OPTIMASI PORTOFOLIO DENGAN MODIFIED RISK MEASURE MEMPERTIMBANGKAN BATASAN KARDINALITAS DAN BOBOT SAHAM

AbstractModified risk measure model is a portfolio optimization model using return scenario based on the forecasting error. This model is a basic model that has not taken the real investment conditions made by investors, such as cardinality and threshold constraints. Therefore, it is necessary to develop a modified risk measure model to be more representative to investment situation and compare the performance between the basic model and the proposed model in optimization. Portfolio optimization will be applied to LQ45 stock list from April-November 2019. Optimization begins by forming 100 scenarios based on error prediction results for each stock with Moving Average methods. Portfolios will be formed at several levels of risk (15%, 20%, 25%, and 30%) to see the impact of limitations on risk and model performance based on the expected return. Optimization using new model tends to reduce the model's performance, but this model reflects the real situation faced by investors.Keywords : modified risk measure model, cardinality, threshold constraintModel modified risk measure merupakan salah satu model optimasi portofolio menggunakan skenario return berdasarkan error hasil prediksi. Sayangnya, model ini merupakan model yang belum mempertimbangkan keadaan investasi nyata yang dilakukan oleh investor, seperti batasan kardinalitas, dan batasan bobot saham. Oleh karena itu, perlu dilakukan pengembangan model modified risk measure agar lebih representatif terhadap keadaan investasi dan membandingkan performa antara model dasar dengan model usulan. Optimasi portofolio diterapkan pada saham yang termasuk dalam daftar LQ45 Bursa Efek Indonesia Februari 2019 untuk periode bulan April-November 2019. Optimasi diawali dengan membentuk 100 skenario berdasarkan error hasil prediksi return untuk masing-masing saham. Optimasi dilakukan menggunakan CPLEX Optimizer untuk penyelesaian model linear. Portofolio akan dibentuk pada beberapa tingkatan risiko, yaitu 15%, 20%, 25% dan 30% untuk melihat dampak adanya batasan tambahan terhadap risiko optimasi menggunakan model modified risk measure. Hasilnya adalah optimasi model dengan batasan tambahan cenderung menurunkan performa model, tetapi di sisi lain, portofolio menjadi lebih efisien dan representatif terhadap keadaan investasi.Kata Kunci : model modified risk measure, kardinalitas, batas bobot saham

A constrained swarm optimization algorithm for large-scale long-run investments using Sharpe ratio-based performance measures

We study large-scale portfolio optimization problems in which the aim is to maximize a multi-moment performance measure extending the Sharpe ratio. More specifically, we consider the adjusted for skewness Sharpe ratio, which incorporates the third moment of the returns distribution, and the adjusted for skewness and kurtosis Sharpe ratio, which exploits in addition the fourth moment. Further, we account for two types of real-world trading constraints. On the one hand, we impose stock market restrictions through cardinality, buy-in thresholds, and budget constraints. On the other hand, a turnover threshold restricts the total allowed amount of trades in the rebalancing phases. To deal with these asset allocation models, we embed a novel hybrid constraint-handling procedure into an improved dynamic level-based learning swarm optimizer. A repair operator maps candidate solutions onto the set characterized by the first type of constraints. Then, an adaptive l1-exact penalty function manages turnover violations. The focus of the paper is to highlight the importance of including higher-order moments in the performance measures for long-run investments, in particular when the market is turbulent. We carry out empirical tests on two worldwide sets of assets to illustrate the scalability and effectiveness of the proposed strategies, and to evaluate the performance of our investments compared to the strategy maximizing the Sharpe ratio

A heuristic framework for the bi-objective enhanced index tracking problem

The index tracking problem is the problem of determining a portfolio of assets whose performance replicates, as closely as possible, that of a financial market index chosen as benchmark. In the enhanced index tracking problem the portfolio is expected to outperform the benchmark with minimal additional risk. In this paper, we study the bi-objective enhanced index tracking problem where two competing objectives, i.e., the expected excess return of the portfolio over the benchmark and the tracking error, are taken into consideration. A bi-objective Mixed Integer Linear Programming formulation for the problem is proposed. Computational results on a set of benchmark instances are given, along with a detailed out-of-sample analysis of the performance of the optimal portfolios selected by the proposed model. Then, a heuristic procedure is designed to build an approximation of the set of Pareto optimal solutions. We test the proposed procedure on a reference set of Pareto optimal solutions. Computational results show that the procedure is significantly faster than the exact computation and provides an extremely accurate approximation

Twenty years of linear programming based portfolio optimization

a b s t r a c t Markowitz formulated the portfolio optimization problem through two criteria: the expected return and the risk, as a measure of the variability of the return. The classical Markowitz model uses the variance as the risk measure and is a quadratic programming problem. Many attempts have been made to linearize the portfolio optimization problem. Several different risk measures have been proposed which are computationally attractive as (for discrete random variables) they give rise to linear programming (LP) problems. About twenty years ago, the mean absolute deviation (MAD) model drew a lot of attention resulting in much research and speeding up development of other LP models. Further, the LP models based on the conditional value at risk (CVaR) have a great impact on new developments in portfolio optimization during the first decade of the 21st century. The LP solvability may become relevant for real-life decisions when portfolios have to meet side constraints and take into account transaction costs or when large size instances have to be solved. In this paper we review the variety of LP solvable portfolio optimization models presented in the literature, the real features that have been modeled and the solution approaches to the resulting models, in most of the cases mixed integer linear programming (MILP) models. We also discuss the impact of the inclusion of the real features

Contract Selection Problem in Singapore Electricity Market

Master'sMASTER OF ENGINEERIN

On the effectiveness of scenario generation techniques in single-period portfolio optimization

In single-period portfolio selection problems the expected value of both the risk measure and the portfolio return have to be estimated. Historical data realizations, used as equally probable scenarios, are frequently used to this aim. Several other parametric and non-parametric methods can be applied. When dealing with scenario generation techniques practitioners are mainly concerned on how reliable and effective such methods are when embedded into portfolio selection models. In this paper we survey different techniques to generate scenarios for the rates of return. We also compare the techniques by providing in-sample and out-of-sample analysis of the portfolios obtained by using these techniques to generate the rates of return. Evidence on the computational burden required by the different techniques is also provided. As reference model we use the Worst Conditional Expectation model with transaction costs. Extensive computational results based on different historical data sets from London Stock Exchange Market (FTSE) are presented and some interesting financial conclusions are drawn