Analysis and Comparison of Leveraged ETFs and CPPI-type Leveraged Strategies

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 provide and analyze various properties of the value process of a leveraged ETF. We examine its main statistical properties and point out that there is some probability that the stock index price increases while, at the same time, the leveraged fund decreases. This is an event that is difficult to accept for an investor in such a fund. In the continuous-time framework, we prove an equivalence result stating that a leveraged ETF can also be viewed as a CPPI fund with a floor proportional to the portfolio value itself. Next, from a more practical point of view, we compare Leveraged ETFs and Leveraged CPPI having 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, using Monte Carlo simulations, we compare the Leveraged ETFs and Leveraged CPPI return distributions by means of their moments as well as by relying on Omega and Kappa performance measures.