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

32 Pages Posted: 8 Jun 2011

See all articles by Philippe Bertrand

Philippe Bertrand

AMGSM-IAE Aix-en-Provence, Aix Marseille University, CERGAM; KEDGE Business School

Jean-Luc Prigent

University of Cergy-Pontoise - ThEMA

Date Written: June 7, 2011

Abstract

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.

Keywords: Leveraged ETF, CPPI, Constant mix strategy

JEL Classification: C6, G11, G24, L10

Suggested Citation

Bertrand, Philippe and Prigent, Jean-Luc, Analysis and Comparison of Leveraged ETFs and CPPI-Type Leveraged Strategy (June 7, 2011). Available at SSRN: https://ssrn.com/abstract=1859235 or http://dx.doi.org/10.2139/ssrn.1859235

Philippe Bertrand (Contact Author)

AMGSM-IAE Aix-en-Provence, Aix Marseille University, CERGAM ( email )

Chemin de la Quille - Puyricard
Aix en Provence, 13089
France

KEDGE Business School ( email )

Domaine de Luminy - BP 921
BP 921
Marseille, PACA 13288
France

Jean-Luc Prigent

University of Cergy-Pontoise - ThEMA ( email )

33 boulevard du port
33 bd du Port
F-95011 Cergy CEDEX
France

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