5.1 結論
在金融市場上，期貨商品一直是投資人重要的避險工具，因此如何選擇避險比率 以獲得較高的避險效率，就成為投資人重要的課題。本研究以六個國際股價指數期貨為 例，利用不同的避險模型，估計最適避險比率，並分析各模型在避險效率上的表現。由 於股價指數的現貨與期貨報酬率變異數具有異質性，故本文在靜態模型外，加入動態避 險模型，以 Bivariate GARCH 模型分析動態避險比率，再與靜態避險模型比較。
根據實證研究，本論文將結果歸納如下：
一、各國的股價指數現貨與股價指數期貨價格時間序列具有單根，非穩定序列，經一階 差分後，現貨與期貨報酬率時間序列成為穩定序列。
二、各國的股價指數現貨與股價指數期貨報酬率數列並非常態分配，且具有異質變異數 及自我相關的存在。
三、動態 Bivariate GARCH 模型所得到各參數估計值，皆呈顯著現象，說明期貨的條件 變異不僅受到過去期貨條件變異數及殘差項的影響，同時也受過去現貨條件變異及 殘差項的影響，同理，現貨的條件變異亦受到過去現貨、期貨之條件變異數及殘差 項的影響。
四、避險比率的比較上，S&P500 指數期貨和 Kospi200 指數期貨以 Sharpe 避險比率為 最大，日經指數期貨、恆生指數期貨與新加坡海峽時報指數期貨則以平均數-變異 數避險比率最大，而台灣股價加權指數以平均擴展吉尼係數避險比率最大。動態
與靜態避險比率的比較上，利用 GARCH 模型估計的最小變異避險比率之平均值皆 稍大於 OLS 模型估計之最小變異避險比率。綜合動態模型與所有靜態模型，S&P500 指數期貨在各種避險模型所得到的避險比率皆高於其他指數期貨的避險比率，
Nikkei225 指數期貨次之。
五、避險效率的比較上，S&P500 指數期貨在各種靜態模型下皆具有最高的避險效率。
若單看亞洲市場，則是以 Nikkei225 指數期貨的避險效率最高，依序為恆生指數 期貨，新加坡海峽時報指數期貨，漢城 Kospi200 指數期貨，而台灣加權指數期貨 則為避險效率最差的市場。
六、在動態模型與靜態模型的比較上，除了 S&P500 指數與 Nikkei225 指數沒有明顯的 差異，雙變數 GARCH 模型的避險效率大致上高於傳統 OLS 模型，顯示在股價指數期 貨的直接避險策略上，雙變數 GARCH 模型略優於 OLS 模型。可能由於美國市場相較 於亞洲市場而言較完整健全，市場較具效率，因此採取動態避險策略並沒有比靜態 避險策略增加避險的效率。
七、以 OLS 方法估計各個指數期貨的避險比率大致上有隨避險期間的增加而增加的趨 勢，而 Chen, Lee and Shrestha(2004)迴歸模型的短期避險比率除了避險期間為 一日較低，其他依避險期間不同互有高低，長期避險比率則不因避險期間而有所不 同，但全部都高於短期避險比率且相當接近 1。因此當避險期間夠長，不須估計避 險比率的簡單避險(固定避險比率為 1)就是最小變異避險比率。
八、以 OLS 方法估計的結果，S&P500 指數期貨以一週為避險期間的避險效率最佳，恆 生指數和新加坡海峽時報指數以兩週為避險期間最佳，台灣股價加權指數和日經指 數以三週為避險期間最佳，漢城 Kospi200 指數以七週為避險期間得到最佳避險效
上就有良好的避險效率。
九、使用 Chen, Lee and Shrestha(2004)的方法時，避險效率皆高於傳統 OLS 方法，
顯示此法在估計短期避險比率有較好的效果。
十、實證結果發現並沒有一個絕對的方法可以使避險效率達到最高，因此投資人在進行 不同期貨商品的避險交易時，應選擇較佳的方法求算其避險比率，其避險效率才會 提高。雖然不同市場的最佳避險模型不同，但不論採取何種避險策略或選取避險期 間，皆能有效降低持有現貨的風險，實證顯示股價指數期貨契約為一有效良好的直 接避險工具。
5.2 建議
本研究並未考慮交易成本、稅賦以及保證金追繳的問題，後續研究可以加入實務 上會出現的成本問題，將可以對期貨避險的實務操作更有所助益。另外，對跨國投資者 而言，經常使用交叉避險的策略，交叉避險的問題也不在本研究的討論範圍內，若考慮 交叉避險，則在探討避險績效的同時，也必須將匯率風險一併考慮。
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