建立指數基金時，通常是利用追蹤指數的技巧，選取少量的股票建構指數基金使得報酬率與標的指數(benchmark index)報酬率同步的投資組合。如果能建立包含少量股票的投資組合，就可達到指數追蹤的效果，那麼也能利用少量的股票建立績效可以超越指數基金的投資組合。本論文利用建構指數基金的方法以及大中取小的概念，挑選出一個績效可以超越標的指數的投資組合。本論文提出的模型亦考慮實務上交易所需的各項成本、整數交易單位與資產總類數等限制。因此，模型包含整數變數與二元變數。最後以台灣加權股價指數的相關資料做為實證研究的對象，實證結果顯示本論文提出的模型所建立的投資組合超越標的指數的績效平均年化報酬率25%。 / Setting up an index fund usually uses techniques of index-tracking that choosing few stocks forming a portfolio to obtain the same return rate as the benchmark index. Similarly we can use the same concept to set up a portfolio such that the performance is better than index’s. In this thesis we use index-tracking methods and minimax rule to obtain a portfolio which outperforms the benchmark index. In the proposed mathematical model we will consider the transaction costs, integer trading unit volume, and the total number of assets in the portfolio. Therefore the resulting model is a mixed integer nonlinear programming including integer variables and binary variables. Finally, the empirical study will be performed by using the data from the Taiwan stock market to verify the performance of our model. The empirical study shows that the portfolios created by our models outperform the benchmark index up to 25% in average.