動態條件風險值下最佳化投資組合

Abstract

在現代資產組合理論(modern portfolio theory)中，投資人為了分散投資組合的風險，進而追求投資組合的最小變異數配置，但由於此理論將金融資產的波動性視為恆定且採用變異數作為風險評斷的依據。因此，本篇論文將使用Chou、Wu與Liu (2009)提出的變幅條件相關係數模型(Range-based Dynamic Conditional Correlation, Range-based DCC)來捕捉投資組合的動態波動性，並採用具有一致性風險測度(Coherent Risk Measure)的條件風險值(Conditional Value-at-Risk, CVaR)來控制投資組合的風險。我們採用Rockafellar與Uryasev(2000)提出的最佳化資產組合的條件風險值法，實證分析的資料則使用標準普爾500(S&P 500)指數期貨與美國十年期公債(10-year T-bond)來架構投資組合。在本文的實證結果下，變幅條件相關係數模型在樣本內與樣本外的表現優於其他兩個對照模型，且能夠幫助投資者在控制適當風險下，得到理想報酬的投資組合。此結果支持我們以變幅條件相關係數模型在考量條件風險值下發展良好的動態投資策略。

In modern portfolio theory (MPT), investors use minimum portfolio variance strategy to allocate their assets and optimize their portfolios, but MPT assumes portfolio variance never changes and uses the historical parameter “volatility” as a proxy for risk. We use range-based dynamic conditional correlation (DCC) and choose the coherent risk measure, Conditional Value-at-Risk (CVaR), as a portfolio risk management tool. We collected Standard & Poor’s 500 Composite Index (S&P 500) futures, 10-year U.S. Treasury bond (10-year T-bond) futures as our sample data. In our empirical study, we found that range-based DCC performance is superior to another two models, which are used as model comparison, in in-sample and out-of-sample comparison, and it can help investors construct optimal portfolio with profitable expected return and manageable portfolio risk. The empirical results support our main idea that we can develop promising dynamic investment strategies by using a range-based DCC model in portfolio optimization of conditional value-at-risk framework.