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研究生： 高裕哲
Yu-Zhe Kao
論文名稱： Portfolio Selection Based on C-Vine Pair-Copula Constructions
Portfolio Selection Based on C-Vine Pair-Copula Constructionsand Markowitz Mean-Variance Model
指導教授： 傅承德
Cheng-Der Fu
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 統計研究所
Graduate Institute of Statistics
畢業學年度： 100
語文別： 英文
論文頁數： 49
中文關鍵詞： 投資組合 、關聯性結構
外文關鍵詞： portfoilo selection, copula
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    • 如何有效率的分配有限的資金在各種不同的投資工具上對投資人而言是一個重要的課題，尤其是處於動盪不安的經濟情況下。最近在金融實證的文獻中指出，股價報酬率間呈現複雜的尾端相關性，我們可以使用 copula來描述這些複雜的相關性結構。此類方法所產生的隨機變數不同於傳統的分配，可以將邊際分配與相關性結構作任意的組合，使得在聯合分配的配適上有較大的靈活度。
    而此論文使用Pair-copula constructions則提供一個彈性方法來建構高維度copula。在Markowitz 的Mean-Variance架構之下，我們比較報酬率在傳統多維度常態分配假設與pair-copula constructions建立的模型之下的投資組合表現。若報酬率間的相關性結構偏離傳統假設，則pair-copula constructions的確具有較佳的投資組合表現。

    How to allocate his/her wealth among di erent investment tools more e ciently for
    individual investor is an important issue especially in the volatile economic situation.
    The stock index returns exhibit complex patterns of tail dependence which can be
    captured by copula models. We apply pair-copula constructions for reducing the
    load of estimation. Under Markowitz''s mean-variance framework, we construct two
    portfolios based on two di erent return models: the multivariate normal distribution
    and the C-vine pair-copula decomposed model. By examining four Taiwan stock
    indices from 2002 to 2011, we nd that C-vine provides a better performance.

    1 Introduction 1 2 Preliminaries 3 2.1 Bivariate copulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Kendall''s tau . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Mean-variance model . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3 Pair-copula constructions 7 3.1 A pair-copula decomposition of a general multivariate distribution . . 7 3.2 C-vine pair-copula constructions . . . . . . . . . . . . . . . . . . . . . 9 3.3 Four-dimensional C-vines . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.4 h-function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.5 Statistic inference of C-vine copulas . . . . . . . . . . . . . . . . . . . 13 4 Simulation 15 4.1 Model selection for bivariate copulas . . . . . . . . . . . . . . . . . . 15 4.2 Simulation from a C-vine pair-copula decomposed model . . . . . . . 17 4.3 Selection among C-vine copula models . . . . . . . . . . . . . . . . . 19 5 Real data analysis 21 5.1 Data set and model selection . . . . . . . . . . . . . . . . . . . . . . . 21 5.2 Long term portfolio . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 6 Conclusion 33 6.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 6.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 A Pair-copulas 35 A.1 The bivariate Gaussian copula . . . . . . . . . . . . . . . . . . . . . . 35 A.2 The bivariate t copula . . . . . . . . . . . . . . . . . . . . . . . . . . 35 A.3 The bivariate Clayton copula . . . . . . . . . . . . . . . . . . . . . . 36 A.4 The bivariate Gumbel copula . . . . . . . . . . . . . . . . . . . . . . 37

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