臺灣博碩士論文加值系統

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。

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.

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

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