This is an analysis of how skewness in option prices made it impossible that Madoff could have simultenaously avoid nearly all monthly losses and achieve net zer hedging costs.

1. How Skewness would hurt Madoff proclaimed strategy . Guy Lion May 2010 That was another red flag Madoff was running a Ponzi scheme

3. 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.

4. 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 the investor against any additional losses as he can sell back the stock at the strike price. Buying a Put establishes a floor on losses.

5. 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 or ceiling on returns because you are forced to sell the stock at the strike price. This is to earn the premium from selling the Call to finance the premium you pay on the Put.

6. 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 as shown a few slides back.

7. Mapping the Skewness challenge For the same premium level at same stock price, a Put is more expensive than a Call. Thus, you have to retain a greater level of losses (red box top graph). And, you can keep only a smaller proportion of gains (green box below). Similarly, the Put coverage (blue box above) provides less coverage than the gains you have to give up by selling the Call (orange box below). Even if your net option premium is zero, volatility insurance is really expensive.

8. Skewness 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 skewness. And, that’s bad. Madoff indicated he hedged his portfolio with S&P 100 options of around 1 mth maturity to cover all monthly losses.

9. Skewness curve 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.

10. Skewness: Implied Volatility Also, the greater the strike price distance from the current S&P 100 level the greater the Puts Implied Volatility. Meanwhile, for Calls the greater the strike price distance the lower the Implied Volatility. Thus, the greater the strike price distance from the current S&P 100 level the greater the skewness or disparity in premiums between Puts and Calls. This is bad. At any strike price distance from the current level of the S&P 100, the Puts have a much higher Implied Volatility vs the Calls. Implied Volatility is the major driver of option prices. This indicates that Puts are much more expensive than Calls.

11. Skewness: Implied Volatility (cont.) This compares Implied Volatility vs premiums. Remember the higher the premium the shorter the strike price distance from the current S&P 100 level. The smaller the premium price, the greater the difference in Implied Volatility and strike price distance between Puts and Calls.