Anomalies in Taylor-Series; and Tracking-Errors and Homomorphisms in the Returns of Leveraged/Inverse ETFs and Synthetic ETFs/Funds
33 Pages Posted: 13 Jun 2010 Last revised: 3 Nov 2015
Date Written: 2015
Abstract
While Leveraged/Inverse ETFs, synthetic funds and synthetic ETFs have grown in popularity during the last fifteen years, there are many structural problems inherent in the legal/economic structure of these ETFs. These problems raise actionable issues of “Suitability” and “fraud” under US securities laws, because the advertised terms of most Leveraged/Inverse ETFs, synthetic funds and synthetic ETFs are mis-leading, and they have substantial tracking errors and can increase market volatility. This article contributes to the existing literature by: i) critiquing the structure of Leveraged/Inverse ETFs, synthetic funds and synthetic ETFs and the inherent decision-making processes (ie. creation and use of the ETFs; re-balancing; biases), ii) showing how Put Call Parity Theorem affects the accuracy of Leveraged/Inverse ETFs and synthetic ETFs; iii) analyzing and showing how Leveraged/Inverse ETFs increase market volatility; iv) explaining the biases and effects inherent in Leveraged/Inverse ETFs and synthetic funds/ETFs such as new types of tracking errors and the downward drift in returns which are Homomorphisms – and which were omitted in Reigneron, Allez & Bouchaud (2011); Avellaneda & Zhang (2010); Bouchaud & Potters (2001); Kenett, et.al. (2012); Tang & Xu (2013); Charupat & Miu (2011); Hongfei & Xu (2013); and Dobi & Avellaneda (2012); and v) explaining an anomaly in the Taylor Series. Hence, these issues have implications for analysis of nonlinearity and chaos in markets.
Keywords: portfolio management, risk management, Indices, Put-Call Parity, ICAPM, complexity
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