This document analyzes Harry Markopolos' findings regarding Bernie Madoff's $65 billion Ponzi scheme. It summarizes that Madoff claimed to use a "split-strike conversion" strategy to generate steady returns with low volatility, but in reality this should have earned close to the risk-free rate. The document outlines four red flags: 1) Madoff's returns were too high compared to what the strategy could produce. 2) He reported losses in only 6% of months which was improbable. 3) Option pricing skewness made his claimed strategy infeasible. 4) His equity positions far exceeded the size of the options market he said he hedged with.

1. Madoff $65 billion Trap Gaetan “Guy” Lion May 2010

2. Introduction Harry Markopolos wrote a book about his uncovering the $65 billion Madoff Ponzi scheme; and, his sharing with the SEC detailed findings in 1999, 2000, 2001, 2005, and 2007. But, the SEC never caught Madoff. This presentation is an analytical review of Markopolos findings.

3. Losses to Investors In a Ponzi scheme, the earlier investors get repaid by the later ones. So, it is not like the entire $65 billion was lost. Investors invested $36 billion in Madoff funds. They got back $18 billion. They lost $18 billion. They also thought they reaped $29 billion in gains that never existed.

6. Benford’s Law used in Fraud Detection Software This test would not have uncovered Madoff’s Ponzi scheme. The Gateway Fund (GATEX) used a strategy most similar to Madoff. It is a benchmark on how Madoff’s fund should have looked if it had been legit.

7. Detecting Fraud using Serial Correlation The greater the serial correlation of monthly returns the more probable such returns are manipulated. Madoff’s low negative correlation does not raise a red flag.

10. So, he has a long position in stocks He bought stocks at prices where the two lines cross. If stocks go up on the horizontal line he makes money (on the blue line) and vice versa.

11. He buys Puts to reduce losses The Put strike price is at the red line inflection point. If stock prices along the horizontal line decline (moving to the left) of the strike price, the Put is in the money and will cover additional losses. Buying a Put establishes a floor on losses.

12. He sells Calls to finance the Puts premium The Call strike price is at the green line inflection point. If stock prices along the horizontal line increase (moving to the right) of the strike price, the Call is in the money. This creates a cap on returns because you are forced to sell the stock at the strike price. This is to earn a premium on the Call to finance the Put premium.

13. Net result is much lower volatility Selling the Calls sets a low Ceiling on stock returns gains. Buying the Puts sets a Floor on stock return losses. Now the return profile looks very different than simply being long the stocks.

14. Problem: Skewness For the same premium level, you have to retain greater losses on the Put (red box top graph) than the gains you can retain on the Call (green box below). Skewness is really bad for a split strike conversion strategy. Skewness implication : Premium paid = Premium earned Losses retained > Gains retained

15. Skewness on S& P 100 Options on May 24, 2010 For about $6 you could sell a Call with a strike price of 510 on the S&P 100. This is 16.1 points away from the S&P 100 current level at the time of 493.9. You could use this $6 to buy a Put with a strike price of 455 or 38.9 points away from the current S&P 100 level. The distance of the Put strike price is more than 2 x the one of the Call strike price (38.9/16.1). That’s bad.

16. Skewness = Asymmetry At all option premium prices, the respective Puts’ strike prices are much further away than the Calls’ strike prices. We highlight the difference in strike price distance for a Call and a Put with a premium close to $6 as shown on the previous slide.

18. Percent of month with loss?! Markopolos states that Madoff’s record from 1993* to 2008 is unheard of in the hedge fund industry. 93.5% month gain… only 12 months losses out of 186 months. His loss frequency is only a fraction of the Gateway Fund (GATEX) that followed a similar strategy. And, that was during a wrenching time for capital markets including the 1997-1998 Asian currency crisis, the three year dot.com crash (2000-2002), and the onset of the financial crisis (2007 onward). *Data for GATEX goes only back to 1993. So, we cut off the time series at this point to make it comparable between Madoff and GATEX.

19. Madoff Expected Returns: Near Risk Free Rate To avoid almost all monthly losses, Madoff’s Put strike price should have been very close to the current price. This takes him almost out of equity returns and leaves him barely with a Risk Free Rate (even less if you factor skewness and basis risk).

20. Returns are way too high to be legit Madoff split strike conversion strategy should have earned close to the Risk Free Rate. Instead, it earned nearly three times that.

21. That’s Consistency!? Madoff perfectly side steps the Dot.com and housing bubbles.

22. No one can duplicate his returns!? Gateway Investment Fund (GATEX) used a similar but superior strategy to Madoff, but it did not come close to replicating Madoff risk-adjusted returns.

23. An Efficient Frontier Map This shows the combination of volatility (x axis) and return (y axis). GATEX that was expecting to do better than Madoff is already above the Efficient Frontier, reflecting a strong performance. But, Madoff’s returns are way above the Efficient Frontier. Can you beat the Efficient Frontier? Yes, but not by that much!

24. Madoff had to earn 15% before fees! Madoff was giving away the entire Hedge fund fee structure to Fund of Funds. This includes a 20% performance fee of returns and a yearly 1% management fee.

28. Financial Crisis & Lehman Chapt. 11 take out Madoff $8 billion investors redemption requests Lehman Chapt. 11 on 9/15/08 Lehman files chapter 11 on September 15, 2008. Within next couple of months, the S&P 500 loses 30% of its value. Investors flee to Treasuries. Their resulting yield drop by 175 bp. Investors request $8 billion in redemptions from Madoff. He is arrested on December 11, 2008.