網路拓樸與市場指數：以生成樹法創建標的組成之解析

Topology and Market Index: A Network Analysis with Spanning Trees

鑒於最小生成樹方法能有效地降低網絡複雜度，更加簡潔標示出最有關聯的公司，本文嘗試以此分析標準普爾 500 指數成分股並創建少量股票投資組合以追蹤市場股票指數，生成樹建構分別參採股價報酬、交易量及波動度等變數相關性及結合三者之傾向分數，同時也檢驗不同門檻值篩選連結邊的差異。研究發現運用連結邊較多之公司來編製新指數將與標準普爾 500 指數具有高度相關性，新指數也與道瓊工業平均指數及那斯達克綜合指數有高度的相關性，尤以波動度建構指數最佳，但以交易量建構之模型最穩健。

Minimum spanning trees are employed to investigate component stocks of S&P 500 index and create new portfolios tracking market indexes. In addition to daily price returns, we further examine the effectiveness of trading volumes, volatilities, and propensity scores in the selection of key stocks for tracking indexes. Our selected portfolios are high correlated with the S&P 500 index, the Dow Jones Industrial Average, and the Nasdaq Composite Index. The model based on daily volatilities could perform best conditional on the chosen threshold. Instead, portfolios created with daily volumes seem to perform quite robustly.