利用VIX 指數和ARMA-GARCH 模型預測波動度之目標波動度策略績效分析

Abstract

本研究延伸Dachraoui (2018)提出之目標波動度策略，探討利用預測之標的波動度帶入其策略中是否能更有效地規避風險，並提升投資組合整體績效，因此，本研究納入及分析VIX 指數、GARCH 模型和ARMA-GARCH 模型所預測之波動度對投資組合之績效評估，並利用偏態、峰態、夏普比率、特雷諾比率、平均每週報酬、每週報酬波動度、最大跌幅來觀察策略之績效。本研究首先利用SPY ETF 1993 至2006 年作為GARCH 和ARMA-GARCH 模型之訓練樣本，並利用ADF檢定其報酬資料是否具穩定性，接著利用AIC、BIC 選取模型參數，接著將模型預測之波動度和歷史波動度、VIX 指數帶入目標波動度策略，並觀察SPY ETF 在2007 至2021 年利用歷史波動度、VIX 指數、GARCH 和ARMA-GARCH\n模型等不同波動度之波動度策略之績效，結果顯示利用VIX 指數之目標波動度策略在報酬率波動度、最大跌幅皆優於利用其他波動度之目標波動度策略，而利用GARCH 和ARMA-GARCH 模型之目標波動度策略能獲得最高的累積報酬，但同時也有較大的報酬率波動度和較大的最大跌幅。接著本研究將GARCH 和ARMA-GARCH 模型的訓練樣本設為2014 至2015 年，並將績效觀察期間設為2016 至2021 年，並納入另一標的QQQ ETF 作比較，結果發現不同的樣本期間 GARCH 和ARMA-GARCH 模型預測之波動度能為投資組合帶來較高的累積報酬，但同時其報酬率波動度和最大跌幅也較其他波動度之目標波動度策略來得大，而不論是SPY ETF 或是QQQ ETF，利用VIX 指數帶入目標波動度策略皆能大幅降低其最大跌幅，並獲得所有策略中最小的報酬率波動度。

According to Dachraoui (2018), Target-Volatility Strategy can reduce the portfolio risk, and also increase the Sharpe Ratio. Extendedly, this paper uses VIX Index, GARCH and ARMA-GARCH Model to project the volatilities and combine each of them with Target-Volatility Strategy to see whether the performance is better or not. This paper uses skewness, kurtosis, Sharpe Ratio, Treynor Ratio, average weekly return, volatility of weekly return, maximum drawdown to observe the performance of the investment strategy. We first use SPY ETF daily closing price from 1993 to 2006 as the training set of GARCH and ARMA-GARCH Model, and then apply ADF Test to check whether the data is stationary. Secondly, this paper uses AIC、BIC to choose the parameter of the model, and then estimate the volatility of return. This paper compares Target-Volatility Strategy using four different volatility projected by different models including realized volatility, VIX Index, GARCH Model, ARMA-GARCH Model, and the results indicated that the strategy using VIX Index can reduce most of the risk during the period. On the other side, the strategy using GARCH and ARMA-GARCH Model owned the bigger return, but they also need to bear the biggest drawdown during the period. Lastly, this paper uses another ETF, QQQ ETF, as the risky asset, and the results were similar to the results of SPY ETF.