Abstract
Leveraged and inverse Exchange-Traded Funds (ETFs) have become increasingly popular in recent years and have attracted significant assets. This paper develops a very general mathematical framework for assessing the long-term performance of leveraged and short investment funds based on stochastic calculus. Our analysis allows for multi-asset and cross-asset class portfolios and explains the role of volatility and correlation of the underlying assets for the long-term performance of the strategy. Further, we show that there is an optimal degree of leverage that maximizes the expected future return of the daily re-balanced leveraged investment strategy that depends on observable market parameters. Thus, we develop an improved methodology for leveraged and inverse ETFs that adjusts the degree of leverage optimally to prevailing market conditions on a regular basis.
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