臺灣博碩士論文加值系統

傳統Fama and French三因子模型只能得知整月或季的因子對股票報酬的影響，為一定值，而無法得知月或季內不同天的風險因子對不同天的股票報酬的影響程度是否不同，以及如何不同。因此本文利用函數型分析方法來建構函數型Fama and French三因子模型，將傳統僅一個數值的季報酬率視為一個由每日日報酬所組成的季樣本函數，以便可以同時探討季內不同天的股票報酬率與風險因子之間的交互影響關係。同時，也以傳統Fama and French三因子模型做分析，來驗證日頻率的三因子模型是否對台灣股票市場也有解釋能力。

從函數型三因子模型中，可以發現一些在傳統三因子模型中無法得知的現象，在低淨值市價比時，規模效應會隨著時間(t)的經過而增加；淨值市價比效應也會在公司規模較小時，隨著時間(t)的經過而增加。此外，也發現雖然股票報酬對風險因子的反應有快有慢，但大致上仍是受到t時點前後附近的因子所影響的程度較大，且隨著時間的間隔距離越遠，因子的影響力會越來越小；值得一提的是，股票報酬對市場風險因子的反應遠較規模因子與淨值市價比因子來得更即時、更具效率性。

Traditionally, the Fama-French three-factor Model are empirically studied with low frequency, for examples monthly or quarterly, time series data. Using functional data analysis techniques, the factor model is studied with higher frequency, daily, time series. The daily stock returns and risk factor data are transformed into functional data, and then the functional regressions are conducted to investigate the adequacy of the functional factor model.

From the estimated results of the functional three-factor model, it has been found that the effects of risk factors on the portfolio returns are time varying. When the firm size is small, the effect of Book-to-Market is getting large as time passed after the announcement of financial statements. However, the effects of the rest factors are commonly getting small as the time passed after the announcement of financial statements. In addition, the reaction of the stock return to the market risk is usually faster and larger than the ones to the Book-to-Market ratio factor and scale factor. Since the effects are statistically significant confirmed by the Wald test, the functional three-factor model is suggestive.

摘要 i
Abstract ii
目次 iii
表目次 iv
圖目次 v
第一章 緒論 1
第一節 研究動機與目的 1
第二節 研究架構 2
第二章 文獻回顧 3
第三章 研究方法 6
第一節 變數衡量與定義 6
第二節 因子與投資組合建構 7
第三節 函數型主成份分析法
(Functional Principal Components Analysis, FPCA) 10
第四節 函數型迴歸模型 (functional regression model) 15
第四章 實證結果 22
第一節 資料來源與整理 22
第二節 函數型三因子模型分析 23
第三節 傳統三因子模型分析 33
第五章 結論與建議 36
參考書目 37

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