Leveraged ETFs and CPPI-Type Strategy : Theory, Simulation and Empirical Study

Leveraged and inverse ETFs are designed to achieve a multiple exposure (positive or negative, e.g., 2x or -2x) of some index returns on a daily basis. Recently, some controversy surrounding leveraged ETFs has appeared in the U.S. market and focused mainly on the performance results delivered by these products over extended periods of time.In France unlike in the U.S., among the first of these leveraged funds were managed with a slightly modified Constant Proportion Portfolio Insurance (CPPI) strategy. Examples include SGAM ETF Leveraged CAC 40 and SGAM ETF Bear CAC 40 launched on the 19th of October 2005 by SGAM Alternative Investment.In this paper, we will derive derive an analytical expression for the value process of a leveraged ETF analyzed as a constant allocation portfolio strategy and then analyze its properties. Then, we establish a CPPI equivalence result and give the value formula for a static leverage strategy. We then propose some comparisons between Leveraged and SGAM portfolio strategy. We first derive an analytic expression in discrete time for the SGAM portfolio value then we conduct some comparison by the mean of Monte Carlo simulations. Finally, we present an empirical study of the SGAM fund and of a CAC 40 LETF issued by Lyxor to highlight their distinct behavior and performance