台灣金融市場於2014年首度發行槓桿型及反向型指數型基金(Leveraged ETF, Inverse ETF)，使國內之ETF市場更加豐富，槓桿型ETF能創造市場的波動性，獲利加乘，反向型ETF則能突破放空限制，以此類商品之特性，若加入市場後應能大幅提升市場效率性。因此本研究探討於有放空限制與無放空限制下，將槓桿型ETF與反向型ETF納入投資組合後，以Markowitz的平均數-變異數模型為基礎，利用平均數變異數擴張檢定方法(Mean-Variance Spanning Test) 探討效率前緣之提升，切點投資組合與最小變異投資組合。除了以2006年7月13至2014年12月12日作為全期間之外，本研究亦區分多頭與空頭市場、高波動度與低波動度市場、高利率與低利率市場，探討不同市況下之變動程度。

結果顯示，於有放空限制條件下，反向型ETF及槓桿反向型ETF在加入市場投資組合後確實能提升效率前緣，而槓桿型ETF卻無直接顯著影響，空頭市況、高波動市況、高利率市況之切點投資組合變化較大，多頭市況、低波動市況、低利率市況之最小變異投資組合變化較大。於無放空限制條件下，加入所有槓桿型與反向型ETF皆能提升效率前緣，空頭市況、高波動市況、低利率市況之切點投資組合變化較大，空頭市況、低波動市況、低利率市況之最小變異投資組合變化較大。此結果顯示出兩種產品之價值，並建議投資人可同時將槓桿型與反向型ETF納入投資組合，以強化投資組合之效率性。

The Leveraged ETFs, which can increase the market volatility and investors’ profit, and Inverse ETFs, which can break through the limitation of short-sales and provide an easy way to invest, emerged in Taiwan’s finance market in 2014. To do research in this kind of products, this study focuses on examining whether investors can improve the efficiency and performance by adding Leveraged ETFs and Inverse ETFs to market portfolio in the U.S. market in two assumption: with short-sales constraints and without short-sales constraints. We use the Mean-Variance model by Markowitz and Mean-Variance Spanning Test by Kan and Zhou to test if the efficient frontier improved and explain the source of spanning. To test if the efficient frontier improved, we consider the change rate of sharpe ratio in tangency portfolio and the change rate of risk in minimum-variance portfolio. The study is also focus on the difference in efficient frontier in different market conditions, including bull and bear market, high and low volatility market, and high and low interest rate period market.

Results show that the efficient frontier with short-sales constraints can be improved by adding Inverse ETFs, but not Leveraged ETFs. The degree of performance improvement of tangency portfolio in bear market condition, high-volatility market condition, and high interest rate period are higher. The degree of performance improvement of minimum-variance portfolio in bull market condition, low-volatility market condition, and low interest rate period are higher. On the other hand, the efficient frontier without short-sales constraints can be improved by adding Inverse ETFs, and Leveraged ETFs. It shows that this kind of products is worth putting in investors’ portfolio to improve efficiency and performance.

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三、網站部分：
51. CBOE Volatility Index: http://www.cboe.com/micro/VIX/vixintro.aspx
52. The National Bureau of Economic Research: http://www.nber.org/
53. ProShares: http://www.proshares.com/
54. Yahoo Finance: http://finance.yahoo.com/