槓、反ETF追蹤誤差與影響因素分析──臺、日、韓之比較

The Factors Affecting Tracking Errors of Leveraged and Inverse ETFs in Taiwan, Japan and Korea

近年來槓桿型與反向型ETF成長非常快速，至2016年3月底止，全球已有1,046檔此類商品，總規模達712億美元，十年成長率達1,073%。亞太地區目前僅臺、日、韓有此類商品之發行與交易，規模雖僅159.8億美元，但十年成長率高達4,104%，遠高於全球增長率。槓、反ETF但是否能按所標榜之倍數來追蹤標竿指數受到標竿指數之變動、波動度與評估期間之影響。本研究首先檢視標竿指數之前後期自我相關程度與追蹤誤差之關係，理論上指數的自我相關若為正（負），槓、反ETF就會超越（落後）所標榜之標竿指數倍數關係，稱為複利效果。本研究也進一步探討持有期間長短、指數波動度與追蹤誤差之關係。研究結果發現：（1）就單日追蹤績效而言，在臺、日、韓12檔槓、反ETF中，僅有日本TOPIX 2x、韓國KODEX 2x、韓國KODEX -1x以及韓國TIGER 2x達成其所宣稱之2倍效果。（2）當持有時間短（5天）時，指數報酬率的自我相關並不影響追蹤偏離度，但中（20天）、長期（60天）之下，指數自我相關對槓反ETF之追蹤偏離度即具有顯著的影響。（3）2倍ETF之追蹤誤差隨標的指數報酬率增加而減小，隨著指數波動度之增加而增加，但不顯著。（4）反向ETF之追蹤誤差隨著標的指數報酬率增加而增加，隨著波動度之增加而減少。

The markets of leveraged and inverse (L&I) ETFs have been growing tremendously in recent years. Globally speaking, the market recorded 1,046 L&I ETFs at the end of March, 2016 with asset under management (AUM) amounting to 71.2 billion USD. In Asia Pacific region, L&I ETFs are only observed in Taiwan, Japan and South Korea with a total AUM 15.98 billion USD. The ten-year growth rate in AUM, however is much higher in Asia Pacific region (4,104%) than in global market (1,073%). Whether the fund managers can track the multiples of the benchmark index return accurately depends on the return and volatility of the index as well as the investment horizon. Theoretically, positive (negative) autocorrelation of the underlying index will induce outperformance (underperformance) of the funds NAVs’ relative to the multiples of the index return. Yet value destruction occurs gradually as the investment horizon gets longer. This research intends to investigate the relationship between the autocorrelation of index returns and the tracking performance of L&I ETFs. We also probe how index movements, volatility and investment horizon influence the tracking errors. The results show that (1) for one-day period, TOPIX 2x, KODEX 2x, KODEX -1x and TIGER 2x ETFs are the only ETFs that performed according to the claimed multiples during the sample period. (2) Autocorrelation of the underlying index returns does not affect the tracking performance for short holding period. The markets of leveraged and inverse (L&I) ETFs have been growing tremendously in recent years. Globally speaking, the market recorded 1,046 L&I ETFs at the end of March, 2016 with asset under management (AUM) amounting to 71.2 billion USD. In Asia Pacific region, L&I ETFs are only observed in Taiwan, Japan and South Korea with a total AUM 15.98 billion USD. The ten-year growth rate in AUM, however is much higher in Asia Pacific region (4,104%) than in global market (1,073%). Whether the fund managers can track the multiples of the benchmark index return accurately depends on the return and volatility of the index as well as the investment horizon. Theoretically, positive (negative) autocorrelation of the underlying index will induce outperformance (underperformance) of the funds NAVs’ relative to the multiples of the index return. Yet value destruction occurs gradually as the investment horizon gets longer. This research intends to investigate the relationship between the autocorrelation of index returns and the tracking performance of L&I ETFs. We also probe how index movements, volatility and investment horizon influence the tracking errors. The results show that (1) for one-day period, TOPIX 2x, KODEX 2x, KODEX -1x and TIGER 2x ETFs are the only ETFs that performed according to the claimed multiples during the sample period. (2) Autocorrelation of the underlying index returns does not affect the tracking performance for short holding period.