異質變異資產之成份風險值評價投資組合風險值：極值方法之應用

Evaluation of Portfolio VaR Using the Component VaR for Heteroskedastic Volatility Assets: An Application of Extreme Value Method

林楚雄(Chu-Hsiung Lin)；王韻怡(Yun-Yi Wang)

成份風險值 ； 投資組合風險值 ； 極值理論 ； GARCH模型 ； Component VaR ； Portfolio VaR ； Extreme Value Theory ； GARCH Model

管理與系統

15卷1期（2008 / 01 / 01）

33 - 53

繁體中文

本研究提出藉由加總個別資產成份風險值(Component VaR)以得到投資組合風險值的一個方法，此方法不但可減少共變異數估計的個數，而且由於成份風險值的計算，提供了各資產部位對於整體投資組合風險值的貢獻程度，因而可作爲風險調整的依據。首先，本文利用成份風險值(Component VaR)的分析方法，解析得到可將一個投資組合風險值分解成爲各項資產成份風險值的總和。因此，估計一個投資組合風險值的問題將可轉化爲估計投資組合中個別資產成份風險值的問題，進而可避免估計投資組合風險值時需要面臨估計變異數與共變異數的複雜問題，尤其當投資組合的數目眾多時。其次，爲了解決資產報酬分配具有厚尾以及異質變異數的問題，本文使用考慮異質變異數的極值方法以估計成份風險值。本研究以4種股價指數所建構的投資組合來驗證本文方法的準確性。經失敗率、平均失敗誤差以及Kupiec(1995)之非條件與條件涵蓋比率檢定結果，顯示在高信賴水準下，新估計法具有高度的準確性。

This study proposes a new approach to efficiently and precisely estimating portfolio VaR. This approach not only simplifies the procedure of estimation, but also solves the bias problems resulted from fat-tails and heteroskedasticity of return distributions. We first employ component VaR (CVaR) analysis to decompose the portfolio VaR as the sum of each CVaR. Consequently, this decomposition can lower down the complexity existing in estimating the variance and covariance of component asset returns. This simplification takes on a special significance when the portfolio is highly complex. In addition, to precisely estimate the portfolio VaR, we fit the component return distributions by the GARCH model, and then turn to estimate their left-tail indices through the application of extreme value theory (EVT). The tail index derived can further lead to the computation of individual VaR and component VaR of each component asset. The aggregate portfolio VaR can thus be determined by adding up the entire CVaRs. To verify the validity of the proposed approach, we present analysis of failure ratio, the bias of failure loss and Kupiec test (1995). All the results show that the proposed approach significantly improves the estimation efficiency and accuracy, which also shed light on the development of risk management theory as well as portfolio strategies.

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