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.

獨立因子模型廣泛的應用在信用風險領域，此模型可用來估計經濟資本與投資組合的損失率分配。然而獨立因子模型假設因子獨立地服從同分配，因而可能會得到估計不精確的違約機率與資產相關係數。因此我們在本論文中提出序列相關因子模型來改進獨立因子模型的缺失，同時可以捕捉違約率的動態行為與授信戶間相關性。我們也分別從古典與貝氏的角度下估計序列相關因子模型。首先，我們在序列相關因子模型下利用貝氏的方法應用馬可夫鍊蒙地卡羅技巧估計違約機率與資產相關係數，使用標準普爾違約資料進行外樣本資料預測，能夠證明序列相關因子模型是比獨立因子模型合理。第二，蒙地卡羅期望最大法與蒙地卡羅最大概似法這兩種估計方法也使用在本篇論文。從模擬結果發現，若違約資料具有較大的序列相關與資產相關特性，蒙地卡羅最大概似法能夠配適的比蒙地卡羅期望最大法好。 / The independent factor model has been widely used in the credit risk field, and has been applied in estimating the economic capital allocations and loss rate distribution on a credit portfolio. However, this model assumes independent and identically distributed common factor which may produce inaccurate estimates of default probabilities and asset correlation. In this thesis, we address a serially dependent factor model (SDFM) to improve this phenomenon. This model can capture both dynamic behavior of default risk and dependence among individual obligors. We also address the estimation of the SDFM from both frequentist and Bayesian point of view. Firstly, we consider the Bayesian approach by applying Markov chain Monte Carlo (MCMC) techniques in estimating default probability and asset correlation under SDFM. The out-of-sample forecasting for S&P default data provide strong evidence to support that the SDFM is more reliable than the independent factor model. Secondly, we use two frequentist estimation methods to estimate the default probability and asset correlation under SDFM. One is Monte Carlo Expectation Maximization (MCEM) estimation method along with a Gibbs sampler and an acceptance method and the other is Monte Carlo maximum likelihood (MCML) estimation method with importance sampling techniques.