隨著ETF市場的蓬勃發展及產品種類的推陳出新，投資人交易與避險的需求逐漸提升，槓桿型及反向型ETF便成為發行商及投資者所熱衷的新型投資商品。簡而言之，槓桿型(Leveraged)ETF為追蹤標的指數報酬率正向倍數的ETF，在台灣多為正向2倍型。而反向型（Inverse）ETF則為追蹤標的指數報酬率反向倍數的ETF，在台灣僅有反向1倍型。為了能獲取目標倍數之報酬，槓反型ETF需利用衍生性商品進行配置，因此發行商需要通過每日重新平衡機制（Daily Rebalancing），以降低單日追蹤誤差。
本文將探討槓反型ETF之追蹤績效如何，觀察其單日及長期追蹤偏離狀況，以及影響追蹤績效之因素。研究樣本為台灣投信公司所發行的7檔槓反型ETF，其追蹤標的皆為中國大陸指數。本研究發現，在樣本期間內，槓桿型ETF之追蹤偏離度以正數居多，即其淨值報酬率高於指數報酬率之次數較多。觀察長期累積報酬率，發現其累積追蹤偏離度達10%以上。如果以Covin-19疫情為時間節點，在疫情發生後槓反型ETF之追蹤偏離程度均加大。至於影響槓反型ETF追蹤績效之因素，以匯率波動度及富時中國A50指數期貨收盤價漲跌幅最為顯著。另外本文也發現樣本期間內槓反型ETF以折價狀態居多，且和追蹤偏離度呈反向關係。本實證以蒙地卡羅法對槓反型ETF及其指數價格進行模擬，證實在長期持有下，其價值會逐漸減損，不適合投資人長期持有。

With the booming ETF market and the introduction of new products, investors' demand for trading and hedging is increasing. Leveraged ETFs track positive multiples of the underlying index return, mostly positive 2X in Taiwan. On the other hand, inverse ETFs track the inverse multiple of the underlying index return, which is only 1X inverse in Taiwan. In order to obtain the target multiple, leveraged and inverse ETFs need to use derivatives for allocation, and therefore issuers need to adopt a daily rebalancing mechanism to reduce the single-day tracking error.
This article examines the tracking performance of leveraged and inverse ETFs, looking at their single-day and long-term tracking difference, and the factors that affect their tracking performance. The sample consists of 7 leveraged and inverse ETFs issued by Taiwan fund companies, all of which track indices in Mainland China. This study found that the tracking difference of leveraged ETFs was mostly positive during the sample period. Looking at the long-term cumulative returns, it is found that the cumulative tracking difference is more than 10%. If we take the Covin-19 outbreak as the time point, the tracking difference of leveraged and inverse ETFs increased after the outbreak. As for the factors affecting the tracking performance of leveraged ETFs, exchange rate volatility and the closing price range of the FTSE China A50 Index Futures were the most significant. This paper also found that leveraged and inverse ETFs were mostly at a discount during the period, with an inverse correlation with tracking difference. This empirical evidence has used the Monte Carlo method to simulate the prices of leveraged ETFs and their indices, and has confirmed that the value of leveraged ETFs will gradually diminish over the long term, making them unsuitable for investors to hold over the long term.

第一章 緒論 1
第一節 研究背景 1
第二節 研究動機與目的 2
第三節 研究架構與流程 3
第二章 文獻回顧 4
第一節 槓桿型及反向型 ETF追蹤誤差 4
第二節 每日重新平衡機制 5
第三節 影響槓桿型及反向型ETF追蹤績效之因素 6
第四節 ETF折溢價之文獻 7
第三章 資料描述 8
第一節 研究對象 8
第二節 資料來源 15
第四章 研究方法 16
第一節 槓桿型及反向型ETF單日追蹤績效之衡量 16
第二節 長期下槓桿型及反向型ETF之追蹤績效 17
第三節 Covin-19疫情前後槓桿型及反向型ETF之追蹤表現 19
第四節 影響槓桿型及反向型ETF追蹤績效之因素分析 19
第五節 槓桿型及反向型ETF之折溢價分析 22
第五章 實證結果與分析 23
第一節 槓桿型及反向型ETF單日追蹤績效之實證 23
第二節 長期下槓桿型及反向型ETF追蹤績效之實證 28
第三節 Covin-19疫情前後槓桿型及反向型ETF追蹤表現之實證 38
第四節 影響槓桿型及反向型ETF追蹤績效因素之實證 41
第五節 槓桿型及反向型ETF折溢價分析之實證 43
第六節 實證結果小結 45
第六章 結論 47
參考文獻 49

1.李存修、徐慧釗(2016)，「槓桿型與反向型ETF是否影響其標竿指數之期貨市場？—SGX之A50股指期貨之實證」，期貨與選擇權學刊，第11卷第2期，1-40。
2.李存修、林澄(2017)，「槓、反ETF追蹤誤差與影響因素分析—臺、日、韓之比較」，期貨與選擇權學刊，第10卷第2期，51-87。
3.林禹岑(2021)，「台灣ETF溢價現象與賭博偏好」，國立政治大學商學院財務管理研究所碩士學位論文。
4.張森林、徐宇薇(2017)，「槓桿型與反向型ETF追蹤績效分析與模擬」，期貨與選擇權學刊，第 10 卷第 3 期，85-165。
5.藍珮瑜(2011)，「A50中國指數ETF與滬深300A股指數ETF之折溢價的資訊內涵與因果關係」，國立台灣大學管理學院財務金融研究所碩士學位論文。
6.蘇亭丰(2016)，「槓桿型與反向型 ETF 長短期追蹤績效之研究」，期貨與選擇權學刊，第9卷第1期，61-101。
7.Bai, Qing, Shaun A. Bond and Brian Hatch (2015), “The Impact of Leveraged and Inverse ETFs on Underlying Stock Returns,” Real Estate Economics, 43(1), 37-66.
8.Bansal, V. K. and Marshall, J. F. (2015) “A Tracking Error Approach to Leveraged ETFs: Are They Really that Bad?” Global Finance Journal, 26, 47-63.
9.Cheng, Minder and Ananth Madhavan (2009), “The Dynamics of Leveraged and Inverse Exchange-Traded Funds,” Journal of Investment Management, 7(4), 43-62.
10. Gerasimos Rompotis (2016), “Return and volatility of emerging markets leveraged ETFs,” Journal of Asset Management, 17(3), 165-194.
11.Hill, J. M. and G. O. Foster (2009), “Understanding Risk Returns of Leveraged and Inverse Funds: Examining Performance over Time,” the Journal of Indexes, Available at https://www.etf.com/publications/journalofindexes/joi-articles/6414-understanding-returns-of-leveraged-and-inverse-funds.html?nopaging=1.
12.Hongfei Tang and Xiaoqing Eleanor Xu (2013), “Leveraging the Chinese Stock Markets: Tracking Performance and Return Deviation of U.S.-Listed China LETFs,” Asia-Pacific Journal of Financial Studies, 42(6), 845-879
13.Hongfei Tang, Xiaoqing Eleanor Xu and Zihui Yang (2014), “Can international LETFs deliver their promised exposure to foreign markets?” Journal of International Financial Markets, Institutions and Money, 31(C), 30-74
14.I. T. Ivanov and S. L. Lenkey (2018), “Do leveraged ETFs really amplify late-day returns and volatility?” Journal of Financial Markets, 41, 36–56.
15.Lu, L., Wang, J. and Zhang, G (2009), “Long Term Performance of Leveraged ETFs,” Available at SSRN, 1344133, 1-31.
16.Narat Charupat and Peter Miu (2014), “A New Method to Measure the Performance of Leveraged Exchange-Traded Funds,” The Financial Review, Eastern Finance Association, 49(4), 735-763.
17.Pauline Shum, Walid Hejazi, Edgar Haryanto and Arthur Rodier(2016), “Intraday Share Price Volatility and Leveraged ETF Rebalancing,” Review of Finance, 20(6), 2379–2409.
18.Wessel M. Badenhorst (2017), “Premiums and discounts of exchanged-traded funds,” South African Journal of Accounting Research,31(3),212-222.