本論文目的是股票投資組合與其資金配重之最佳化,使用通用啟發式演算法(Meta-Heuristic Algorithms, MHA),包括遺傳及其改良演算法(Genetic Algorithms, GA)、粒子群及其改良演算法(Particle Swarm Optimization, PSO)、量子遺傳演算法(Quantum-inspired Genetic Algorithms, QGA),分別對股票投資組合與資金配重問題,做可行解之最佳化搜尋研究。 本研究首先以背包問題進行MHA之測試,從中選出包括QGA共5種性能較佳之尋優演算法,並以之應用於股票投資組合與資金配重問題。研究樣本是從台灣上市股票隨機選出50檔,期間為民國96年1月至97年3月共15個月,以前12個月當訓練樣本,後3個月當測試樣本。使用中選之MHA對訓練樣本進行股票組合尋優,目標函數是風險分之報酬,且限制股票組合小於15檔。結果顯示,尋優所得股票組合之報酬率優於均異模型與股市大盤,此結果實證了MHA尋優股票投資組合可打敗大盤,因此MHA是有價值的投資決策參考資訊技術。 另外,本論文針對MHA之性能進行評估比較,結果顯示就背包問題與投資組合此兩類組合最佳化問題而言,其平均效能PSO速度最慢,QGA尋優能力最佳。
This study attempts to investigate the optimization solution of investments portfolio in terms of the appropriate investments weights. It is to find the feasible solution of this optimization by using Meta-Heuristic Algorithms (MHA) including Genetic Algorithms (GA), Particle Swarm Optimization (PSO), and Quantum-based Genetic Algorithms (QGA) as well. This research is firstly to test MHA by the Knapsack Problem from which we could select five better Algorithms containing QGA, with which tries to find the best investment weights for each asset in the portfolio. The research sample includes randomly selecting 50 listed firms in Taiwan Stock Exchange (TSE) every month during January 2007 to March 2008. It ends up with 15 months during sample period which the first twelve months are used for training sample and last three months are considered as for testing sample. The object function of the investment portfolio is to attain the minimum risk of 15 stocks under certain level of return by applying the appropriate MHA for searching the best investment weights in the portfolio. The results show that the return of chosen investment weights under MHA is superior to the return under mean-variance model, and it also beats the return of market portfolio. The result could provide constructive reference for the market investors, especially for the fund managers. To compare these methods of MHA, we also interestingly find that the PSO is less efficiency in speed and QGA is the best in selecting the investment weights.