如何建構一個兼顧報酬與風險控管的投資組合，是投資共同基金的首要議題。基於 Markowitz(1952)提出的 M-V投資組合模型可能造成變異數及共變異數衡量的偏誤，因此，本文以樣本共變異數模型 (SAM)、內含因素模型(IFAC)等兩種靜態模型，並參酌 Alexander and Leigh(1997)的內含因子 GARCH模型(IFAC-G)與 Vrontos et al.(2003)的全因子多變量 GARCH模型(FFMG)等兩個動態模型，以台灣經濟新報資料庫 (TEJ)所篩選出的標的基金，據以建構投資組合，探討基金組合樣本外 (out-of sample)每期之共變異數矩陣及預期報酬，復以風險值 (VaR)及相對基準點風險值 (BRVaR)之修正夏普指標，驗證各模型風險控管之敏銳度，試圖搜尋出較具效率的共變異數矩陣預測模型。實證結果發現上述四種模型中， FFMG模型擁有相對於其它三種模型較高的平均報酬及修正的夏普指標；換言之， FFMG動態共變異數模型最能有效確保投資報酬並控制投資風險。此項發現有助於投資人及金融機構的基金研究者，據以建構合宜的共同基金投資組合。

It is a key issue to construct a suitable portfolio model for the determination of rate of return and the risk monitoring. Owing to the possible measurement error of variance and covariance for Markowitz’s M-V model, in the present study, it employs two static models and two dynamic models, which are the sample covariance model (SAM), implicit factor model (IFAC), implicit factor GARCH model (IFAC-G) and full-factor multivariate GARCH model (FFMG). The sample is drawn from the database of Taiwan Economic Journal (TEJ). It uses these static and dynamic covariance/correlation prediction models and compares the optimized portfolios’ out-of-sample performance. Furthermore, based on the criteria of Value at Risk (VaR) and benchmark-relative Value at Risk (BRVaR) of the improved Sharpe ratio, it might find more efficient covariance matrix portfolios model of the mutual fund in order to obtain higher and stable returns in the mutual fund markets. The empirically results find out that the average returns and improved Sharpe ratio in FFMG is higher than those in three other models. In other words, FFMG could relatively make returns and efficiently control the risk of the investment in the mutual fund market. This finding provides helpful insights for investors and analysts of financial institutes who wishing to adopt an approach for mutual funds portfolio selection.