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Leveraged exchange-traded funds (ETFs) are designed to provide more than 100% of the exposure of the benchmark. Since July 2006, ProShares has launched a series of Ultra ETFs and UltraShort ETFs. The Ultra ETFs are designed to double the daily returns of the underlying index, while the UltraShort ETFs are designed to provide twice the inverse performance of the underlying index on a daily basis. In November 2008, Direxion introduced triple-leveraged ETFs and triple inverse-leveraged ETFs. All these ETFs have gained acceptance from the market and attracted substantial trading volume.
Starting from the seminal work by Cheng and Madhavan [2009], researchers have pointed out the decay of the leveraged ETF (LETF) and the inverse leveraged ETF (IETF) if one holds these ETFs for a long horizon.1 The noteworthy fact is that both the LETF and IETF decline over the same time period. For example, here is one quote from aSeeking Alpha article:2
Since mid-November (of 2008 to June 2009), the triple long financial ETF (FAS) is down 71% to $10.38, while the triple short financial ETF (FAZ) is down 95% to $4.43. Over the same time period, the financial index that the ETFs track is up 7%! Go figure.
A number of people have argued that one can short both an LETF and IETF, and this strategy appears attractive because it does not depend on the direction of the underlying index.
In this article, we provide a detailed study of the strategy of shorting a pair consisting of an LETF and IETF. First we study the basics and show under what circumstances this strategy makes a profit or loss. This strategy is really a bet on the mean reversion of the underlying benchmark; its profitability does not depend on the direction of the underlying benchmark. As long as the underlying benchmark moves in a mean-reverting fashion, that is, the return goes up one day and down the next day, or vice-versa, this strategy generates a profit. However, if the benchmark moves in a trending fashion, going up for several days or down for several days, the strategy of shorting the ETF pair results in losses.
We derive an approximation formula for the expected returns of the strategy and show they depend on...