槓桿型與反向型ETF追蹤績效分析與模擬

An Investigation of Short- and Long-term Tracking Performance and Portfolio Simulation of Leveraged and Inverse ETFs

本文研究分為四部分。第一部分以台灣上市的兩檔槓桿型反向型ETF（元大T50 2X、元大T50反）為研究對象，檢驗其長短期在單複利效果下，標的指數累積報酬率之追蹤績效。在1%顯著水準下，兩檔基金單日追蹤績效都顯著異於基金投資目標，長天期報酬則均顯著偏離標的指數目標倍數報酬。去除複利效果則對槓桿型ETF有正向的效果，反向型ETF則相反。第二部分以兩樣本期間之歷史數據回測自行模擬之正向2倍型及負1倍型投資組合，在1%顯著水準下，單日追蹤績效普遍顯著異於基金投資目標，但仍可發現回歸係數及t統計量皆優於第一部分研究之元大T50 2X及元大T50反，績效不優則透過研究期貨追蹤指數的效果，推論是由於金融風暴期間的期貨追蹤效果不佳所導致。第三部分著重分析影響基金追蹤績效的因子，透過基金網站上公布的每日基金部位配置，可以發現基金經理人之操作習慣。並同時強化理解市場環境機制，如換約手法、交叉避險比例、申購贖回機制等皆為觀察重點，以這些要素納入模擬投資組合時的考量之中。第四部分則自行模擬正向2倍型及負1倍型投資組合，完全對應台灣上市的兩檔槓桿型反向型ETF（元大T50 2X及元大T50反）的初始規模，並去除先前諸多假設，貼近真實市場操作及機制。在1%顯著水準下，一年期和兩年期為樣本期間之交叉避險比例在負1倍型投資組合之績效最為優良，但就單日報酬追蹤效果而言，使用半年期為樣本期間之交叉避險比例追蹤績效最好，與台灣上市的兩檔槓桿型反向型ETF相比，也能得到同樣的結論。而去除複利效果後，對於槓桿型反向型ETF績效並無顯著提升的效果。雖本文研究已盡力貼近市場，基金收益分配所造成的不同步現象，期貨含有基差風險及規格標準化的限制，投資組合的部位配置差異，以及投資工具的標的指數與槓桿型反向型ETF所追蹤的標的指數不一致而須考慮之交叉避險比例等，推測皆為會影響追蹤績效的要因之一。

This paper is composed of four parts. The first part of the paper examines long-term and short-term tracking performances whether compound effects included or not of two leveraged and inverse ETFs listed on the stock exchange in Taiwan. At 1% level of significance, daily tracking performances of the leveraged and inverse ETFs significantly deviate from the investment objectives of the funds. The cumulative returns of the leveraged and inverse ETFs over holding period are also significantly different from targets’ multiple of cumulative returns of underlying index over corresponding period. Leveraged ETFs are better off by excluding compounding effects, but this result is contrary to inversed ETFs.The second part simulates the leveraged and inverse ETFs using different period of time in history. At 1% level of significance, daily tracking performance of the leveraged and inverse ETFs significantly deviate from the investment objectives of the funds, but find the tracking slope and t statistics are still better than Taiwan’s leveraged and inverse ETFs. The bad performances are deducted that was affected by poor tracking ability of futures during global financial crisis. The third part analyzes other causes for tracking performances, in order to understand fund managers’ management techniques and market environment. Thus, found out that tracking performances would be affected by rolling-over methods, cross-hedging ratio, creations and redemptions mechanism of ETFs.The fourth part fully simulates the leveraged and inverse ETFs in Taiwan, including all the causes and market environment below. At 1% level of significance, daily tracking performance of the inverse ETFs using one and two-year sample period as cross-hedging ratio have the best tracking performances. However, half year sample period as crosshedging ratio has the best daily tracking performances, even compared to Taiwan’s leveraged and inversed ETFs listed on the stock exchange would get the same result. Leveraged and inversed ETFs are no different from compounding effects excluded.Unsynchronized effects caused by profit distribution, the basis risk and standardized contract of futures, the construction of portfolio, and whether underlying index of investment vehicle is consistent with that of leveraged and inverse ETFs, and crosshedging ratios, are the other factors that could also affect tracking performances of leveraged and inverse ETFs.