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http://www.cbsnews.com/news/the-man-who-figured-out-madoffs-scheme-27-02-2009/

Asked how long it took him to figure out something was wrong, Markopolos said, "It took me five minutes to know that it was a fraud. It took me another almost four hours of mathematical modeling to prove that it was a fraud. "

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    $\begingroup$ I think they used factor models which showed that no reasonable combination of assets could achieve such returns. $\endgroup$
    – emcor
    Commented Aug 15, 2015 at 13:20
  • $\begingroup$ The Sharp ratio was a useful tool. "The quantitative analysis Markopolos conducted, showing that over 96% of monthly returns were positive; correlation with the stock market was negligible at around 6%; and the Sharpe ratio was outsize, ranging between 2.5 and 4.0 for most time frames, was literally unbelievable." Source $\endgroup$
    – Jessie
    Commented Dec 27, 2023 at 23:41

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You can find everything you want to know about this here (and in a very readable and easily reproducible form):

How Students Can Backtest Madoff’s Claims by Michael J. Stutzer (2009)

From the abstract:

Markopolos’ writings neither described nor included any specific backtests of the strike conversion strategy. Fortunately, a backtest is relatively easy to implement, using just a few, free data series found online, a single spreadsheet, and the Black-Scholes formula. I developed a disguised, simplified backtest as a home assignment for undergrads students, and extended it into a longer, more realistic paper assignment for another student. Based on those experiences, I describe herein a suitable backtest methodology and questions that may be answered through it.

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