基於 Copula 模型的資產配置及台灣股票市場的應用

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劉佑聖(You-Sheng Liu) 查詢紙本館藏

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統計研究所

論文名稱

基於 Copula 模型的資產配置及台灣股票市場的應用
(Portfolio Selection Based on Copula Models with Applications in Taiwan Stock Market)

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摘要(中)

最近在金融實證上的文獻指出，在股價報酬率的聯合分佈具有不對稱的相關性。Copula 提供一個方便的架構去描述不對稱的相關性結構。在這篇論文中，我們比較傳統上對報酬率作的常態分佈假設與使用Copula 建構出比較彈性的多元分佈。在Markowitz 的Mean-Variance 架構下，我們考慮一個風險趨避的投資者配置財富於不同的資產。我們用Copula 去建構高維度報酬率的分佈並使用模擬退火法去選擇最佳的權重。最後我們應用我們的方法於投資組合在台灣的股票市場。

摘要(英)

Recent studies in the empirical finance literature have reported asymmetric dependence in the joint distribution of stock returns. Copula provides a convenient framework to describe asymmetric dependence structure. In this thesis, we compare traditional multivariate normal distribution assumption for return and a flexible multivariate distribution using copula. Under Markowitz’s mean-variance framework (Markowitz, 1952), we consider a risk averse investor allocating wealth among different assets. We use copula to construct high-dimensional distribution of return, and propose a simulated annealing algorithm to select the optimal portfolio weights. We apply our approach for portfolio selection in Taiwan stock market.

關鍵字(中)

★ 非對稱相關
★ 模擬退火法
★ copula
★ 投資組合

關鍵字(英)

★ simulated annealing
★ portfolio selection
★ copula
★ asymmetric dependence

論文目次

Contents
1 Introduction 1
2 Preliminaries 3
2.1 Portfolio optimization . . . . . . . . . . . . . . . . . . . 3
2.1.1 Mean-Variance Model . . . . . . . . . . . 3
2.1.2 The solution of the Mean-Variance Model . . 4
2.1.3 The Expected Utility model . . . .. . . . . 4
2.2 Copulas . . . . . . . . . . . 5
3 Our approaches 9
3.1 Model calibration . . . . . . . . . . . . 9
3.2 Simulated annealing . .. . . . . . . . . . . 10
4 Simulation 11
4.1 Model calibration . . . .. . . . . . . . . . 11
4.2 Searching optimal weights using simulated annealing 13
5 Real data analysis 16
5.1 Two stocks . . . . . . . . . . 16
5.2 Three stocks . . . . . . . . . . . . 22
6 Conclusion 28
6.1 Summary . . . . . . . . . . . . . . . . . 28
6.2 Future work . . . . . . . . . . . . . . 28
References 30

參考文獻

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tion using hierarchical bayesian analysis and MCMC methods. Journal of Banking
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[5] Joe, H. Multivariate Models and Dependence Concepts. Chapman and Hall., Lon-
don, 1997.
[6] Longin, F., and Solnik, B. Extreme correlation of international equity markets.
Journal of Finance 56 (2001), 649–676.
[7] Markowitz, H. Portfolio selection. The Journal of Finance 7 (1952), 77–91.
[8] Nelsen, R. B. An Introduction to Copulas. Springer-Verlag., New York, 1999.
[9] Patton, A. J. On the out-of-sample importance of skewness and asymmetric de-
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[10] Sklar, A. Fonctions de repartition ´a n dimensions et leurs marges. Publications de
l Institut Statistique de lUniversite de Paris 8 (1959), 229–231.

指導教授

鄧惠文(Huei-Wen Teng)

審核日期

2011-6-30

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