在最基本的投資組合模型–Mean-Variance Model中，預期報酬的估計對模型的結果會有不小的影響；因此，Black-Litterman Model已不再僅是根據標的的歷史報酬作為投資組合建構的依據，除了市場均衡（Market Equilibrium）下的報酬或CAPM外，也加上了投資者觀點（Investor’s Views），協助投資者能夠將自身的看法輸入至模型中。以學術或實作而言，投資者觀點將會以其他報酬估計模型求得，如MCMC、Recovery Theory，甚至是當紅的人工智慧、機器學習。其中機器學習的方法目前皆仍在研究階段。因此本文將以機器學習預測指數報酬為主軸，除了以機器學習基礎模型（Lasso、Random Forest等）進行預測外，也試著利用「Stacking」及將隨機波動模型（Stochastic Volatility Model）所估計之波動作為因子，希望能夠得到較好的結果。除了直接比較預測的準確度之外，也將預測結果帶入Black-Litterman Model中，希望能夠得到較有效、績效較好的投資組合。在本文中，將比較是否將隨機波動模型結果作為因子及分別利用不同機器學習方法預測結果帶入Black-Litterman Model的投資組合，利用美國ETF做實證研究，觀察投資組合績效及在不同市場情形下的結果，以作為機器人理財資產管理模型上的參考及討論對象。

Mean-Variance Model, the basic model for portfolio construction, is very sensitive to the return we estimated. To overcome this disadvantage, Black-Litterman Model do not construct portfolio only according to the historical returns. It not only takes underlying returns under market equilibrium, or returns by CAPM under consideration, but also takes “Investor’s Views” under consideration. This helps investors to put their views into the model. In academic, we’ll use other return estimation models to make the views, such as MCMC, machine learning. Notice that the method of constructing views with MCMC were used by a robo-advisor in China, while the method with machine learning are still under research.
In this thesis, I’d like to make use of machine learning methods to get views for Black-Litterman Model. Not only basic machine learning methods, such as Lasso Regression, Random Forest, will be used, but also the method of “stacking” will be used. Moreover, I’ll add the volatility estimated by Stochastic Volatility Model to the factors used by machine learning, hoping it can both give a more accurate estimation, and help us to construct a more efficient portfolio. In this thesis, I’ll make comparisons between Black-Litterman Model with views constructed by different methods and based on different factors, getting empirical results using US ETF as underlying. Items to compare are accuracy of estimation, performance of portfolio during hole periods and in some specific periods.

摘要 i
Abstract ii
誌謝 iii
目錄 iv
圖目錄 vi
表目錄 vii
Chapter 1 Introduction 1
Chapter 2 Literature Review 3
2.1 Portfolio 3
2.1.1 Markowitz’s Mean-Variance Model 3
2.1.2 Black-Littrerman Model 3
2.2 Return Estimation 4
2.2.1 Capital Asset Pricing Model（CAPM） 4
2.2.2 Machine Learning – Base Model 5
2.2.3 Machine Learning – Stacking 5
Chapter 3 Methodology 6
3.1 標的選取 6
3.2 投資組合模型 7
3.2.1 Markowitz’s Mean-Variance Model 7
3.2.2 Black-Litterman Model 8
3.3 Black-Litterman Model 投資者觀點（Investor’s Views）—報酬率估計 12
3.3.1 Machine Learning—基底模型 12
3.3.2 Machine Learning-Stacking 15
3.3.3 Machine Learning – Parameter Tuning 16
3.3.4 機器學習演算法 – Rolling Prediction 17
3.4 波動率估計 – Stochastic Volatility Model（SVM） 18
3.5 報酬率預測結果與衡量 19
3.6 投資組合績效表現 20
3.6.1年化報酬率（Annualized Return） 20
3.6.2 年化波動度（Annualized Volatility） 21
3.6.3 最大虧損（Maximum Drawdown） 21
Chapter 4 Data and Empirical Study 22
4.1 數據 22
4.1.1 指數 22
4.1.2 標的 22
4.1.3 總經指標 23
4.2 報酬率預測結果 23
4.2.1 不同機器學習模型之比較 23
4.2.2 是否將SVM估計之波動作為因子之比較 25
4.3 投資組合實證研究結果 27
Chapter 5 Conclusion 31
References 33
Appendix A 機器人理財（Robo Advisor） 35
Appendix B The Black-Litterman Formula Derivation 37
Appendix C Stochastic Volatility Model 42

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