應用灰色系統理論改善最小變異數投資組合績效之實證模型－以道瓊30指數成份股為例

An Application of the Grey Forecasting Model on the Minimum Variance Portfolio' Performance: An Example of the Dow Jones 30 Index

10.30087/APEMR.200603.0004

張宮熊；呂維恭

資產配置理論 ； 灰色預測模型 ； 道瓊工業指數 ； 最小變異數投資組合 ； Asset Allocation Theory ； Grey Forecasting Model GM 1,1 ； Dow Jones Industry Index ； Minimum Variance Portfolio

亞太經濟管理評論

9卷2期（2006 / 03 / 01）

61 - 73

繁體中文

馬可維茲(Markowitz)於1952年提出均數－變異數最適化(Mean-Variance Optimization)決定最適資產配置權重後，後續學者陸續以此理論為基礎，嘗試建立能更精準預測之風險計量模型。本研究擬將最小變異數投資組合理論(Minimum Variance Portfolio)與灰色預測模型(Grey Forecasting Model)加以結合，以道瓊工業指數(the Dow Jones Index)所定義之30個成份股1999/1到2004/6日資料為研究對象，透過GM(1,1)去除資料中的雜訊，盼能建構出MVP法下，報酬與風險變異程度相對穩定之最佳投資組合。在績效衡量方面，本研究採用Naive Index、Sharpe Index、Treynor Index與Jensen's α Index之四種績效指標進行驗證。 實證結果顯示，傳統MVP法之投資組合A與灰色預測模型改良MVP法之投資組合B、C、D，相較於市場組合（道瓊工業指數），皆可獲得較高報酬，且在利用灰色預測模型所產生之投資組合C、D，因能明確找出國家間之共變異程度，故可改善傳統MVP法之投資組合A，獲取較高報酬。而投資組合C在長期下仍維持穩定之績效表現，各績效指標皆排名第一，另外本研究意外發現，績效最佳之投資組合C皆在各期中挑選最少持股個數，而績效最差之投資組合B卻挑選最多持股個數，故本研究對投資組合持股增加可有效降低總風險的論點提出懷疑。

After Harry M. Markowitz introduced Mean-Variance Optimization with Efficient Frontier and Best Capital Portfolio in 1952, many scholars have went further research to improve the asset allocation theory. This research applies both Minimum Variance Portfolio Theory (MVP Theory) and Grey Forecasting Model to establish sets of Minimum Variance Portfolio, which uses component equity indices of the Dow Jones Industry Index from 1999/1 to 2004/6 as the samples. This research uses Naive Index、Sharpe Index、Treynor Index and Jensen's α Index to measure the returns of MVPs and compare them with the Dow Jones Index. After portfolio A produced by traditional MVP method and the portfolio B, C and D produced by Grey Forecasting Model are established, compare them with the market portfolio (Dow Jones Index), they all get higher returns. In deed, portfolio C has a stable performance in all periods and came first among the other portfolios. In addition, the numbers of optimal portfolio asset allocation have clearly decreased in portfolio C selects the least securities of the other portfolios with the best performance. It's double about the opinion of larger components of asset allocation could reduce portfolio risk.

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