本論文研究如何建立一個投資組合用來追蹤穩定成長的目標線。我們將這個目標線追蹤問題建構成混合整數非線性數學規劃模型。由於用以追蹤目標線的投資組合，經過一段時間後其追蹤效能可能未如預期，本論文提出調整投資組合的數學規劃模型。這些模型中除了考量實務中的交易成本，亦考慮限制放空股票，所以將期貨加入投資組合中作為避險部位。最後，以台灣股票市場與期貨交易市場作為實證研究對象，探討投資組合建立與調整的表現，亦分析不同成長率設定之目標線與期貨投資比重上限對投資組合價值的影響。 / This thesis studies how to construct a tracking portfolio for the benchmark of a stable growth rate. This tracking problem can be formulated as a mixed-integer nonlinear programming model. Since the performance of the tracking portfolio may get worse when time elapses, this thesis proposes another mathematical programming model to rebalance the tracking portfolio. These models not only consider the transaction cost but also take into account of the limitation of shorting a stock; thus the tracking portfolio will include a futures position as a hedging position. Finally, an empirical study will be performed by using the data from the Taiwan stock market and the futures market to explore the performance of the proposed models. We will analyze how the different benchmark settings and the futures position limits will affect the value of the tracking portfolio.

本論文提出追蹤特定目標線的二階段混合整數非線性隨機規劃模型，以建立追蹤目標線的投資組合。藉由引進情境樹(scenario tree)，我們將此類二階段隨機規劃問題，轉換成為等價的非隨機規劃模型。在金融商品的價格波動及交互作用下，所建立的投資組合在經過一段時間後，其追蹤目標線的能力可能會日趨降低，所以本論文亦提出調整投資組合的規劃模型。為符合實務考量，本論文同時考慮交易成本、股票放空的限制，並且加入期貨進行避險。為了反應投資者的預期心理，也引進了選擇權及情境樹。最後，我們使用台灣股票市場、期貨交易市場及台指選擇權市場的資料進行實證研究，亦探討不同成長率設定之目標線與投資比例對於投資組合的影響。 / To construct a portfolio tracking specific target line, this thesis studies how to do it via two-stage stochastic mixed-integer nonlinear model. We introduce scenario tree to convert this stochastic model into an deterministic equivalent model. Under the volatility of price and the interaction of each financial derivatives, the performance of the tracking portfolio may get worse when time elapses, this thesis proposes another mathematical model to rebalance the tracking portfolio. These models consider the transactions cost and the limitation of shorting a stock, and the tracking portfolio will include a futures as a hedge position. To reflect the expectation of investors, we introduce scenario tree and also include a options as a hedge position. Finally, an empirical study will be performed by the data from Taiwan stock market, the futures market and the options market to explore the performance of the proposed models. We will analyze how the different benchmarks settings and invest ratio will affect the value of the tracking portfolio.