Modeling the Re-Balancing Slippage of Leveraged Exchange-Traded Funds

16 Pages Posted: 27 Aug 2013

Date Written: August 27, 2013

Abstract

Leveraged exchange-traded funds are designed to track a multiple of the daily return of an underlying benchmark index. In order to keep a fixed exposure to the benchmark index, leveraged ETFs have to re-balance their positions everyday, generating a structural ’re-balancing slippage’ which has been documented in several empirical studies.

This paper quantifies the re-balancing slippage of leveraged ETFs by developing a tractable model for the dynamics of leveraged funds, which takes into account the impact of active management by leveraged ETFs. We characterize the re-balancing strategy of the leveraged fund and its impact on the value of the leveraged ETF and we model its dynamics in discrete-time. We show that the re-balancing impact systematically diminishes the daily return of the leveraged ETF and that, over a holding period of more than one day, leveraged ETFs develop a tracking-error which can be decomposed between a compounding deviation – that has already been documented and quantified in previous studies – and a re-balancing deviation. The study of the continuous-time limit of the multi-period model allows us to obtain analytical formulas for the re-balancing slippage and the tracking-error of the leveraged ETF. Our theoretical results are consistent with empirical studies which find that tracking-error and re-balancing impact are larger in periods of high volatility and for leveraged ETFs with negative leverage ratios.

Keywords: leveraged ETF, ETF, liquidity, active management, fund re-balancing, regulation

Suggested Citation

Wagalath, Lakshithe, Modeling the Re-Balancing Slippage of Leveraged Exchange-Traded Funds (August 27, 2013). Available at SSRN: https://ssrn.com/abstract=2316855 or http://dx.doi.org/10.2139/ssrn.2316855

Lakshithe Wagalath (Contact Author)

IESEG School of Management ( email )

1 Parvis de la Défense
Paris, 92044
France

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