摘 要
過去探討指數追蹤之文獻中，大部分皆設定追蹤投資組合為固定權重之投資組合，實際上指數本身之成分股權重並非固定，本研究中主張，欲以固定權重之追蹤投組複製本身為買入持有投資組合之目標指數，將造成追蹤誤差。本文對於過去於指數追蹤問題上之研究加以整理，並提出以一買入持有投資組合追蹤目標指數之模型，本研究以S&P 500指數資料作為實證資料，與過去研究者所提出之模型做一比較。
本文利用S&P 500 指數以及其各成分股於1997年至2002年之日資料進行實證分析。在指數追蹤中的選股問題方面，分別利用二次規劃法模型、市值加權模型以及遺傳演算法選股模型；資金配置問題上，以傳統法建構固定權重投資組合與以遺傳演算法買入持有投資組合之觀念分別決定買進單位數，共建構六種追蹤投資組合投資於樣本外測試期。
綜合而言，以遺傳演算法選股雖然隱含較大之交易成本，但能避免報酬率表現持續向上或向下偏離目標指數報酬率之情況，且投組之價值走勢長期貼近目標指數，較符合指數型基金經理人之目標。另外，以建構買進持有投資組合之觀念取代以建構固定權重投組之方法決定各投組成份股所需買入之單位數，將能有效降低追蹤誤差。

Abstract
Index-tracking problem used to be defined as to construct a constant-weight rebalanced portfolio to chase target index. Since index itself is a buy-and-hold portfolio, we argue that instead of building a constant-weighted tracking portfolio, to construct a buy-and-hold one is more realistic.
Index-tracking problem contains the stock selection problem and the problem of how many shares to buy. In stock selection problem, we discussed optimization model, capitalization-based model and GA selection model. On the other hand, when we try to build a buy-and-hold portfolio, we employed genetic algorithm to solve the complex non-linear problem, and compare the out-of-sample result with the traditional constant-weight rebalance tracking portfolio.
To test our model, we used S&P 500 daily price data from 1997 to 2002, and concluded that GA stock selection model implies higher transaction cost while it could prevent long-term downside or upside biases; the buy-and-hold tracking portfolio leads to a relatively small tracking when we compare it with a constant-weight rebalanced one.

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