摘要
本篇論文研究Fama-French(1992, 1993, 1995)模型的三個解釋因子: 市場風險溢酬(MRP)、公司規模(SMB)、和公司淨值市價比(HML) 與基準項相比後，所帶出來的三個風險係數的風險變化範圍是否會落於所預設的風險區間之內。進而延伸到Carhart(1997)的四因子模型以及台灣特有的八因子模型。分析風險係數變化值的範圍及報酬率之間的抵換關係。從過去文獻得知三因子確實能大量解釋股票投資組合的報酬率，因此基於Fama-French的模型，以台灣股票市場為例，利用台灣經濟新報資料庫，依公司規模及公司淨值市價比作為投資組合的分類標準，創造六種類型的股票投資組合，以三因子模型測試六類股票投資組合報酬率變異的能量，發現三因子解釋能力高達93%至97%。因此本篇研究首先利用統計學上的等價性檢定(TOST)去分析六類投組的三因子的風險係數變化的範圍，探討風險和報酬之間的抵換關係。先以等價性檢定計算出六類投組每個風險係數的信賴區間(ER)，再與實證上所預期的風險區間(EM)比較後做成投資參考。六類投組的特性與台灣50(ETF)的特性雷同，而ETF的值與市場很接近，所以將ETF的值視為風險係數的基準。因此所預設風險區間(EM)的計算為利用報酬率的最小變化量推出風險係數的最小變動量，此為風險區間的下界；再以台灣股市交易成本(約0.6%)反推回去得到風險係數的變動量，綜合風險區間的下界，即可得到風險區間的上界。此上下界即構成所謂的風險等價區間(EM)。比較ER與EM分析每類型股票投資組合特性以做為投資參考。

ABSTRACT
In this research the three-factor Fama-French regression model (1992, 1993, 1995) is investigated, in which the factors include the market risk premium (MRP), small-minus-big risk premium (SMB) and high-minus-low risk premium (HML) associated with the regression parameters , and its extensions to four-factor and eight-factor models. It is known that the MRP, SMB and HML can affect a stock portfolio’s return. Based on the Fama-French model, six types of stock portfolios (namely, BH, BL, BM, SH, SL, and SM) are created according to company size (Small or Big) and the ratio of book-to-market equity (High, Medium or Low). Using the data from the Taiwan Economic Journal (TEJ), a traditional multiple regression equation is proposed, which can explain the returns of six types of portfolios (BH, BL, BM, SH, SL, and SM) with R-square ranging from 93% to 97% based on these three explanatory factors. This study also tests the equivalence of the regression parameters using two one-sided tests (TOST) for all six types of portfolios under each factor using the TEJ data, the economically meaningful equivalence margins of these regression parameters are selected by investors in advance in order to achieve their investment goals. Similar analysis is made for four-factor and eight-factor models. The findings of this work can help investors better understand the common variations of stock portfolio returns, and thus make better decisions.

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