以regular vine copula模型做動態資產配置

Abstract

許多實證研究結果發現，股票的報酬率分佈並非常態，反而此分配具有不對稱、高峽峰和厚尾等性質；並且對於由股票所組成之投資組合之報酬率而言，其共跌之相關係數較共漲之相關係數為高。在Riccetti的研究之中，其對於債券和股票運用了copula-GARCH資產模型，進行對於宏觀資產配置模型之研究，並且得到了良好的實證結果。而Claudia Czado等人則是認為高維度的Copula函數(multivariate copula function)將可以更良好的捕捉依存結構(dependency structure)，甚至比絕大多數的資產模型更靈活；這是由於高維度的copula函數可以由從二元Copula函數構建，因此Copula函數可以根據不同之資產進行二二維的變數估計以及建立模型。因此，我們採用skewed t-GARCH模型估計資產的時間序列變數以及分析殘差項(residuals)，並且此殘差項估計出最配適之vine copula模型，並且利用蒙地卡羅法進行模擬，計算出最佳化的資產組合權重。其資料包含美國十個不同的指數，每個資產共有2408個日資料，近十年的歷史數據組合，以進行動態資產配置。在我們的實證結果，Copula函數能夠更精準的捕捉相依結構，並且較multivariate normal資產模型的進行動態資產配置之結果更好，具有較高的報酬與較低的資產波動。

Some empirical studies have showed that returns of some stocks are distributed in a non-Normal way, being asymmetric or even leptokurtic which indicates equity returns are negatively skewed and fat tails. In Riccetti , a copula–GARCH model is applied and can be useful in a macro asset allocation model including bonds and stocks. And Claudia Czado et al. even suggested that multivariate copulas provide more flexibility in dependency structure than some of asset model, vine copulas which are built from bivariate copulas can even be ordered and chosen individually according to their influences under class of mixed C-vine copulas. \nHence we apply skewed t GARCH model for negatively skewed and fat tails returns and time varying vine copula model to measure conditional dependence under class of mixed Regular vine copulas for the dynamic asset allocation of portfolios containing ten different indices in America with nearly ten years historical data, compared with multivariate normal asset model. The use of Copulas makes it possible to separate the dependence model from the marginal distributions.\nWe find that the copula model appears to be useful better than the multivariate normal one for the dynamic asset allocation in our empirical result, even if it is not dominantly better than other asset models, performance of vine-copula asset model would have lower empirical volatility.