| 姓名 |
卓穎聖(Yin-Shen Cho)
查詢紙本館藏 |
畢業系所 |
財務金融學系 |
| 論文名稱 |
正則化與Bootstrap對於投資組合最適化的效用
(The effectiveness of regularization and Bootstrap for portfolio optimization)
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| 相關論文 | |
| 檔案 |
 [Endnote RIS 格式]
[Bibtex 格式]
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| 摘要(中) |
在投組的最佳化問題中會出現結果不穩定的情況發生，對於結果的可信度造成影響。為了瞭解這樣的問題，本文採用了兩種方法， Performance-Based Regularization (PBR) 和拔靴法 (Bootstrap) 的方法，用於投資組合最佳化並且觀察兩種方法對於最佳化投資組合的效用。首先，投資組合最佳化問題考慮在得到要求報酬率的條件下最小化投組風險Mean-Variance ，最佳化方法本文引用了經由 Sample Average Approximation (SAA) 修改後，考慮結果穩定性以及可信度的正則化方法 PBR ，其主要想法為約束配飾結果的變異程度，並且利用柴比雪夫不等式使配適結果趨近於真實理論值，增加其可信度。 Bootstrap 則是利用重抽後得到的大量估計值計算該估計的信賴區間，將離群值刪除後使估計結果更穩定，並且 Bootstrap 在小樣本下會比依賴大數法則的 SAA 和 PBR 更具有優勢。對於最佳化投資組合的效用衡量，本文利用兩項指標在各種不同的資料生成過程 (DGP) 下進行衡量。第一，在不同要求報酬率下， PBR 是否都有改善 SAA 的效果，稱為改善比例；第二，縮小配適結果變異數的程度，稱為改善程度。使用兩種最佳化方法以及兩種衡量方法後，本文發現這不同DGP和衡量方法下， Bootstrap 的表現都明顯優於 PBR ，且在小樣本下 Bootstrap 仍然表現的很好。 |
| 摘要(英) |
In the portfolio optimization problem, unstable results will occur, which will affect the credibility of the results. In order to understand such problems, this article uses two methods, Performance-Based Regularization (PBR) and Bootstrap methods, for portfolio optimization and examines the effectiveness of the two methods. First, the portfolio optimization problem considers the Mean-Variance of the portfolio risk to be minimized under the certain target rate of return. The first optimization method is PBR, which is modified by Sample Average Approximation (SAA), considers the stability and reliability of the results. The main idea is to constrain the variance of the results from optimization, and use Chebyshev′s inequality to make sure that the results of optimization approach the theoretical value. The second optimization method, Bootstrap, uses a large number of estimators getting from redrawing sample and removing the outliers of results from optimization. The estimated result will be more stable. In a small sample, Bootstrap has more advantages than SAA and PBR that rely on the law of large numbers. I use two criterions to evaluate the performance of the two methods: one is the improvement ratio, which is the numbers of target rate of return have been improved under all different target rate of return, and the other is the degree of improvemen, which is the degree of reducing the variance of the optimization results. This article found that under these different DGPs and measurement methods, Bootstrap′s performance is significantly better than PBR, and Bootstrap still performs well in a small sample. |
| 關鍵字(中) |
★ 拔靴法
★ 最適化 |
關鍵字(英) |
★ Bootstrap
★ Optimization |
| 論文目次 |
第一章、 緒論………………………………………………………………………………...1
第二章、 文獻回顧…………………………………………………………………………...3
第三章、 研究方法…………………………………………………………………………...4
第1節、 Sample Average Approximation (SAA) 介紹………………………………..4
第2節、 Performance-Based Regularization (PBR) 介紹…………………………….4
第3節、 Bootstrap介紹………………………………………………………………..6
第4節、 效用比較方法………………………………………………………………...8
第四章、 研究結果………………………………………………………………………….10
第1節、 模擬資料下 PBR 的優化效果…………………………………………….10
4.1.1、 Normal 分配……………………………………………………………..10
4.1.2、 Heavy-tailed 分配………………………………………………………..11
4.1.3、 相關性…………………………………………………………………….12
4.1.4、 PBR 結論………………………………………………………………...13
第2節、 模擬資料下 Bootstrap 的優化效果……………………………………….14
4.2.1、 大樣本下的 Bootstrap…………………………………………………...14
4.2.2、 大樣本下的 Bootstrap…………………………………………………...15
4.2.3、 Bootstrap 結論…………………………………………………………...16
第五章、 結論……………………………………………………………………………….17
參考文獻……………………………………………………………………………………...18
表目錄
表1、 不同要求報酬率下的上下界 (Normal)……………………………………………...19
表2、 不同要求報酬率下的上下界 (Normal 低母體變異)………………………....…….20
表3、 不同要求報酬率下的上下界 (Heavy-tailed)………………………………...…........21
表4、 FAANG 敘述統計………....………………………………………………………..22
表5、 FAANG correlation matrix....………………………………………………………..22
圖目錄
圖1、 Normal 分配 PBR 上下界最佳化效果……………………………………….…...23
圖2、 不同DGP下 PBR 最佳化效果……………………………………………..……..24
圖3、 Heavy-tailed 分配下低U的PBR最佳化效果…………………………………….25
圖4、 Bootstrap 大樣本下最佳化效果……………………………………………………26
圖5、 Bootstrap 小樣本下最佳化效果……………………………………………………27 |
| 參考文獻 |
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Automatic Control, 51, 742-753
[3] DeMiguel V, Garlappi L, Nogales FJ, Uppal R (2009b) A generalized approach to portfolio optimization:
Improving performance by constraining portfolio norms. Management Science, 55(5), 798-812.
[4] Frost PA, Savarino JE (1988) For better performance: Constrain portfolio weights. The Journal of Portfolio
Management, 15(1), 29-34.
[5] Hastie T, Tibshirani R, Friedman J (2009) The elements of statistical learning: Data mining, inference, and
prediction, 2nd ed. (Springer, New York).
[6] Ivanov VK (1962) On linear problems which are not well-posed. Soviet Mathematics Doklady, 145(2), 981-983.
[7] Jagannathan R, Ma T (2003) Risk reduction in large portfolios: Why imposing the wrong constraints helps.
Journal of Finance, 58(4), 1651-1684.
[8] Phillips DL (1962) A technique for the numerical solution of certain integral equations of the first kind.
Journal of the ACM, 9(1), 84-97.
[9] Shapiro A, Dentcheva D, Ruszczynski A (2009) Lectures on stochastic programming: Modeling and
theory. (Society for Industrial and Applied Mathematics, Philadelphia).
[10] Tikhonov A (1963) Solution of incorrectly formulated problems and the regularization method. Soviet
Mathematics Doklady, 5, 1035-1038.
[11] Vapnik V (2000) The nature of statistical learning theory. (Springer, New York). |
| 指導教授 |
葉錦徽(JIN-HUEI YEH)
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審核日期 |
2021-8-10 |
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