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Volume 34 - Numéro 1

March 2013

Is the Market Portfolio Efficient? A New Test of Mean-Variance Efficiency when all Assets are Risky - 15 March 2013

M. Brière, B. Drut, V. Mignon, K. Oosterlinck, A. Szafarz

The market portfolio efficiency remains controversial. This paper develops a new test of portfolio mean-variance efficiency relying on the realistic assumption that all assets are risky. The test is based on the vertical distance of a portfolio from the efficient frontier. Monte Carlo simulations show that our test outperforms the previous mean-variance efficiency tests for large samples since it produces smaller size distortions for comparable power. Our empirical application to the U.S. equity market highlights that the market portfolio is not mean-variance efficient, and so invalidates the zero-beta CAPM.

On the Bankruptcy Risk of Insurance Companies - 15 March 2013

Olivier Le Courtois et Rivo Randrianarivony

The fall of AIG proved that the insurance business is not immune to bankruptcy, contrary to the actuarial literature which postulates that insurance firms can survive forever. In this article we model the surplus process of an insurance firm firstly by a stable Lévy process, secondly by a double exponential compound Poisson process. We compute finite-time survival and bankruptcy probabilities under such hypotheses. To achieve this, we make use of the Wiener-Hopf factorization and compute bankruptcy formulas written in terms of inverse Laplace transforms. The Abate and Whitt, and Gaver-Stehfest algorithms are used to obtain numerical estimations. This article can be viewed as an illustration of a general approach to the bankruptcy of financial institutions.

Analysis and Comparison of Leveraged ETFs and CPPI-type Leveraged Strategies - 15 March 2013

Philippe Bertrand et Jean-Luc Prigent

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.