關聯結構與最適投資組合－Copula模型的應用

Dependence Structure and Optimal Portfolio Choice-Copula Function Approach

李美杏(Mei-Hsing Lee) ； 丁聖祐(Sheng-Yu Ting)

《統計與資訊評論》 13卷 (2011/12) Pp. 69-100

https://doi.org/10.29862/JSC.201112.0005

摘要

很多實證顯示資產報酬間的關聯性具有不對稱的現象，而且資產報酬並非常態分配，而是呈現左偏及厚尾的型態。這些不對稱的現象隱含當股市在面臨空頭的情形下，由於資產報酬間的關聯性增加以及報酬分配呈左偏的特性，投資者可能會喪失分散投資所帶來的利益，降低了分散風險的效果，而使得損失增加。本文採用GJR-GARCH-偏斜t模型捕捉資產報酬的左偏及厚尾現象，進行各個資產報酬的邊際分配模型估計；再利用Copula模型以描述非線性相關與不對稱性的特質，建構資產間的關聯結構。最後，在Copula-GARCH的架構下，利用已開發國家（G7）與新興國家市場（BRIC）在近十年來股市報酬間關聯性結構，以CRRA效用函數當作投資者決策法則計算最適的權重。實證結果可以發現，使用加入時間變動因子的動態Copula進行權重估計的投資組合的效益會比忽略關聯結構的變化的二元常態模型所建構的投資組合有較高的績效。因此，在建構最適投資組合的問題上，不僅需要考慮資產間的關聯結構會隨著時間的變化而且及時的將投資組合權重分配進行改變，才能使投資組合具有最大的效益。

關鍵字

關聯結構 ； 左偏 ； 厚尾 ； 最適投資組合

並列摘要

A vast amount of empirical evidence demonstrates that correlations between international equity returns are higher during bear markets than during bull markets. Moreover, equity returns generally exhibit leptokurtic behaviors, i.e. equity returns are negatively skewed and fat tails. The phenomenon implies that due to increased dependence during bear markets and negatively skewed returns, investors might lose the benefits of diversification when such benefits are most valuable.In this study, an important issue is how dependence between international equity returns can be measured when equity returns are non-normal. We apply the skewed t GARCH model for negatively skewed and fat tails returns, and we use the time-varying conditional Copula to measure conditional dependence in a GARCH context. The use of Copulas makes it possible to separate the dependence model from the marginal distributions.This paper applies above methodology to the weekly returns of G7 (U.S., Germany, U. K., Japan, Canada, France, Italy) and BRIC (Brazil, Russia, India, China). We solve the optimal investment problem in the presence of asymmetric dependence and skewness for investors with constant relative risk aversion (CRRA) preferences. We consider both unconstrained and short sales constrained estimates of the optimal portfolio weight. For investors with unconstrained or short sales constrained, we find that the model capturing asymmetric dependence and skewness yields better portfolio performance than the bivariate normal model.

並列關鍵字

leptokurtic behaviors ； GARCH ； Copula ； asymmetric dependence