考慮高階動差的避險組合風險值回顧測試與避險效益

Backtesting of Value-at-Risk and Hedging Effectiveness of the Hedged Portfolio in Consideration of the Higher Moments of Returns

葉財榮(Tsai-Jung Yeh)

指導教授 ： 莊忠柱

共同指導教授 ： 王譯賢(Yi-Hsien Wang)

淡江大學/商管學院/管理科學學系博士班/博士(2015年)

https://doi.org/10.6846/TKU.2015.01120

摘要

面對多元的市場投資機會，投資者追求獲利極大化利用衍生性金融商品來規避風險。當投資組合報酬具有高狹峰時，若不考慮分配的峰度而估計風險值，則估計風險值將會產生偏誤。在利用多變量GARCH-type模型捕捉多變量波動性與考慮分配的峰度下，本論文首先探討股價指數利用期貨避險的最小變異數避險組合的風險值，並藉著回顧測試法比較各模型的優劣。研究發現，恆生、S&P 500與東京的股價指數期貨，在考慮分配峰度的最小變異數避險組合之風險值績效比不考慮分配峰度較準確。此外，服從多變量 分配模型決定的最小變異數避險組合風險值績效優於多變量常態分配模型，而且利用多變量波動性不對稱模型決定的最小變異數避險組合風險值績效優於多變量波動性對稱模型。此外，當避險組合報酬高階動差下，發現大中華地區股價指數期貨空頭與多頭避險最小變異數避險組合之風險值績效，是以具有波動性不對稱與水準效果的多變量GARCH-type模型決定的避險組合風險值績效最好。
本論文進一步利用多變量波動性模型的特性，定義動態對稱模型與動態不對稱模型的避險效益，並發現台灣股價指數期貨動態避險模型的避險效益比固定避險模型的避險效益好。具有偏態與厚尾的投資組合報酬會影響不同部位投資組合的風險值。為建構期貨空頭(多頭)避險組合，本論文提出風險值受限下的期望效用最大化(Expected Utility Maximization Subject to the Value-at-Risk, EUM-VaR)模型與考慮高階動差風險值受限下的期望效用最大化(Expected Utility Maximization Subject to the Value-at-Risk in Consideration of the Higher Moments, EUM-MVaR)模型，並分別利用多變量常態、 與偏 分配的GARCH-type模型捕捉多變量波動性，並進一步探討大中華地區股價指數期貨空頭(多頭)避險組合的避險效益。研究發現藉著EUM-MVaR模型決定大中華地區空頭(多頭)避險組合的避險效益優於藉著EUM-VaR模型決定空頭(多頭)避險組合的避險效益。此外，多變量偏 分配的VEC-ADVECH-L模型能捕捉避險組合內資產的波動性水準效果、波動性不對稱與跨市場波動性不對稱外，亦能捕捉偏態與厚尾現象。因此，多變量偏 分配的VEC-ADVECH-L模型決定空頭(多頭)避險組合在被研究模型中有較佳避險效益。本論文結果可提供投資人風險管理的參考。

關鍵字

避險效益 ； 回顧測試 ； 風險值 ； 空頭(多頭)避險組合 ； 多變量VEC-ADVECH-L-skt 模型 ； 水準效果

並列摘要

Faced with diverse market investment opportunities, investors pursuing profit maximization would use derivative financial products to reduce risks. However, when returns on assets display leptokurtosis, estimating Value-at-Risk (VaR) without considering distribution kurtosis can cause estimation bias. This study first uses a multivariate GARCH-type model to capture multivariate volatility considering the kurtosis of distribution. It then utilizes various models to examine the VaR of minimum-variance portfolios (incorporating both stock index and futures), performing backtests to compare individual model performance. The results, based on the Hang Seng Index, S&P 500, and the TOPIX stock index futures, demonstrate the improved accuracy of models using distribution kurtosis to estimate VaR. Furthermore, distributed models outperformed both those with a normal distribution and symmetric volatility models in terms of the VaR of minimum-variance portfolios. In addition, this study found that a multivariate GARCH-type model with asymmetric volatility and level effects provided the best hedging performance for the VaR of minimum-variance long and short hedge portfolios of stock index futures from the Greater China Region with high moments of returns.
This study went a step further and used the features of the multivariate volatility model to evaluate the hedging effectiveness of the dynamic symmetric and asymmetric models. The results show that the hedging effectiveness of the dynamic hedge model is superior to that of the fixed hedge model for Taiwan stock index futures.
A portfolio with skewed and heavy-tailed returns will influence the VaR of different portfolio positions. This study proposes expected utility maximization (EUM) subject to VaR (EUM-VaR) as well as EUM-VaR modeling higher moments of asset returns (EUM-MVaR) to construct short and long hedged portfolios. A multivariate GARCH-type model with normal, and skewed distributions was used in this study to capture multivariate volatility, and the hedging effectiveness was investigated for the short (long) hedged portfolios of stock index futures from the Greater China Region based on the EUM-MVaR model. The results show that the hedging effectiveness of the short (long) hedged portfolios from the Greater China Region is greater with the EUM-MVaR model than with the EUM-VaR model. Additionally, the VEC-ADVECH-L model allows for level effect, asymmetry and cross-market asymmetry in the volatility of asset returns in the hedged portfolio, and the multivariate skewed distribution can capture the skewness and kurtosis of asset returns. Among the researched GARCH-type models, the multivariate VEC-ADVECH-L model with a skewed distribution to capture multivariate volatility provides the best hedging effectiveness for short (long) hedged portfolios. These results provide investors with reference data for risk management.

並列關鍵字

Hedging Effectiveness ； Backtest ； Value-at-Risk ； Short (Long) Hedged Portfolio ； Multivariate VEC-ADVECH-L-skt Model ； Level Effect

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