相關資產與投資組合效率前緣的估計

Related Assets and Approximation of Portfolio Efficient Frontier

王瑋鈴(Wei-Ling Wang)

指導教授 ： 林張群

崑山科技大學/商業管理學院/企業管理研究所/碩士(2003年)

https://doi.org/10.6828/KSU.2003.00028

摘要

Markowitz投資組合最佳化模式未被廣泛地使用於建立投資組合，其中最主要的原因在於解決大規模的二次規劃問題時，隨著繁雜的共變數矩陣，會產生大量運算成本，所以本文使用不同的取樣方式以求得構成效率前緣的相關資產，及藉由此相關資產進行投資組合運算，以減少求解效率前緣的時間。相關資產為一構成所有效率投資組合的資產集合。本文研究對象以台灣的共同基金為資料進行實證研究。實證結果發現，相關資產的數目及共變數矩陣皆小於原來的資產，再以相關資產建構投資組合的執行時間因而減少，研究並發現相關資產的數目並不隨著資產的增加而增加，且近似效率前緣與真實效率前緣之間的誤差皆很小。一般而言，平均分段取樣與對數分段取樣能得到同樣地相關資產。所以，相關資產的確為一構建效率投資組合及減少執行時間之有效的方法。

關鍵字

效率前緣 ； 投資組合 ； 相關資產

並列摘要

Markowitz’s portfolio optimization model has not been used extensively in its original form to construct a large-scale portfolio. One of the most significant reasons behind this is the mass computational cost associated with solving a large-scale quadratic programming model. This thesis use different sampling methods to obtain the related assets of efficient frontiers to reduce the computation time in constructing portfolios. Related assets comprise assets involved in all efficient portfolios, which are the building. blocks of efficient frontier. Empirical studies were conducted with the data of the mutual funds in Taiwan. The results of empirical studies indicate that the number and covariance matrix of related assets are much smaller that those of the original assets. The computation load in constructing a portfolio thus is significantly reduced. Also, it was found that the number of related assets is generally irrelevant to the number sampling points. The difference between the approximated efficient frontier and the real ones are quite small. Generally speaking, average sampling and logarithmic sampling give the same related assets. Therefore, the related asset is an efficient approach of constructing efficient portfolio and reducing computation time.

並列關鍵字

Related Assets ； Efficient Frontier ； Portfolio

參考文獻

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