在傳統的均值－變異數架構當中，投資人只要利用過去資產報酬資料計算出平均報酬和共變異數矩陣，就可以進一步得出最適權重。然而，平均數與共變異數矩陣兩者都很容易受到估計期間的極端報酬影響。行為財務學認為投資人是不理性的，而市場的非理性反應造成極端報酬的出現；若用這些報酬數字估計其未來報酬就可能會產生錯誤估計的問題。本文使用符號等級(signed rank) 取代原本的平均數與共變異數矩陣去計算最適化權重，試圖利用符號等級這種只考慮報酬間相對位置而不管數字大小的估計量去減輕上述提到的錯誤估計問題。實證結果發現，改為使用符號等級後，最適化投組之績效有顯著的提升，同時並未承擔更高的投組報酬風險。最後，本研究也發現過去一段時間報酬的平均符號等級比原本的報酬平均數更能預測未來資產報酬，且研究也發現基於符號等級的最適投組，其更好的報酬表現是來自於符號等級降低估計期間的極端報酬對最適投組的影響程度。;In the mean-variance model of Markowitz (1952), given the expected returns and covariance matrix of a set of stocks, investors can obtain the optimal weight on each stock. However, the estimates of expected returns and covariance matrix are very sensitive to outliers which might be generated from market irrationality. To reduce this kind of estimation error, this study uses signed rank as the input to solve the portfolio optimization problem. The evidence shows that the signed rank based optimal portfolio outperforms the original tangency portfolio, based on a sample of the US stocks. Furthermore, the results indicate that the signed rank of past returns is more effective than sample mean in predicting future returns. Finally, the better performance is due to the fact that the signed rank attunuates the impact of extreme values on the optimal portfolio.
