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標題: | 高維度資料之 Markowitz 平均數變異數模型最適化-平均加權投資組合為最佳策略? High Dimensional Markowitz Mean-Variance Optimization: Is Equal Weighted the Best Strategy? |
作者: | Hsuan-Ling Chang 張瑄凌 |
指導教授: | 莊文議(Wen-I Chuang) |
關鍵字: | Orthogonal greedy algorithm (OGA),高維度矩陣,馬可維茲平均數-變異數最佳化,投資組合選擇, Orthogonal greedy algorithm (OGA),high dimension matrix,Markowitz mean-variance optimization,portfolio selection, |
出版年 : | 2020 |
學位: | 博士 |
摘要: | 在財務金融和風險管理中,估計大量資料的變異數共變異數矩陣是一項重要的議題。Ing 與 Lai (2011) 發展了一套更精確且縮短時間成本的大量資料矩陣估計方法, 稱為Orthogonal Greedy Algorithm (OGA)。這篇論文採用OGA方法於馬可維茲最小變數投資組合理論上,透過提升高維度矩陣的估計精準度達到最小變數投資組合理論最佳化,同時找到其相對應之預期報酬。p 和 n 分別定義為股票數量和歷史資料筆數,我們首先透過模擬財務報酬之理論分配生成模擬數據,用以比較OGA方法和Chen, Huang 與 Pan (2015) 的Thresholding方法進行比較。這兩種矩陣估計方法的模擬結果顯示,OGA方法有效降低估計誤差和擁有較高的估計穩定性,尤其在資料為 p 大於 n 的情況下,效能更為卓越。實證部分,我們採用1980到2016年間的美國普通股資料,透過隨機選取100 (200, 300) 張股票創建投資組合並評估投資組合的績效。結果顯示,運用OGA方法達到投資組合最適化的結果更勝於平均權重法 (1/N strategy) 的結果,享有高平均夏普比率 (Sharpe ratio) 和高累積報酬率。 Estimating and assessing the variance-covariance matrix (risk) of a large portfolio is an important topic both in financial econometrics and risk management. Ing and Lai (2011) proposed the novel technique, Orthogonal Greedy Algorithm (OGA), with higher accuracy and less computational cost to deal with the estimation error in high dimensional (large) matrix. In this paper, we adopt OGA on Markowitz minimum variance optimization by increasing the accuracy of the high dimensional matrix estimation to obtain the pure theoretical optimal and corresponding expected return. Here, p and n denote the number of stocks and that of historical data, respectively. First, we generate the simulated data which mimic the theory distribution of financial return data to compare the accuracy of the OGA and the thresholding method in Chen, Huang, and Pan (2015). The simulation result shows that the OGA with lower estimation error and higher stability than the thresholding method, especially in great distance between p and n. Second, we randomly select 100 (200, 300) stocks to form the portfolio as the investment target during 1980 to 2016. After assessing the performance of portfolio, the OGA method has higher portfolio expected return, higher Sharpe ratio on average, and higher cumulated investment return than naïve 1/N strategy. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/8028 |
DOI: | 10.6342/NTU202000879 |
全文授權: | 同意授權(全球公開) |
電子全文公開日期: | 2025-06-05 |
顯示於系所單位: | 財務金融學系 |
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ntu-109-1.pdf 此日期後於網路公開 2025-06-05 | 2.13 MB | Adobe PDF |
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