槓桿型及反向型ETF追蹤誤差與套利之研究

An Investigation of Tracking errors and arbitrage of Leveraged and Inverse ETFs

蔡林峻(Gene Tsai-Lin)

指導教授 ： 黃漢青

中原大學/商學院/財務金融研究所/碩士(2017年)

https://doi.org/10.6840/cycu201700440

摘要

摘要
本研究分為三部分來探討槓桿型ETF及反向型ETF之追蹤績效及套利策略建構績效。第一部分檢驗T502X及T50反的單日追蹤績效，並探討其追蹤績效是否隨牛熊市的變化，而產生結構性改變。結果指出兩檔ETF的單日績效皆顯著異於其目標倍數，兩ETF單日報酬的正負向效果不具對稱性，且當市場從牛市轉熊市時，T502X及T50反的報酬項會產生結構性改變，而市場自熊市轉為牛市時，兩ETF的報酬項僅T50反會產生結構性改變，T502X則無此現象。
第二部分探討槓桿型ETF及反向型ETF自身的前日成交量、前日報酬率，是否與槓桿型ETF及反向型ETF追蹤績效偏誤有關。研究發現對兩ETF而言，前日成交量為影響其偏誤率的因素，推測可能是成交量的多寡對ETF的流動性造成影響，進而影響其偏誤率。另外T502X之前日成交量對其偏誤率有顯著的正向關係，T50反之前日成交量對偏誤率有顯著的反向關係；而兩ETF前日報酬率的係數均不顯著，故前日報酬率不為偏誤因素。
第三部分中擬訂了兩種策略，探討利用兩ETF單日報酬與目標倍數報酬間的偏誤率來套利的可行性及報酬績效。實證結果發現，若使用本研究擬定的「高低估判斷策略」，在考慮了交易成本後，僅T50反組合中採用偏誤率為±1.5及±2的進場標準其總報酬仍為正值。其餘各組合報酬為負值的原因除了遭交易成本侵蝕之外，基金動態調整及每日重新平衡機制的執行成效不彰亦是可能原因之一。但投資人仍可利用偏誤率為±1.5及±2的進場標準在T50反組合中進行有風險套利。

關鍵字

槓桿型ETF ； 反向型ETF ； 追蹤誤差 ； 套利

並列摘要

Abstract
This paper investigates the tracking error and arbitrage of leveraged and inverse ETFs. We test one-day tracking performances of Taiwan 50 Bull 2X ETF and Taiwan 50 Bear -1X ETF and investigate whether the tracking performances produce a structural change in bull and bear markets. We find that one-day performances of two ETFs are significantly different from its target. The positive and negative effect of one -day performance is not symmetric. When bull market changes to bear market, two ETFs returns have structural changes. Specifically, when bear market changes to bull market, only Taiwan 50 Bear -1X ETF return has a structural change.
We also investigate whether the prior-day’s volume and the return of the leveraged and inverse ETFs affect the tracking performances bias. The prior-day’s volume is the influencing factors for two ETFs, implying that the inference of volume may affect ETFs’ mobility. On Taiwan 50 Bull 2X ETF, the prior-day’s volume has a positive relationship on tracking performances bias. As for Taiwan 50 Bear -1X ETF, the prior-day’s volume has a negative relationship on tracking performances bias. Nonetheless, the prior-day’s returns of these two ETFs are not the influencing factors.
Lastly, we use the bias rate between single - day ETF and target multiple to develop two tactics to explore the arbitrage feasibility and reward performance. The result shows that if by using the "tactics of overestimate and underestimate", as well as considering the transaction cost, the outcome for the combination of Taiwan 50 Bear -1X ETFs would come to a bias ratio of ±1.5 and ±2, and all the other total remunerations would still be positive. The other combination would still be negative, other than the transaction cost been corrupted, the moving adjust and daily rebalance are not as effective as expected could be one of the reasons too. However, the investors, could still use the bias ratio of ±1.5 and ±2 along with "tactics of overestimate and underestimate" for the combination of Taiwan 50 Bear -1X ETFs as the risk of arbitrage.

並列關鍵字

Inverse ETFs ； Leveraged ETFs ； Tracking errors ； arbitrage

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