits from the subsequent market recovery.

Keywords: Portfolio Optimization, Financial Crises, comfort, risk monitoring

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10 Portfolio Optimization under a Hybrid Stochastic Volatility and Constant Elasticity of Variance Model

Authors: Jai Heui Kim, Sotheara Veng


This paper studies the portfolio optimization problem for a pension fund under a hybrid model of stochastic volatility and constant elasticity of variance (CEV) using asymptotic analysis method. When the volatility component is fast mean-reverting, it is able to derive asymptotic approximations for the value function and the optimal strategy for general utility functions. Explicit solutions are given for the exponential and hyperbolic absolute risk aversion (HARA) utility functions. The study also shows that using the leading order optimal strategy results in the value function, not only up to the leading order, but also up to first order correction term. A practical strategy that does not depend on the unobservable volatility level is suggested. The result is an extension of the Merton's solution when stochastic volatility and elasticity of variance are considered simultaneously.

Keywords: Asymptotic analysis, Stochastic Volatility, Portfolio Optimization, Stochastic Optimal Control, constant elasticity of variance

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9 Financial Portfolio Optimization in Electricity Markets: Evaluation via Sharpe Ratio

Authors: F. Gökgöz, M. E. Atmaca


Electricity plays an indispensable role in human life and the economy. It is a unique product or service that must be balanced instantaneously, as electricity is not stored, generation and consumption should be proportional. Effective and efficient use of electricity is very important not only for society, but also for the environment. A competitive electricity market is one of the best ways to provide a suitable platform for effective and efficient use of electricity. On the other hand, it carries some risks that should be carefully managed by the market players. Risk management is an essential part in market players’ decision making. In this paper, risk management through diversification is applied with the help of Markowitz’s Mean-variance, Down-side and Semi-variance methods for a case study. Performance of optimal electricity sale solutions are measured and evaluated via Sharpe-Ratio, and the optimal portfolio solutions are improved. Two years of historical weekdays’ price data of the Turkish Day Ahead Market are used to demonstrate the approach.

Keywords: Portfolio Optimization, electricity market, risk management in electricity market, sharpe ratio

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8 Financial Portfolio Optimization in Turkish Electricity Market via Value at Risk

Authors: F. Gökgöz, M. E. Atmaca


Electricity has an indispensable role in human daily life, technological development and economy. It is a special product or service that should be instantaneously generated and consumed. Sources of the world are limited so that effective and efficient use of them is very important not only for human life and environment but also for technological and economic development. Competitive electricity market is one of the important way that provides suitable platform for effective and efficient use of electricity. Besides benefits, it brings along some risks that should be carefully managed by a market player like Electricity Generation Company. Risk management is an essential part in market players’ decision making. In this paper, risk management through diversification is applied with the help of Value at Risk methods for case studies. Performance of optimal electricity sale solutions are measured and the portfolio performance has been evaluated via Sharpe-Ratio, and compared with conventional approach. Biennial historical electricity price data of Turkish Day Ahead Market are used to demonstrate the approach.

Keywords: Risk management, Portfolio Optimization, value at risk, electricity market

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7 Portfolio Optimization with Reward-Risk Ratio Measure Based on the Mean Absolute Deviation

Authors: Wlodzimierz Ogryczak, Tomasz Sliwinski, Michal Przyluski


In problems of portfolio selection, the reward-risk ratio criterion is optimized to search for a risky portfolio with the maximum increase of the mean return in proportion to the risk measure increase when compared to the risk-free investments. In the classical model, following Markowitz, the risk is measured by the variance thus representing the Sharpe ratio optimization and leading to the quadratic optimization problems. Several Linear Programming (LP) computable risk measures have been introduced and applied in portfolio optimization. In particular, the Mean Absolute Deviation (MAD) measure has been widely recognized. The reward-risk ratio optimization with the MAD measure can be transformed into the LP formulation with the number of constraints proportional to the number of scenarios and the number of variables proportional to the total of the number of scenarios and the number of instruments. This may lead to the LP models with huge number of variables and constraints in the case of real-life financial decisions based on several thousands scenarios, thus decreasing their computational efficiency and making them hardly solvable by general LP tools. We show that the computational efficiency can be then dramatically improved by an alternative model based on the inverse risk-reward ratio minimization and by taking advantages of the LP duality. In the introduced LP model the number of structural constraints is proportional to the number of instruments thus not affecting seriously the simplex method efficiency by the number of scenarios and therefore guaranteeing easy solvability. Moreover, we show that under natural restriction on the target value the MAD risk-reward ratio optimization is consistent with the second order stochastic dominance rules.

Keywords: Portfolio Optimization, Linear Programming, reward-risk ratio, mean absolute deviation

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6 Electricity Sector's Status in Lebanon and Portfolio Optimization for the Future Electricity Generation Scenarios

Authors: Nour Wehbe


The Lebanese electricity sector is at the heart of a deep crisis. Electricity in Lebanon is supplied by Électricité du Liban (EdL) which has to suffer from technical and financial deficiencies for decades and proved to be insufficient and deficient as the demand still exceeds the supply. As a result, backup generation is widespread throughout Lebanon. The sector costs massive government resources and, on top of it, consumers pay massive additional amounts for satisfying their electrical needs. While the developed countries have been investing in renewable energy for the past two decades, the Lebanese government realizes the importance of adopting such energy sourcing strategies for the upgrade of the electricity sector in the country. The diversification of the national electricity generation mix has increased considerably in Lebanon's energy planning agenda, especially that a detailed review of the energy potential in Lebanon has revealed a great potential of solar and wind energy resources, a considerable potential of biomass resource, and an important hydraulic potential in Lebanon. This paper presents a review of the energy status of Lebanon, and illustrates a detailed review of the EDL structure with the existing problems and recommended solutions. In addition, scenarios reflecting implementation of policy projects are presented, and conclusions are drawn on the usefulness of a proposed evaluation methodology and the effectiveness of the adopted new energy policy for the electrical sector in Lebanon.

Keywords: Portfolio Optimization, EdL Electricite du Liban, electricity generation mix, mean-variance approach

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5 Random Matrix Theory Analysis of Cross-Correlation in the Nigerian Stock Exchange

Authors: Chimezie P. Nnanwa, Thomas C. Urama, Patrick O. Ezepue


In this paper we use Random Matrix Theory to analyze the eigen-structure of the empirical correlations of 82 stocks which are consistently traded in the Nigerian Stock Exchange (NSE) over a 4-year study period 3 August 2009 to 26 August 2013. We apply the Marchenko-Pastur distribution of eigenvalues of a purely random matrix to investigate the presence of investment-pertinent information contained in the empirical correlation matrix of the selected stocks. We use hypothesised standard normal distribution of eigenvector components from RMT to assess deviations of the empirical eigenvectors to this distribution for different eigenvalues. We also use the Inverse Participation Ratio to measure the deviation of eigenvectors of the empirical correlation matrix from RMT results. These preliminary results on the dynamics of asset price correlations in the NSE are important for improving risk-return trade-offs associated with Markowitz’s portfolio optimization in the stock exchange, which is pursued in future work.

Keywords: Portfolio Optimization, random matrix theory, correlation matrix, eigenvalue and eigenvector, inverse participation ratio

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4 Dynamic Correlations and Portfolio Optimization between Islamic and Conventional Equity Indexes: A Vine Copula-Based Approach

Authors: Imen Dhaou


This study examines conditional Value at Risk by applying the GJR-EVT-Copula model, and finds the optimal portfolio for eight Dow Jones Islamic-conventional pairs. Our methodology consists of modeling the data by a bivariate GJR-GARCH model in which we extract the filtered residuals and then apply the Peak over threshold model (POT) to fit the residual tails in order to model marginal distributions. After that, we use pair-copula to find the optimal portfolio risk dependence structure. Finally, with Monte Carlo simulations, we estimate the Value at Risk (VaR) and the conditional Value at Risk (CVaR). The empirical results show the VaR and CVaR values for an equally weighted portfolio of Dow Jones Islamic-conventional pairs. In sum, we found that the optimal investment focuses on Islamic-conventional US Market index pairs because of high investment proportion; however, all other index pairs have low investment proportion. These results deliver some real repercussions for portfolio managers and policymakers concerning to optimal asset allocations, portfolio risk management and the diversification advantages of these markets.

Keywords: Portfolio Optimization, CVaR, Dow Jones Islamic index, GJR-GARCH-EVT-pair copula

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3 Supplier Risk Management: A Multivariate Statistical Modelling and Portfolio Optimization Based Approach for Supplier Delivery Performance Development

Authors: Jiahui Yang, John Quigley, Lesley Walls


In this paper, the authors develop a stochastic model regarding the investment in supplier delivery performance development from a buyer’s perspective. The authors propose a multivariate model through a Multinomial-Dirichlet distribution within an Empirical Bayesian inference framework, representing both the epistemic and aleatory uncertainties in deliveries. A closed form solution is obtained and the lower and upper bound for both optimal investment level and expected profit under uncertainty are derived. The theoretical properties provide decision makers with useful insights regarding supplier delivery performance improvement problems where multiple delivery statuses are involved. The authors also extend the model from a single supplier investment into a supplier portfolio, using a Lagrangian method to obtain a theoretical expression for an optimal investment level and overall expected profit. The model enables a buyer to know how the marginal expected profit/investment level of each supplier changes with respect to the budget and which supplier should be invested in when additional budget is available. An application of this model is illustrated in a simulation study. Overall, the main contribution of this study is to provide an optimal investment decision making framework for supplier development, taking into account multiple delivery statuses as well as multiple projects.

Keywords: Supply Chain Management, Decision Making, Portfolio Optimization, empirical bayesian, supplier development

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2 A Mean–Variance–Skewness Portfolio Optimization Model

Authors: Kostas Metaxiotis


Portfolio optimization is one of the most important topics in finance. This paper proposes a mean–variance–skewness (MVS) portfolio optimization model. Traditionally, the portfolio optimization problem is solved by using the mean–variance (MV) framework. In this study, we formulate the proposed model as a three-objective optimization problem, where the portfolio's expected return and skewness are maximized whereas the portfolio risk is minimized. For solving the proposed three-objective portfolio optimization model we apply an adapted version of the non-dominated sorting genetic algorithm (NSGAII). Finally, we use a real dataset from FTSE-100 for validating the proposed model.

Keywords: Evolutionary Algorithms, Portfolio Optimization, Skewness, stock selection

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1 Multi-Criteria Based Robust Markowitz Model under Box Uncertainty

Authors: Pulak Swain, A.K. Ojha


Portfolio optimization is based on dealing with the problems of efficient asset allocation. Risk and Expected return are two conflicting criteria in such problems, where the investor prefers the return to be high and the risk to be low.Using multi-objective approach we can solve those type of problems. However the information which we have for the input parameters are generally ambiguous and the input values can fluctuate around some nominal values. We can not ignore the uncertainty in input values, as they can affect the asset allocation drastically. So we use Robust Optimization approach to the problems where the input parameters comes under box uncertainty. In this paper we solve the multi criteria robust problem with the help of ϵ - constraint method

Keywords: Multi-objective optimization, Portfolio Optimization, Robust Optimization, ϵ - constraint method, Box Uncertainty

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