Black-Litterman 模型為一考慮個人主觀觀點的投資組合模型。此模型改善了 Mean-Variance 模型諸多應用上的問題，且可以根據個人的觀點進行資產配置，因此受到不少投資人青睞。然而，此模型當中仍有不符實務的假設，加上個人觀點不確定性難以合理的被量化，使得此模型應用於真實市場時並不如想像中理想。為解決上述問題，並同時提升投資組合績效，本研究以 3 種 copula 模型取代 Black-Litterman 模型中的常態假設，以此估計市場均衡報酬。於個人觀點建構部分，以集成式機器學習方法預測資產的報酬作為個人觀點，此外，我們以機器學習模型的誤差作為觀點之不確定性，提供估計觀點不確定性的量化依據。本文比較不同 copula 模型與機器學習模型的搭配之下，所建構之投資組合策略於風險調整後報酬的差異。結果顯示以 copula 模型與機器學習觀點所建構之投資組合表現皆優於傳統 Black-Litterman 模型與基準投資組合。另外，在台股樣本上，以機器學習模型誤差作為個人觀點不確定性能降低投資組合的最大回檔，進一步提升投資組合的表現。

The Black-Litterman model is an asset allocation method that merges investors' subjective views with market equilibrium returns using Bayesian theory. This model addresses some limitations of the Mean-Variance portfolio and attracts significant attention from investors due to its ability to incorporate subjective views in the portfolio optimization process. However, the Black-Litterman model assumes normality, which does not hold in the real world, and it is difficult to quantify the uncertainty of views, making its implementation less ideal. To address these issues and enhance performance, we utilize three vine-copula models to estimate the market equilibrium return. Additionally, two ensemble machine learning methods are employed to forecast asset returns as subjective views. We set the error of the machine learning models as the uncertainty of these views, providing a more reasonable quantification of such uncertainty measure. Different portfolio strategies are constructed using various copula models and machine learning models, and their performance is compared. The results indicate that incorporating copula models and machine learning methods enhances portfolio performance compared to benchmark portfolios and the original Black-Litterman portfolio. We also find that estimating the uncertainty of views using the error of the machine learning models improves the maximum drawdown of the portfolio in Taiwan’s stock market.

1. 前言.....................................................................1
2. 文獻回顧.................................................................4
2.1 Black-Litterman 模型....................................................4
2.2 Copula 模型於財金領域...................................................5
2.3 機器學習於財金領域......................................................6
3. 研究方法.................................................................7
3.1 資料....................................................................7
3.2 模型....................................................................9
3.2.1 Black-Litterman模型...................................................9
3.2.2 Copula模型...........................................................11
3.2.3 集成式機器學習模型...................................................15
3.3 最佳化資產配置策略.....................................................18
3.3.1 資產配置流程.........................................................18
3.3.2 最佳化目標...........................................................20
4. 實證結果................................................................21
4.1 投資組合策略...........................................................21
4.2 投資組合策略績效分析...................................................23
4.3 穩健性測試.............................................................27
5. 結論....................................................................30
附錄.......................................................................32
參考文獻...................................................................33

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