本文提出一個動態多因子波動度模型並分別測驗此模型在橫斷面 上和時間變異上對價格的影響。動態因子的產生係經由無跡卡爾曼濾波 法則 (unscented Kalman filter) 及一般化自我相關條件異質變異模型，進 而討論組合波動度與報酬之間的關係。相對於靜態模型，動態因子係以 Fama and French (2015) 的五因子模型來進行研究，此一特色包括了市場 組合、公司規模、價值效果、營運利潤與投資類型所計算出來的預期報 酬。我們提供了事後因子與落後事後因子實證研究，發現在橫斷面迴歸 上有助於增進解釋力並提高在樣本內與樣本外預測對組合報酬的預測 能力。我們的分析指出公司規模與帳面對市值比的分類組合會產生正面 且顯著的風險溢酬，但是以市值來預期的動態因子對組合報酬的影響卻 是顯著的負面效果。我們也再執行向前一期的樣本外預測並與其他模型 進行配對以比較預測的正確性，此比較採用Diebold-Mariano 測試的方 法。我們發現動態因子對營運利潤溢酬和投資獲利溢酬會產生顯著的正 面效果，此結果更加支持Bali and Cakici (2008) 的理論可測性。而且我 們的實證結果也進行了穩健性測試，相較於其他不同的模型設定和估計 結果都要穩妥。

This paper proposes a dynamic factors volatility model and examines its cross-sectional and time-varying impacts on assets prices. The dynamic factors were extracted by using both the unscented Kalman filtering method and the GARCH model. We then investigated the relationship between the volatility of the portfolio dynamic factors and the portfolio returns. In contrast to the static model, the dynamic factors incorporate features of Fama and French 5-factor models, which capture the characteristics of market portfolio, size, value effect, operating profitability, and investment patterns in average returns. We provide evidence that the ex post and lagged ex post factors can improve cross-sectional explanatory power and can increase the predictability of portfolio returns both in-sample and out-of-sample. Our analyses demonstrate that the size and book-to-market sorted portfolios earn a significant positive variance risk premium. However, the dynamic factors predicted by market value have significant negative effects on portfolio returns. We also perform the one-prior-period out-of-sample Diebold-Mariano test of forecasting accuracy paired with other models and find that the dynamic factors have significant effects on the risk premia of both operating profitability and investment policies. This finding supports the theoretical prediction of Bali and Cakici (2008). Finally, our evidence is robust to various specifications and estimation results.