較常被使用來估計風險值的方法有歷史模擬法、變異數─共變異數法以及蒙地卡羅模擬法，本研究亦以這些方法來建構風險值模型，其中變異數─共變異數法計算中所需的變異數─共變異數矩陣之估計是利用指數加權移動平均；而蒙地卡羅模擬法又細分為考慮投資組合中各資產間相關性的模擬，在此使用Cholesky分解法的技巧擬合；另一方面，因為投資組合其損益報酬率之分配通常具有厚尾特性，故本研究採用一般化誤差分配(Generalized Error Distribution, GED)，來描述報酬率的分配，以它的厚尾特性來捕捉其尾部機率，最後，為了比較以上四種估計風險值的方法，因此利用實證的資料，對風險值的估計模式進行回溯測試並且比較各方法資金運用的效率性。實證結果顯示，無論是回溯測試的檢定或是資金運用效率性方面，皆以變異數─共變異數法中的指數加權移動平均法最佳，其次為蒙地卡羅法下的一般化誤差分配法。 The objective of the research is to study the risk measurement Value-at-Risk (VaR) that is most relevant to financial institutions worldwide. Modeling and estimating techniques for measuring risks is quite a challenge. Four VaR estimation methods are studied in this research and they are (1) Historical simulation, (2) Variance-covariance method incorporating the exponential weighted moving average (EWMA) method, (3) Monte Carlo simulation under normal distribution incorporating Cholesky decomposition and (4) Monte Carlo simulation under generalized error distribution (GED), correspondingly. Backtesing and Christoffersen (1998) tests are adapted to validate the accuracy of the four estimation approaches. At last, a case study of the mutual fund is provided to increase clarity of the VaR estimation methods and deliver actionable results. The empirical results obtained shows that exponential weighted moving average (EWMA) model in variance-covariance method out performs the GED model in Monte Carlo method and the historical simulation method.
