Tracking error decomposition and return attribution for leveraged exchange traded funds

Leveraged exchanged traded funds (LETFs) have been severely criticized in recent years.They have been attacked in the academic literature, the trade literature, and the popular press.Most often, the focus of these attacks is the volatility drag on return introduced by the interaction of leverage, dynamic rebalancing and compounding.But return enhancement is simultaneously generated by these same forces whenever there is a trend in the underlying index's return.Often overlooked in the many studies of this subject are the effects of financing costs incurred in the creation of leverage, and the costs and benefits introduced by the employment of professional management. Collectively, the trend, volatility, financing and management components of LETF return, give rise to tracking error.In this paper, we introduce a framework for a complete decomposition of LETF tracking error into its component parts.By simple extension the framework makes possible a very straightforward procedure for return attribution that can be used to compare LETFs written on the same index, and to judge the performance of management.