槓桿型 ETF，會隨著” 每日” 的價格波動來調整手上的持倉部位，以達到宣 告的槓桿倍數，因為每日的調整，會導致震盪耗損的出現，當標的物價格 跳動後，回到原始的價位，槓桿型 ETF 的價格必定會低於原始價格，槓桿 型 ETF 的價格差距，即為震盪耗損的產生之結果。過往許多文獻討論，槓 桿型 ETF 因為震盪耗損而不適合長期持有，也有人討論以股市大盤指數 為標的之槓桿型 ETF，長期持有正向兩倍槓桿型 ETF，其放大的獲利，能 夠勝過震盪耗損帶來的虧損，因此適合長期持有正向兩倍槓桿型 ETF。但 前述論點都是將震盪耗損視為虧損，但事實真是如此嗎?本篇論文希望改 變視角，以作空反向型 ETF 來獲得與正向型 ETF 一樣的標的物上場的報 酬，同時將震盪耗損從虧損轉變為獲利。我們將以那斯達克 100 指數槓桿 型 ETF 為標的，用來證實此想法可行。

Leveraged ETFs adjust their positions daily to achieve the declared leverage mul- tiple, which means their holdings fluctuate with the daily price movements. This daily adjustment leads to the phenomenon of volatility decay. When the price of the underlying asset fluctuates and returns to its original level, the price of the leveraged ETF will inevitably be lower than the original price. The price differ- ence of the leveraged ETF represents the result of volatility decay. Many studies in the past have discussed that leveraged ETFs are not suitable for long-term hold- ing due to volatility decay. However, some argue that for leveraged ETFs tracking broad market indices, holding a leveraged ETF with twice the leverage for the long term can outweigh the losses from volatility decay and is therefore suitable. How- ever, all the above arguments treat volatility decay as a loss. But is this really the case? This paper aims to change the perspective by short selling inverse leveraged ETFs to achieve the same returns as traditional leveraged ETFs while transforming volatility decay into profit. We will use the Nasdaq100 Index leveraged ETF as the underlying to verify the feasibility of this idea.

Avellaneda, M. and Zhang, S. (2010). Path-dependence of leveraged etf returns. SIAM Journal on Financial Mathematics, 1(1):586–603.
Charupat, N. and Miu, P. (2011). The pricing and performance of leveraged exchange-traded funds. Journal of Banking & Finance, 35(4):966–977.
Charupat, N. and Miu, P. (2016). Performance and tracking errors. In Leveraged Exchange- Traded Funds: A Comprehensive Guide to Structure, Pricing, and Performance, pages 73–109. Springer.
Cheng, M. and Madhavan, A. (2009). The dynamics of leveraged and inverse exchange-traded funds. Journal of investment management, 16(4):43.
Cooper, T. (2010). Alpha generation and risk smoothing using managed volatility. Available at SSRN 1664823.
Dai, M., Kou, S., Soner, H. M., and Yang, C. (2023). Leveraged exchange-traded funds with market closure and frictions. Management Science, 69(4):2517–2535.
Guedj, I., Li, G., and McCann, C. (2010). Leveraged etfs, holding periods and investment shortfalls. The Journal of Index Investing, 1(3):45–57.
Guo, K. and Leung, T. (2014). Commodity leveraged etfs: Tracking errors, volatility decay and trading stategies. The Journal of Risk, page 8.
Ivanov, I. T. and Lenkey, S. L. (2018). Do leveraged etfs really amplify late-day returns and volatility? Journal of Financial Markets, 41:36–56.
Jiang, X. and Peterburgsky, S. (2017). Investment performance of shorted leveraged etf pairs. Applied Economics, 49(44):4410–4427.
Loviscek, A., Tang, H., and Xu, X. E. (2014). Do leveraged exchange-traded products deliver their stated multiples? Journal of Banking & Finance, 43:29–47.
Lu, L., Wang, J., and Zhang, G. (2009). Long term performance of leveraged etfs. Available at SSRN 1344133.
Shum Nolan, P. (2012). The long and short of leveraged etfs: The financial crisis and perfor- mance attribution. Available at SSRN 1646160.
Tang, H. and Xu, X. E. (2013). Solving the return deviation conundrum of leveraged exchange- traded funds. Journal of Financial and Quantitative Analysis, 48(1):309–342.