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.

本文以臺灣證交所上市的前九檔槓桿及反向指數股票型基金(LETFs)作為 樣本,根據 Charupat and Miu(2014)研究方法衡量其績效。傳統衡量指數股票 型基金(ETFs)績效的方式,為單純將基金淨值報酬對指數累積報酬做簡單迴 歸,若將此方法應用在衡量 LETFs 之績效上,由於許多影響基金淨值報酬的因素 沒被分離出來,常造成迴歸結果存在嚴重偏誤,或是難以解釋。本文是第一篇研 究國內 LETFs 績效的著作,透過在迴歸式中納入複利效果、融資效果,以更精確 的方式比較分析影響 LETFs 基金淨值報酬的因素,及各 LETFs 之管理績效。本 文實證結果除了證實融資效果確實存在,也證實大部分複利效果及融資效果的理 論性質,最重要的是,顯示出追蹤上証 180 指數的三檔 LETFs 在準確複製報酬槓 桿倍數上比較傑出,而追蹤台灣 50 指數的三檔 LETFs 在基金管理效率方面有比 較優秀的表現。 / Using Leveraged and Inverse Exchange-Traded Funds (LETF) listed in the Taiwan Stock Exchange, this thesis evaluates the performance of these LETFs based on the methodology proposed by Charupat and Miu (2014). The traditional approach of performance evaluation of ETFs is to regress the fund’s net asset value (NAV) returns on the underlying index’s returns. However, such an approach fails to account for important factors, such as compounding and financing effects, that affect the NAV of the LETFs, and unavoidably leads to serious estimation biases. This is the first thesis which evaluates the performance of LETFs listed in the Taiwan Stock Exchange. By considering compounded effect and financing effect in the regression model, the proposed method is more precise and appropriate in disentangling factors that affect the performance of the LETFs. Our empirical evidence shows how compounding effect, financing costs, and management factors influence LETFs’ tracking errors. Most of all, the three LETFs tracking the SSE180 index have the best tracking ability of the underlying asset return, while the LETFs tracking the FTSE TWSE Taiwan 50 index have the best management performance among all LETFs examined in this these.