SPY之不對稱GARCH市場風險值之研究

Abstract

市場風險值VaR 已是受到廣泛應用的風險控制工具。在近年VaR模型效果估計比較的多篇研究證實了GARCH 模型在估計市場風險值的有效性及精確性後，本研究檢驗包含旋轉效果的GJR GARCH及平移效果的NA GARCH兩種不對稱GARCH模型與對稱的GARCHM模型比較，在不同的報酬結構之下，找出對於SPY指數型基金的投資組合具有較佳VaR值預測表現的模型。研究作法主要為蒐集SPY較近期之1800筆日交易資料並將其分為兩個群組進行模型配置及市場風險值估算之用，依據不同信賴區間下估算出的市場風險值與實際報酬表現做比較，並另外運用其他穿透測試等項目檢驗模型的精確性。 本研究主要發現包含以下部分：首先除了由穿透數字的評估與巴塞爾協定的規定比較發現穿透次數皆能落入安全範圍而再次證實GARCH模型對於VaR皆具有良好且有效的預測效果之外，不對稱GARCH模型的預測表現更優於對稱模型。其中旋轉效果的GJR-GARCH模型在各種報酬結構及不同信賴水準下的穿透率皆低於平移效果的NA-GARCH，顯示旋轉效果的GARCH模型在預測VaR的功能上有較為顯著的效果。而其中ARMA(1,1)-GJR GARCHM(1,1)的穿透數字更遠低於其他模型，在同時利用其他指標進行分析之後，本研究獲得較客觀及全面性的發現顯示其為對於SPY指數型基金有良好預測效果的VaR市場風險模型。

VaR is more applicable as a financial management tool to control risk. Since the GARCH model is proved to be the useful and more accurate model in estimating VaR, in this paper, we employ the asymmetric GARCH models including the innovation-rotated GJR GARCH and the innovation-shifted NA GARCH models with different mean equations in comparison with symmetric GARCHM model to find out a more appropriate GARCH method in estimating VaR of SPY portfolio as the representative of the also popular investment tool, ETF. We gathered the latest 1800 daily information of SPY portfolio performance and divided into two groups to fit the models and get the VaR estimates under each confidence level we chose. Our major findings contain several aspects that first we prove that GARCH model is useful and efficient since all VaR forecasts fall into the safe range in terms of the regulation by Basel Accord. Specifically, asymmetric GARCH model outperforms the symmetric one, and GJR-GARCH as the representative of rotated GARCH model has better performance than NA-GARCH as that of shifted GARCH model. Among GJR-GARCH model with different mean equations, ARMA(1,1)-GJR GARCHM(1,1) has the most outstanding result in risk control by the fewest violation number it has, and we also conduct analysis through indicators other than violation number used as a standard mainly employed by Basel Accord to have more objective and thorough confirmation that ARMA(1,1)-GJR GARCHM(1,1) is the best fitted model to SPY portfolio in estimating VaR.