槓桿型ETF的投資組合分散效益分析

Abstract

近年來槓桿型ETF發展迅速，成為投資人熱門的標的之一。本研究旨在探討槓桿型ETF在投資組合中的分散效益，並具體分析了標普500指數、美國20年期以上公債、房地產和黃金四個主題的槓桿型ETF。研究的主要目標是檢驗將槓桿型ETF納入投資組合是否能夠擴張效率前緣曲線，並探討不同主題類型對此效果的影響。 本研究對槓桿型ETF進行平均數變異數擴張檢定，結果顯示，加入槓桿型ETF能顯著擴展投資組合的效率前緣曲線，特別是對全域最小變異數投資組合，而切點投資組合的改善則相對不顯著。然而，若將原型ETF納入基準投資組合並加入槓桿型ETF，則切點投資組合和全域最小變異數投資組合皆能獲得顯著擴張，且任一基準投資組合結果一致。同時，夏普比率和M2測度變化量也顯示，投資組合的效益得到了顯著改善。 本研究進一步探討了切點投資組合中槓桿型ETF和原型ETF的配置權重，發現多數情況下，槓桿型ETF與相應原型ETF在投資組合中的最佳配置為近似-1：2比例的權重，這種配置策略能有效降低整體投資組合風險，同時提高風險調整後的報酬。此外，研究發現波動率和無風險利率皆會影響該配置策略的報酬率，並根據ETF主題影響程度有所不同。最後，樣本外測試結果與平均數變異數擴張檢定結果多數一致，進一步證實了槓桿型ETF的分散效益。 總體而言，本研究表明槓桿型ETF在投資組合中，透過特定的配置，能顯著提升投資組合的分散效益，為投資者提供了有價值的參考，協助其做出更明智的投資決策。

In recent years, leveraged ETFs have developed rapidly and become a popular investment choice for investors. This study aims to explore the diversification benefits of leveraged ETFs in investment portfolios through analyzing leveraged ETFs tracking the S&P 500 Index, U.S. 20+ year Treasury bonds, real estate, and gold. The primary objective is to examine whether incorporating leveraged ETFs into investment portfolios can expand the efficient frontier and to investigate the effects of different thematic types on this outcome. This study conducted mean-variance spanning tests on leveraged ETFs. The results indicate that adding leveraged ETFs can significantly expand the efficient frontier of investment portfolios, particularly for the global minimum variance portfolio, whereas the improvement for the tangency portfolio is relatively insignificant. However, if prototype ETFs are included in the benchmark portfolio along with leveraged ETFs, both the tangency portfolio and the global minimum variance portfolio can achieve significant expansion, with consistent results across various benchmark portfolios. Additionally, changes in the Sharpe ratio and M2 measure demonstrate significant improvements in portfolio performance. Further analysis of the allocation weights of leveraged and prototype ETFs in the tangency portfolio reveals that, in most cases, the optimal allocation is approximately a -1:2 ratio of leveraged to prototype ETFs. This allocation strategy effectively reduce the overall portfolio risk while improving risk-adjusted returns. Additionally, the study finds that both volatility and risk-free interest rates affect the returns of this allocation strategy, with varying impacts depending on the ETF theme. Finally, the out-of-sample test results are largely consistent with the mean-variance spanning test results, further confirming the diversification benefits of leveraged ETFs. Overall, this study demonstrates that leveraged ETFs, when appropriately selected and allocated in investment portfolios, can significantly enhance the diversification benefits of the portfolio, providing valuable insights for investors to make more informed investment decisions.