An Empirical Analysis of Fama and French Three Factor Model－An Application of GARCH Model and Quantile Regression

[[abstract]]本研究利用Bollerslev（1986）所提出的一般化自我迴歸條件異質（generalized autoregressive conditional heteroskedasticity, GARCH）模型與 Koenker and Bassett(1978)所提出的分量迴歸法(quantile regression)，檢視Fama－French三因子模式橫斷面的解釋能力。實證結果發現殘差項考慮一階自我相關與GARCH模型修正後之三因子模式，顯示規模效應與淨值市價比效應均存在於台灣股票市場。然而，市場因素亦有相當程度的解釋能力，並不能抹殺其重要性。此外，大多數的模式均能完全地解釋台灣股票市場的報酬，表示三因子模式在一定的程度上能夠完全地解釋國內的股票報酬。至於分量迴歸估計結果部分，除了中位數分量之外，其餘的分量皆顯示在Fama－French三因子模式中尚有其他因素被忽略未加以考慮到。在大規模/中淨值市價比之組合中，規模因素僅在高分量時才具有解釋股票報酬的能力，儘管其係數為負。在大規模/低淨值市價比之組合中，最小平方法估計結果顯示規模因素不顯著，然而在分量0.7下規模因素呈現顯著，對此結果我們可以由Jarque-Bera與Breusch-Pagan檢定結果顯示模式之殘差項不服從常態且規模因素具有異質性等情況下，藉由分量迴歸法能夠區別出最小平方法之缺漏。最後，就模式的解釋能力部分，所有模式的Pseudo R2由低分量至高分量皆呈現遞增的現象，表示在愈高的分量下，Fama－French三因子愈能夠解釋股票平均報酬。[[abstract]]This research we apply GARCH model proposed by Bollerslev（1986） and quantile regression proposed by Koenker and Bassett(1978), to survey the cross section ability of Fama－French three factor model.Our finding is as follows. When error term is taken into account together with first order autocorrelation and GARCH model, Fama－French three factor model exists size effect and book-to-market effect to Taiwan stock market. However, market factor also has quite explaining importance that we couldn’t ignore. Furthermore, most models can explain the return of Taiwan stock market , and this kind of explaining ability means that Fama－French three factor model can explain domestic security return completely in extent well. The empirical result from quantile regression is found that, excepted for median quantile, at other quantile points show that there are still some factors omitted to consider in Fama－French three factor model. In big-size/median-book to market portfolio, size factor only can explain returns at higher point even although coefficient is negative. In big-size/low-book to market portfolio, the estimated result of OLS exhibit size factor is insignificant, but is significant at 70 percent quantile. Under the condition of that the error term can’t follow normality and size factor is heteroskedasticity, the result is found that quantile regression could retrieve the shortage of OLS. Finally, with the respect to the model explaining ability, Pseudo R2 of all models, has the phenomenon of increasing from lower quantile to higher quantile, which means that at higher quantile, Fama－French three factors can explain stock average returns more