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研究生： 黃鈺庭
Huang, Yu-Ting
論文名稱： 以幾乎隨機優勢法檢驗槓桿型ETF投資組合之優劣關係
Portfolio of Leverage Exchange Traded Fund : An Analysis Based on Almost Stochastic Dominance
指導教授： 張焯然
Chang, Jow-Ran
口試委員: 陳政琦
蔡璧徽
學位類別： 碩士
Master
系所名稱： 科技管理學院 - 計量財務金融學系
Department of Quantitative Finance
論文出版年： 2023
畢業學年度： 111
語文別： 中文
論文頁數： 44
中文關鍵詞： 槓桿型ETF 、分散型投資組合 、再平衡策略 、隨機優勢 、幾乎隨機優勢
外文關鍵詞： Leverage Exchange Traded Funds, Diversified Portfolio, Rebalance Strategy, Stochastic Dominance, Almost Stochastic Dominance
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    • 槓桿型ETF為近年來熱絡交易的產品，因其倍數放大投資者績效的特性，廣為投資人所偏好。然而，其槓桿衰退 ( Leverage Decay ) 以及高昂管理費用 ( Expense Ratio ) 的特性降低投資人對於長期持有槓桿型ETF產品的意願，過往的文獻也指出其不適宜作為長久持有的標的。但近年來的研究亦指出，透過合適的資產配置方式以及交易策略，亦能夠使槓桿型ETF被長期持有，彌平其所帶來的負面效應。本篇論文將建構槓桿型ETF投資組合，並搭配合適的再平衡策略 ( Rebalance Strategy )，在幾乎隨機優勢 ( Almost Stochastic Dominance )的框架之下對其績效進行探討，旨在於驗證高槓桿型ETF投資組合之績效是否能夠擊敗無槓桿型ETF投資組合績效，並進一步觀察延長投資期間是否能夠對績效進行提升。研究結果指出，在2014~2022的資料區間之內，經歷數次市場震盪的壓力之下，在幾乎隨機優勢法則之下，高槓桿型ETF之投資績效優越於無槓桿型投資組合之績效，且投資期間越長佔優的效果越強烈。

    Leveraged ETFs have become popular trading products in recent years due to their ability to amplify investor returns. However, the characteristics of leverage decay and high expense ratios have diminished investors' willingness to hold leveraged ETFs for the long term. Previous literature has also indicated that leveraged ETFs are not suitable for long-term holdings. However, recent studies have suggested that through appropriate asset allocation and trading strategies, leveraged ETFs can be held for the long term, mitigating their negative effects. This paper aims to construct a leveraged ETF investment portfolio and apply suitable rebalance strategies within the framework of almost stochastic dominance to investigate its performance. The goal is to verify whether a high leveraged ETF portfolio can outperform a non-leveraged ETF portfolio and further observe if extending the investment horizon can enhance performance. The research findings indicate that within the data period from 2014 to 2022, despite several market fluctuations, the investment performance of high leveraged ETFs was superior to that of non-leveraged ETF portfolios under the framework of almost stochastic dominance. Moreover, the longer the investment period, the stronger the advantage of high leveraged ETFs.

    目錄 摘要 I Abstract II 致謝詞 III 目錄 IV 圖目錄 VI 表目錄 VII 第一章 緒論 1 第二章 文獻回顧 4 第三章 研究方法 8 3.1 隨機優勢 ( Stochastic Dominance ) 8 3.1.1 一階隨機優勢法則( First Orders Stochastic Dominance ) 9 3.1.2 二階隨機優勢法則( Second Order Stochastic Dominance ) 10 3.1.3 極端病態偏好 ( Pathological Preference ) 12 3.1.4 幾乎一階隨機優勢( Almost First Order Stochastic Dominance ) 14 3.1.5 幾乎二階隨機優勢( Almost Second Order Stochastic Dominance ) 16 3.2 分散化投資組合 ( A Diversified Portfolio ) 18 第四章 實證結果 21 4.1 樣本來源與研究期間 21 4.2 簡單型投資組合－ASD實證結果 23 4.3 分散型投資組合－ASD實證結果 25 4.3.1 再平衡策略 ( Rebalance Strategy ) 25 4.3.2 1X ETF vs. 2X ETF ASD實證結果 27 4.3.3 1X ETF vs. 2X ETF vs. 3X ETF ASD實證結果 29 4.4 績效表現驗證 30 第五章 結論 34 參考文獻 35 附錄 37 圖目錄 圖3.1 一階隨機優勢 10 圖3.2 二階隨機優勢 11 圖3.3 幾乎一階隨機優勢違反面積比例 15 圖3.4 幾乎二階隨機優勢違反面積比例 17 圖4.4 槓桿型ETF投資組合績效比較 32 表目錄 表3.1 極端病態偏好實例 12 表3.1 ETF & LETF 投資組合以及其組成元素 20 表4.1 SPY、SSO、BND報酬率之敘述統計量 22 表4.2 簡單型投資組合AFSD實證結果 23 表4.3 簡單型投資組合ASSD實證結果 24 表4.4 再平衡策略敘述統計比較 26 表4.5分散型投資組合AFSD實證結果 27 表4.6分散型投資組合ASSD實證結果 28 表4.7 分散型投資組合1X vs. 3X ASD 結果 29 表4.8 分散型投資組合2X vs. 3X ASD實證結果 30 表4.9 槓桿型投資組合年度績效表現 31

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