臺灣博碩士論文加值系統

一般傳統上常討論到使用Markowitz 的均異最適化(mean-variance optimization)的方式進行資產配置。由於Markowitz模型有估計誤差極大化的傾向，可發現報酬率些微改變將造成重大影響，因此我們必須尋找較佳的方法估計報酬率以及變異數，以求得較合理之投資權重。
Black and Litterman 以及其他學者運用不同的資訊，提出相對應的報酬率或變異數的貝氏估計式，以改善Markowitz模型的缺點。本研究在Black and Litterman模型上做了應用，本研究不僅估計報酬率同時也一起估計變異數。在根據這些不同的估計方法，創造出最佳的資產配置，並且比較傳統Markowitz模型、Bootstrap法及各種貝氏估計法所得的投資組合Sharpe ratio。
實證結果在我們的資料上發現在Black and Litterman模型與Shrinkage下，會得到比較高的Sharpe ratio。由於此兩種方法不僅對報酬率的估計上做了修正，也對變異數方面做了估計，可以得到一個風險比較小的投資組合。表示此兩種方法在我們的資料下，風險及報酬的表現優於其他兩種方法。

This paper applies some popular asset allocation models, like Black-Litterman model on an index fund. First, an overview is given of the foundations of modern portfolio theory with the mean-variance model. Although the model inspired a rich field of science and was used by many investors, it does have some obvious flaws. Next, we discuss some improvements that could be made over the mean-variance model. Finally, we compare the performance of the bootstrap methodology, Black-Litterman model, Bayesian approach and shrinkage methodology with the Sharpe ratio. The conclusion in our data can be drawn that BL-model improves the mean-variance model and has a better performance than other methods.

1、Introduction 1
2、Literature Review 2
2.1 Introduction of Index fund 2
2.1.1 The advantages of Index Fund 3
2.2 Markowitz Mean-Variance Portfolio Selection Model 3
2.2.1 Portfolio Selection Problem Formulations 4
2.3 The Black Litterman Model 5
3、 Methodology 8
3.1 Bootstrap Methodology 8
3.2 Black-Litterman Methodology 9
3.2.1 Computing the CAPM Equilibrium Excess Returns 11
3.2.2 Computing Via Reverse Optimization 11
3.2.3 Specifying the Views 13
3.2.4 Predicting of Covariance Matrix by GARCH Model 14
3.2.5 The Black-Litterman Formula 15
3.3 Bayesian Approach 17
3.4 Shrinkage Methodology 18
4、Empirical Results 19
4.1 Data 19
4.2 Foreign Exchange Risk 20
4.3 Markowitz Method 20
4.4 Bootstrap Method 21
4.5 Black-Litterman Method 21
4.6 Bayesian Approach 22
4.7 Shrinkage Method 23
4.8 Comparison of Markowitz Method and Other Approaches 23
4.8.1 Comparison of Portfolio Weights 23
4.8.2 Comparisons of Return, Risk and Sharpe Ratio 24
5、 Conclusion and Suggestions 25
5.1 Conclusion 25
5.2 Suggestions 25
6、 Reference 26
Appendix A 41

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