根據Bollerslev, Engle and Wooldridge (1988)的BI-GARCH (1, 1)模型，本研究探討公司特徵及超額報酬與共變異數矩陣之關係。而許多的研究主要著重在公司特徵與報酬的線性關係上，少有研究是將重心放在其二階動差之關係。然而，在資產評價的過程中，波動性是個不可忽略的重要因素。本研究分別以十八個產業收益率以及五個因子來探討公司特徵與報酬之共變異數的關聯，而五個因子分別為：市場報酬超過30天期商業本票報酬、公司大小、帳面價值對市值比以及兩個動能因子。因此，藉由實證分析我們得到以下結果：（1）資產報酬之條件變異數矩陣是具有高度自我相關性的。（2）實證結果顯著拒絕共變異數矩陣不隨時間變動。（3）資產的超額報酬會受到條件變異數之顯著影響。

Based on Bollerslev, Engle and Wooldridge’s (1988) BI-GARCH (1, 1) model, this study investigates the premium associated with firm characteristics related to the covariance matrix of returns. While literature primarily focuses on the first moment of returns, very little is known about their relation to the second moment of returns. However, as everyone knows, the volatilities also play a vital role in asset pricing theory. We employ 18 industry indexes and five well-known factors which are SMB, HML, PR1YR, IM, and market return in excess of the commercial paper rate to analyze how the premium associated with firm characteristics related to the covariance matrix of returns. As a consequence, we provide the following general results. First, the conditional covariance matrix of the assets returns is strongly autoregressive. Second, the data clearly reject the covariance is constant over time. Moreover, the expected risk premia for the assets are significant influenced by the second moment of the returns.

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