Dynamic Portfolio Selection with Predicted Return and Risk

[[abstract]]本研究提出Fuzzy GP/SC與Fuzzy Piecewise MOGP/SC兩種預測模型。Fuzzy GP/SC模型主要用於處理精確觀察值及模糊輸出資料的問題，其特色為：適用於小樣本觀察值、可提供決策制定者可能最佳解及可能最差解、受離群值的影響較小，經由最小化Mean Absolute Deviations (MAD)，發現其整體表現優於Fuzzy ARIMA ( Tseng et al., 2001)。Fuzzy Piecewise MOGP/SC模型主要用於處理模糊觀察值及模糊輸出資料的問題，其特色為：適用於小樣本觀察值、可處理模糊輸入資料、可自動偵測並處理離群值而非捨棄、沒有多階段之繁複估計過程。 本研究將預測報酬取代傳統歷史資料之算術平均報酬並加入多準則決策以配置投資組合權重，共使用GP/SC模型及ARIMA兩種預測模型，並使用GARCH模型以估計預測風險來取代以往所使用的歷史資料標準差方法，而多準則決策所考慮的四個準則為預測報酬、預測風險、β值和偏態，經由模糊多準則決策產生衝突目標間的妥協解以配置投資組合權重。最後，透過移動視窗法以及交易成本之考量模擬真實美國股市交易狀況，經由模擬發現本研究所提GPSC-GARCH比MVBS (卓如茵, 民96)、GPSC-STD和ARMA-GARCH等方法佳。[[abstract]]This study proposed two forecasting models, which are Fuzzy GP/SC and Fuzzy Piecewise MOGP/SC. Fuzzy GP/SC is used to deal with crisp observations, and can be applied in small observations and provide decision makers the best-possible and worst-possible situations. The experiments found that Fuzzy GP/SC is better than Fuzzy ARIMA (Tseng et al., 2001) with minimizing Mean Absolute Deviations (MAD). Fuzzy Piecewise MOGP/SC is used to deal with fuzzy observations, and can be applied with small observations and get smaller MAD than Fuzzy ARIMA does because it can solves problem of outliers instead of deleting all the outliers. This study used predicted return instead of arithmetic mean for Multiple Criteria Decision Making (MCDM) to conduct portfolio selection. GARCH model was used to calculate the risk for standard deviations. Moreover, there are two forecasting models used to forecast predicted return, which are GP/SC model and ARIMA model. MCDM is consisted of four criteria, which are predicted return, predicted risk, β value, and skewness. The experiments found that the GPSC-GARCH model outperformed the MVBS (Cho, 2007), GPSC-STD, and ARMA-GARCH.[[note]]碩