多準則投資組合最佳化分析：結合K-MOPSO及TOPSIS

Multi-criteria Portfolio Optimization Analysis by Combining K-MOPSO with TOPSIS

10.29735/SJEB.200906.0004

許晉雄(Chin-Hsiung Hsu)；鄒慶士(Ching-Shih Tsou)

投資組合 ； 多目標最佳化 ； 背包型多目標微粒群最佳化 ； 多屬性決策分析 ； Portfolio ； Multi-Objective Optimization ； Knapsack Multi-objective Particle Swarm Optimization ； Multi-Attribute Decision Making Method

東吳經濟商學學報

65期（2009 / 06 / 01）

109 - 138

繁體中文

如何將有限的資金在眾多投資標的中作有效的配置，是財務管理領域中一個重要的議題，此議題稱為投資組合選擇，基本上它是屬於一個多目標最佳化的問題。在過去的文獻中，處理投資組合選擇問題大多是將具有衝突性的目標合併為單一目標的形式，並以單目標最佳化的技術來進行求解，但所得到的解未必是令人滿意的，主要是因為並不能保證得到的解為非凌越解，特別是當投資組合最佳化模型中包含一些實務上所需的限制條件時，例如：基數限制。故本研究將以啟發式多目標微粒群最佳化技術為基礎，運用背包型多目標微粒群最佳化演算法，針對投資組合問題進行求解，並在賣空與基數限制的條件下獲得效率之投資組合。最後，針對有效的投資組合，應用多屬性決策分析中的TOPSIS法，對投資組合進行分析排序，提供投資者更多樣化之投資組合選擇，由研究結果可發現投資者在選擇其投資組合時，應考慮更多元的投資績效指標。

The allocation of limited capital to a variety of assets available is one of the important problems in financial management. It is actually a constrained multi-objective optimization problem called portfolio selection. Most studies have been made to solve the problem with single-objective optimization techniques by aggregating conflicting and incommensurate objectives into a single one. The solutions obtained may be unsatisfactory because their nondominance is not guaranteed, especially when some practical constraints, such as cardinality constraints, are incorporated into the portfolio optimization models. This paper presents an evolutionary multi-objective optimization technique, which called Knapsack Multi-Objective Particle Swarm Optimization (K-MOPSO) to generate the efficient portfolios in terms of expected return and variance under short sales and/or cardinality constraints. Finally, a Multi-Attribute Decision Making (MADM) method named Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is employed to outrank the efficient portfolio that decision makers satisfy most.

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