為解決資產報酬資料的變動所造成的資料不確定性問題,本研究利用模糊數表示個別資產的報酬率,針對投資組合,考慮了投資報酬、風險、偏態與賣空等多個決策因素,並設定了各投資權重的上下限。此外,為了更貼近實際交易情形,提出了考慮交易成本的投資組合重新調整模型,以模擬股票市場的實際交易情形。因此,本研究提出了同時考慮投資報酬、風險、偏態、賣空與交易成本的多準則模糊投資組合重新調整模型。實例分析中,以台灣與紐約證券交易所中的股票資料來做投資組合的分析,透過每期權重重新調整後所求出的市場價值,來比較投資組合模型中,偏態與賣空對於投資組合價值的影響。最後,本篇論文的貢獻在於解決投資報酬為不精確時,多準則考量投資組合的情形,並證明在投資組合中考慮投資偏態與投資賣空能讓模型產生較高的績效。
In order to deal with the uncertainty issue in returns, fuzzy variables are employed to indicate the assets’ return rate and consider portfolio return, as well as risk and skewness in the portfolio. To approach a real transaction, the criteria of the short sale and transaction cost in the portfolio are considered simultaneously. Therefore, a rebalancing model with multiple criteria, including return, risk, skewness, short sale proportion, and transaction cost in portfolio selection is proposed. Two data sets, from Taiwan and the New York Stock Exchange, are analyzed and compared to find the impact when skewness and short sales are considered in a fuzzy portfolio model. The contribution of this article is to solve a multiple criteria portfolio when the return data has fuzzy variables and to prove that it can generate a better result when considering skewness and short sales in portfolio selection.