自從槓桿型指數基金於各股票市場發行後，各國主管機關皆紛紛發出聲明表示，該商品並不適合長期持有；因此，該類型投資商品的公開說明書皆會註明不宜長期投資。然而，本研究實證結果發現，持有期間長短並非主要風險來源。雖然，如大家所知，槓桿型指數基金多是以「日」為單位追蹤指數，而導致複利效果 (Compounding Effect) 使基金長期報酬與槓桿倍數不同。
根據算出上述的報酬差異(Return Difference)可以發現不論是正向2倍或是反向1倍皆與台灣50報酬率的標準差有統計上顯著關係。反向1倍皆與台灣50報酬率的標準差有顯著負相關；反之，正向2倍與台灣50報酬率的標準差有顯著正向相關。然而，從已實現乘數(Realized Multiple)的分佈中可發現，不合理值並不隨投資期間越長而越多。意即儘管投資期間越長，並不一定會導致複利效果越大，而與目標槓桿倍數脫節。再者，隨著投資期間越長，波動度(volatility)的對於報酬差異的解釋力越強；因此，若想長期投資槓桿型指數資金，預測標的波動度的能力更顯為重要。

When we browse the reports about the inverse and leveraged ETF, most of them emphasize that the LETF is not appropriate to long-term investors. However, in this research, we attempt to demonstrate the main factor of the performance of the leveraged and inverse ETF is not how long the LETF we hold, but the volatility of the underlying index or ETF.
Observing the empirical test, no matter how long the investment horizon is, the coefficient of the variance of the Taiwan 50 is statistically significant both in the Taiwan 50 Bear -1X and the Taiwan 50 Bull. However, its effect on the Bear -1X is opposite to that on the Bull 2X. First, the relationship between the volatility and the return difference of Taiwan 50 and the Bear -1X is negative. In contrast, the relationship between the volatility and the return difference of Taiwan 50 and the Bull 2X is positive. However, in accordance with the distribution of the realized multiples, the frequency of either the Bear -1X or Bull 2X was not more and more when the holding period is longer.
As a result, our research show the variance has a significant effect on both, no matter how long investors hold. If the volatility is moderate, the return difference may be close to zero; then the LETFs would be a convenient way to investors who desire to magnify the market return. Moreover, due to the increasing explanatory power of the volatility, we may make a further inference that whether the compounding effect is positive or negative depends on the volatility, especially within longer holding period. Therefore, without the great ability to forecast the variance, the LETFs are not recommended to the long-term investors.

Cheng, Minder, and Ananth Madhavan, (2009). The Dynamics of Leveraged and Inverse Exchange- Traded Funds. Journal of Investment Management 7, 43-62.
Financial Supervisory Commission (FSC), (2015). 2015 Annual Report R.O.C.
Joanne M.Hill and George O.Foster, (2009). Understanding Returns of Leveraged and Inverse Funds and Examining Performance over Time. IEOR Columbia, 10-16.
Lu, Lei, Jun Wang and Ge Zhang, (2009). Long-term Performance of Leveraged ETFs. Working paper, SSRN.
Little, P.K., (2010). Inverse and Leveraged ETFs: Not Your Father’s ETF. The Journal of Index Investing, 1, pp. 83-89.
Marco Avellaneda, Stanley Zhang, (2009). Path-Dependence of Leveraged ETF Returns. Society for Industrial and Applied Mathematics, 2, 586-596.
Richard Co, (2009). Leveraged ETFs vs. Futures: Where Is the Missing Performance? CME Group Research & Product Development, 1-4.
Robert Murphy and Colby Wright, (2010). An Empirical Investigation of the Performance of Commodity-Based Leveraged ETFs. Journal of Index Investing, 3, 14-23
Trainor, W.J., and E. Baryla, (2008). Leveraged ETFs: A Risky Double That Doesn’t Multiply by Two. Journal of Financial Planning, 21 , 48-55.
Trainor, W.J., (2011). Solving the Leveraged ETF Compounding Problem. Journal of Index Investing, 21, 1-9.