長期性資料(longitudinal data)的最主要特徵是為對多個被觀測個體在不同的時間點上重複測量一個或多個反應變數。而在分析長期性資料的方法中，Laird & Ware(1982)建議以線性混合效果模型(linear mixed effects model，LME)來進行估計分析，此模型方法中，資料可以允許遺失值，並可將受測個體間與個體內的變異分開說明。 另在配適最小平方法(OLS)的迴歸模型中，係數估計經常會受到異常值的影響，而Rousseeuw & Leroy(1987)提出最小消去平方法(least trimmed squares，LTS)的穩健迴歸模型，即是解決最小平方法中對於異常值敏感的問題。 本研究主要針對台灣股票預期報酬之三種模型：資本資產定價模型、特徵模型、因子模型分別以OLS、LTS、LME三種估計方法做配適，並比較配適模型之適當與否，樣本資料為民國七十年七月至九十年六月共252個月516家上市公司股票報酬。實證結果顯示，不論是採用OLS、LTS、LME的估計方法，股票報酬解釋變數：系統風險、公司規模、帳面權益對市值比、SMB、HML皆為股票報酬的顯著解釋因子；而在模型比較方面，不論是配適資本資產定價模型、特徵模型或因子模型，LME都較OLS為較適當配適模型。這顯示了在分析長期性資料時，LME的確是一個較佳的統計分析模型。

資本資產定價模型 (CAPM) 由Sharp (1964)、Lintner (1965)及Black (1972)發展出後，近年來已被廣泛的應用於衡量證券之預期報酬率與風險間之關係。一般而言，衡量結果之估計有兩個階段，首先由時間序列分析估計出貝它(beta)係數，然後再檢定廠商或投資組合之平均報酬率與貝它係數之關係。 Fama與MacBeth (1973)利用最小平方法估計貝它係數，再將由橫斷面迴歸方法所得出之斜率係數加以平均後，以統計t-test檢定之。然而以最小平方法估計係數，其估計值很容易受離群值之影響，因此本研究考慮以穩健估計 (robust estimator)來避免此一問題。另外，本研究亦將長期資料分析 (longitudinal data analysis) 引入CAPM裡，期望能檢定貝它係數是否能確實有效地衡量出系統性風險。 論文中以台灣股票市場電子業之實證分析來比較上述不同方法對CAPM的結果，資料蒐集期間為1998年9月至2001年12月之月資料。研究結果顯示出，穩健估計相對於最小平方法就CAPM有較佳的解釋力。而長期資料分析模型更用來衡量債券之超額報酬部分，是否會依上、中、下游或公司之不同而不同。 / The Capital Asset Pricing Model (CAPM) of Sharp (1964), Lintner (1965) and Black (1972) has been widely used in measuring the relationship between the expected return on a security and its risk in the recent years. It consists of two stages to estimate the relationship between risk and expected return. The first one is that betas are estimated from time series regressions, and the second is that the relationship between mean returns and betas is tested across firms or portfolios. Fama and MacBeth (1973) first used ordinary least squares (OLS) to estimate beta and took time series averages of the slope coefficients from monthly cross-sectional regressions in such studies. However it is well known that OLS is sensitive to outliers. Therefore, robust estimators are employed to avoid the problems. Furthermore, the longitudinal data analysis is applied to examine whether betas over time and securities are the valid measure of risk in the CAPM. An empirical study is carried out to present the different approaches. We use the data about the Information and Electronic industry in Taiwan stock market during the period from September 1998 to December 2001. For the time series regression analysis, the robust methods lead to more explanatory power than the OLS results. The linear mixed-effect model is used to examine the effects of different streams and companies for the security excess returns in these data.

資本資產定價模型已被廣泛使用於分析股票風險與要求報酬率之間的關係。然而，個別股票風險Beta是否足以解釋其報酬，也受到愈來愈多的質疑。Fama和French在1993年提出額外兩個因子來解釋股票報酬。我們將應用資本資產定價模型和三因子模型來分析1963年7月至2002年12月之美國的三大股票交易所上市公司。藉由一次改變分析過程中的一部分，以觀察參數估計值是否穩定。結果發現Beta_HML總是顯著且最為穩定，而Beta_SMB並不顯著。Beta經常顯著，但變動情況較大。另外，我們將考慮個別股票本身的變異，亦即將隨機效果納入考量。 / The Capital Asset Pricing Model (CAPM) has been widely used to analyze the relationship between risk and required rate of return on a stock, while it is doubted that individual stock's risk Beta has enough explanatory power for it's returns. Fama and French (1993) proposed two more factors to help explaining stock returns. We use the CAPM and the three-factor model to analyze listed companys in American stock exchanges, during the period from July 1963 to December 2002. We change part of the analyzing process a time to see if the estimates of the parameters are stable. The risk-premium Beta_HML is always significant and it performs most stable, while another risk-premium Beta_SMB is never significant. Beta is usually significant but it varies. Furthermore, we take within-stock variation into account, so random effects are considered.