Optimal Asset Allocation using Black-Litterman with Smooth Transition Model

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陳冠宇(Kuan-Yu Chen) 查詢紙本館藏

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論文名稱

(Optimal Asset Allocation using Black-Litterman with Smooth Transition Model)

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摘要(中)

在現今的金融市場上，Markowitz 提出的模型普遍地被運用在投資上。然而，由於參數過於敏感，所以在實務上很容易產生誤差導致報酬率不好。在我們的研究中使用了 Black-Litterman 模型來建立投資組合，藉由隱含報酬率結合投資者的觀點可以修正預期的報酬率。此外，我們也運用了 ST-GARCH 模型去捕捉資料中大波動的問題，其中的 ST 模型可以用來調整模型中的參數，使得 ST-GARCH 模型比起單純的 AR-GARCH模型更加靈活一點。最後，我們再運用台灣各行業的龍頭股來做一些實
證分析。

摘要(英)

In fi nancial markets, the model proposed by Markowitz is widely used in investment.However, the sensitive parameters lead to make errors in practice easily that results in poor returns. In this project, we use the Black-Litterman model to establish the portfolio, and the expected rate of return can be corrected by the implied return combined with the investor’s views. In addition, we also use the ST-GARCH model to capture large fl uctuations in the data. The ST model can be used to adjust parameters in the model, making the ST-GARCH model more fl exible than the simple AR-GARCH model. Finally, we use the leading stocks in various industries in Taiwan stock market in empirical analysis.

關鍵字(中)

★ 平穩過渡GARCH模型
★ 布萊克-李特曼模型
★ 馬克維茲

關鍵字(英)

★ Smooth Transition GARCH
★ Black-Litterman
★ Markowitz

論文目次

摘要 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
誌謝 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Time series model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1 ARMA model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 GARCH model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 Smooth transition GARCH model with second order logistic function . . . . . . 8
3 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.1 Markowitz mean-variance model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.2 Black-Litterman model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.2.1 The market model with implied equilibrium returns . . . . . . . . . . . . . . . . . . 15
3.2.2 Investors’ views model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2.3 The combined return model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
iv3.3 The innovation method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.3.1 AR-GARCH model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.3.2 STAR-GARCH model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4 Bayesian Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.1 The prior of each parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23
4.2 Bayes estimate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.3 Metropolis-Hastings algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
5 Simulation study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
5.1 Simulation Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
5.2 Simulation Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
6 Empirical Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
6.1 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
6.2 Sample construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

參考文獻

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[3] Black, F. and R. Litterman (1991). Global Portfolio Optimization. Financial Analysts Journal 48(5), 28-43.

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指導教授

孫立憲(Li-Hsien Sun)

審核日期

2018-7-23

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