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

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Abstract
A very popular derivatives combination position is to own an underlying asset, buy an out-of-the-money put to protect the downside and finance the put by writing an out-of-the-money call that caps potential profit on the upside. The position is known as a collar, a split-strike conversion, or several other names, depending on the market. Bernie Madoff called it a split-strike conversion and stated that following the strategy with equity index options was how he achieved consistently high returns with very low volatility. As we have now learned, he actually employed the more direct strategy of reporting fictitious returns and covering investors’ withdrawals by stealing the funds of other investors in a vast Ponzi scheme. This article analyzesMadoff’s claimed returns and shows that they were essentially impossible from trading split-strike conversions. Bernard and Boyle then extend the analysis to establish theoretical properties of the returns that can be achieved by the strategy, including bounds on the m...

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