حل مسيله‌ي انتخاب سبد سرمايه گذاري با استفاده از الگوريتم جست‌وجوي هارموني در شرايط مجاز بودن فروش استقراضي

Solving a Portfolio Selection Problem using a Harmony Search Algorithm in terms of Justifiability Short Selling

تصميم‌گيري درمورد نحوه‌ي تشكيل سبد سرمايه‌گذاري بهينه در شرايط بحراني بازار (يعني در زمان افت قيمت دارايي‌ها) با فرض مجاز بودن فروش استقراضي ازجمله مسايل مهم پيشروي سرمايه‌گذاران در بازار سرمايه است. از اينرو در اين تحقيق مدلي در حوزه‌ي مسايل انتخاب سبد سرمايه‌گذاري پيشنهاد ‌شده كه فرض مجاز بودن فروش استقراضي را در كنار برخي محدوديت‌هاي كاربردي بازار سرمايه در نظر مي‌گيرد. مدل پيشنهادي داراي ماهيت برنامه‌ريزي عدد صحيح غيرخطي بوده و با توجه به پيچيدگي محاسباتي آن، نيازمند بهره‌گيري از الگوريتم‌هاي فراابتكاري است. با توجه به پيوستگي فضاي جواب مدل پيشنهادي، الگوريتم جست‌وجوي هارموني به‌عنوان يك الگوريتم نوين و كارا در حل مسايل پيوسته به كار گرفته شده است. نتايج حاصله نشان‌گر عملكرد مناسب اين الگوريتم در حل مدل پيشنهادي است.

Optimal capital allocation in assets is an important issue facing investors. The first model of portfolio selection was proposed by Markowitz in 1952. This portfolio optimization model is also known as the mean-variance model and endeavors to minimize portfolio variance by considering only returns and budget constraints. Solving the Markowitzʹs quadratic model creates an investment efficient frontier as a solution set for investors, and selecting a portfolio from an efficient frontier depends on their risk-taking or risk aversion. In recent years, introduction of other practical constraints (e.g. short selling, floor and ceiling, cardinality constraints) has caused the development of the primary Markowitz model. Decision making regarding optimal portfolio formation under critical market conditions (i.e. reduction in asset prices) is an important issue leading investors into terms of justifiability short selling. Hence in this paper, we consider a fair model (for both call and short positions in the capital market) in the portfolio selection problem area that allows short selling under some capital market practical constraints. We propose a new mathematical model for the problem and explain its practical constraints. This proposed model has a mixed integer non-linear programming (MINLP) nature and, with respect to its computational complexity, standard mathematical tools (e.g. LINGO and GAMS) only enable it to solve very small sizes; it needs to use meta-heuristic algorithms for relatively large problem sizes. The continuity of the model solution space leads it to use a harmony search algorithm as an efficient and new algorithm in solving continuous problems. We explain the elements of the proposed harmony search algorithm, such as solution encoding, the fitness function, and its flowchart and parameters. For evaluation of the algorithm, we consider a real problem and solve it by the proposed algorithm and an exact method. The comparison of results indicates the good performance of the harmony search algorithm in solving the proposed model.