應用成分資料統計於最佳投資組合信賴區間之研究

Applying Compositional Data Analysis to Create Confidence Intervals of Optimal Portfolios

10.6338/JDA.201012_5(6).0009

陳信宏(Hsin-Hung Chen)；林榮鎮(Jung-Chen Lin)

成分資料 ； 信賴區間 ； 平均值－變異數投資模型 ； 投資組合 ； Compositional data ； confidence interval ； MV model ； portfolio

Journal of Data Analysis

5卷6期（2010 / 12 / 01）

135 - 150

繁體中文

一般而言，國內外基金之實際資產配置比重均需隨市場環境之變化而作適度之調整。因此基金之管理除需要有中心配置之固定比重以外，更需建立一個變動之區間，以統計的觀點而言即是建立一個最佳投資組合比重的信賴區間。而最佳投資組合比重向量的性質與成分資料向量近似，其信賴區間的估計，可以利用求解成分資料的成分向量期望值與變異數來推估。因此本研究之主要目的即是利用成分資料的統計分析方法，建立最佳投資組合比重之信賴區間，以提供基金管理單位作決策之參考，其研究結果對於投資比重允許變動區間的客觀性與理論基礎將有莫大的助益。

Generally, national and international fund managements have to adjust investment proportions of financial assets by observing environment and market changes. Therefore, fund management units have to establish intervals of investment proportions of portfolios besides estimating optimal investment proportions. That is to find the confidence intervals of investment proportions in the point view of statistics. In fact, the nature of optimal investment proportions is similar to compositional data. The method of estimating mean and variance matrix of compositional data can be used to estimate those of investment proportions. Therefore, the purpose of this research is to establish the confidence intervals of optimal investment proportions by applying compositional data analysis of statistics. The results of this research are contributed to the theoretical foundation and objectivity for creating intervals of investment proportions in portfolios.

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