Analysis and Comparison of Leveraged ETFs and CPPI-Type Leveraged Strategy

Among leveraged funds, leveraged ETFs are designed to achieve multiple exposure (e.g., twice) to some financial index returns, on a daily basis. In this paper, we derive an analytical expression for the value process of a leveraged ETF. We analyze it as a convex constant allocation portfolio strategy and examine its properties. In the continuous-time framework, we prove an equivalence result stating that a CPPI with a floor proportional to the portfolio value itself is also a constant allocation portfolio strategy. Next, we focus on another CPPI type strategy with a specific variable leverage. This type of Leveraged CPPI portfolio is not fully equivalent to a Leveraged ETF because the leverage is reduced in falling markets as well as bounded from above. We derive a quasi explicit expression for the value of such Leveraged CPPI. Then, we compare Leveraged ETFs and Leveraged CPPI by means of Monte Carlo simulations. Finally, we present an empirical study and comparison of the Leveraged CPPI (illustrated by the SGAM Leveraged CAC 40 ETF) and of the Leveraged ETF (issued by Lyxor), to highlight differences in their behavior and performance