使用目標規劃建立指數基金

Abstract

指數基金的投資策略，已經被愈來愈多的投資者和投資機構所接受。在實務上，指數基金的建構方法大多都採取簡化的方法或是最佳化的方法，簡化的方法可以快速求得解答，但答案未必是最佳，而一般的最佳化方法又過於耗時；為了在效率和最佳化之間求得平衡，這篇論文中提出了目標規劃的模型以及一套有效率的演算法來計算實際的問題；本文還提出了一個新的測度方法，用來衡量指數追蹤的誤差，衡量的方法主要是依據指數的數值和所建構的投資組合其價值相差的絕對值。本文的實證分析採用了摩根台灣加權指數來測試所建構的模型和演算法，結果顯示所建構的投資組合能準確的追蹤指數，誤差不超過0.8%。

Creating index-tracking stock baskets has been accepted by more and more investors or institutes as one part of a total investment strategy. In practice, the selection methods widely adopted are some simplified methods (e.g. stratification) combined with some criteria, and some optimization models to minimize the traditional tracking error. Simplified method facilitates for obtaining a feasible answer, optimal in no sense, while the optimization model usually requires larger computational efforts. For bridging the gap between having efficiency and seeking optimality, we propose a goal programming model and develop an efficient solution algorithm. We also suggest a new measure of tracking error basing on the absolute difference between the value of the benchmark and the index computed from the portfolio obtained from our model. Empirical analyses employ the Morgan Stanley Capital International (MSCI) Taiwan Index to assess the tracking efficacy of the model. Computational results show that the constructed portfolio can track the index with error less than 0.8%.