Madoff

Mr. Madoff ’s Amazing Returns: An Analysis of the Split-Strike Conversion Strategy

Carole Bernard∗ Phelim Boyle†‡

University of Waterloo Wilfrid Laurier University May 18, 2009

Abstract It is now known that the very impressive investment returns generated by Bernie Madoff were based on a sophisticated Ponzi scheme. Madoff claimed to use a splitstrike conversion strategy. This strategy consists of a long equity position plus a long put and a short call. In this paper we examine Madoff’s returns and compare his investment performance with what could have been obtained using a split-strike conversion strategy based on the historical data. We also analyze the split-strike strategy in general and derive expressions for the expected return, standard deviation, Sharpe ratio and correlation with the market of this strategy. We find that Madoff’s returns lie well outside their theoretical bounds and should have raised suspicions about Madoff’s performance.

Keywords: Madoff, split-strike conversion strategy, performance measurement, derivatives.

University of Waterloo, email: c3bernar@uwaterloo.ca. Corresponding author. Phelim Boyle is with the School of Business and Economics, Wilfrid Laurier University, 75 University Avenue West, Waterloo, ON, N2L 3C5, CANADA. email: pboyle@wlu.ca. Tel: +15198840710 extension: 3852 ‡ We thank Prof. Gurdip Bakshi for giving us the implied volatility skew data. We would like to acknowledge support from the Natural Sciences and Engineering Research Council of Canada. We also thank Petr Kobelevskiy for excellent research assistance and M. Suchanecki for his careful comments on a previous version of this paper.

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Mr. Madoff ’s Amazing Returns: An Analysis of the Split-Strike Conversion Strategy

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Introduction

In December 2008, the investment operation of Bernie Madoff was exposed as a giant Ponzi scheme1 . Madoff had attracted a wide following because he delivered consistently high returns with very low volatility over...