Leveraged Funds: Robust Replication and Performance Evaluation

Leveraged and inverse ETFs seek a daily return equal to a multiple of an index' return, an objective that requires continuous portfolio rebalancing. The resulting trading costs create a tradeoff between tracking error, which controls the short-term correlation with the index, and excess return (or tracking difference) - the long-term deviation from the leveraged index' performance. With proportional trading costs, the optimal replication policy is robust to the index' dynamics. A summary of a fund's performance is the implied spread, equal to the product of tracking error and excess return, rescaled for leverage and average volatility. The implied spread is insensitive to the benchmark's risk premium and offers a tool to compare the performance of funds tracking the same index with different factors and tracking errors.