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由 HH Chen 著作 - 2004 - 相關文章
允許買空賣空（投資權重允許為負值）的情況下，本研究將利用柯西-史瓦茲極. 大值定理(Cauchy-Schwarz maximization)提出一個可以直接獲得最大Sharpe 指標| 一般基金管理單位經常採用Sharpe指標作為基金操作績效之評估指標，因此基金經理人的主要目標通常為建立能夠獲得最大Sharpe指標之投資組合。過去的方法通常以修改Markowitz平均值-變異數投資組合模型（MV模型）之目標函數，並求解非線性規劃問題，以得到最大Sharpe指標之最佳投資組合。在允許買空賣空（投資權重允許為負值）的情況下，本研究將利用柯西-史瓦茲極大值定理(Cauchy-Schwarz maximization)提出一個可以直接獲得最大Sharpe指標投資組合之公式解(closed-form solution)，這個方法不需要利用非線性規劃方式求解，不但較傳統方法更容易使用，且可以節省運算時間與成本，同時方便未來推估最佳投資權重之信賴區間。在不允許買空賣空（投資權重不得為負值）環境與條件下，我們則進一步利用Kuhn-Tucker 條件的觀念求解最大Sharpe指標之最佳投資組合。 另外，Markowitz的MV投資模型所產生的效率前緣會有高報酬伴隨高風險的現象，因而造成投資者在高風險高報酬與低風險低報酬之間取捨的決策兩難。本研究應用品質工程損失函數的概念，提出一個可以適當反映期望報酬率與風險間均衡關係的投資組合績效指標（簡稱IRp績效指標），並比較各種投資組合指標(包括Sharpe指標與效用函數投資組合指標)以確認其適合用來評估效率前緣中投資組合之績效。實證分析中將採用國內外金融市場歷史資料，來測試及確認新的運算方法及IRp指標之可行性與適用性。本研究將多變量分析中之Cauchy-Schwarz極大值定理與作業研究之Kuhn-Tucker條件及品質工程中的損失函數應用於投資組合決策領域，使其理論更加完整，對實務界與學術界均具有重大的意義。 | |||
| 摘要(英) | Since most financial institutions use the Sharpe Ratio to evaluate the performance of mutual funds, the objective of most fund managers is to select the portfolio that can generate the highest Sharpe Ratio. Traditionally, they can revise the objective function of the Markowitz mean-variance portfolio model and resolve non-linear programming to obtain the maximum Sharpe Ratio portfolio. In the scenario with short sales allowed, this project will propose a closed-form solution for the optimal Sharpe Ratio portfolio by applying Cauchy-Schwarz maximization. This method without using a non-linear programming computer program is easier than traditional method to implement and can save computing time and costs. Furthermore, in the scenarios with short sales disallowed, we will use Kuhn-Tucker conditions to find the optimal Sharpe Ratio portfolio. On the other hand, an efficient frontier generated by Markowitz mean-variance portfolio model normally has higher risk higher return characteristic, which often causes dilemma for decision maker. This research applies generalized loss function to create a family of decision-aid performance measures called IRp which can well tradeoff return with risk. We compare IRp with Sharpe Ratio and utility functions to confirm that IRp measures are approapriate to evaluate portfolio performance on efficient frontier and to improve asset allocation decisions. In addition, empirical data of domestic and international investment instruments will be used to examine the feasibility and fitness of the new proposed method and IRp measures. This study applies the methods of Cauchy-Schwarz maximization in multivariate statistical analysis and loss function in quality engineering to portfolio decisions. We believe these new applications will complete portfolio model theory and will be meaningful for academic and business fields. | ||
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