Madoff's supposed option magic

Everyone in the investing universe has heard of Bernard Madoff by now, and the press has reported a mixture of details of the asset management strategy he claimed to be using to generate incredibly smooth highly positive returns. Because Madoff used an option fund as cover for his deceit, I feel compelled to step in to rescue the instruments themselves from the allegedly tainted hands that claimed to wield them.

First off, let's make it crystal clear that Madoff's alleged deceit had absolutely nothing to do with options. A Ponzi scheme is an out-and-out fraud, and if he executed a Ponzi scheme, Madoff's purported use of options was no more at fault than Ponzi's own deceit was the fault of the international postal coupons that he proposed to use as an investing arbitrage.

When discussing the use of options, the trading community always applies a veneer of mystical-sounding lingo. In keeping with tradition, the investment strategy Madoff claimed to be using is commonly called a "split strike conversion." For those unfamiliar with the lingo, I'll try to make this jargony strategy more comprehensible and explain the risk/reward trade-offs. For those familiar with some option lingo, the payoff of the split strike conversion is the same as writing an at-the-money call spread in the same way that a covered call is the same as a cash-secured put. Let's go into a little more detail to understand how this strategy has the potential to make money, and the risks involved.

Madoff's strategy would be better described as taking bounded risk. Using the S&P 100 Index as an example, if an investor buys the index for $500, then sells the upside gains above $510 and buys downside protection below $490, the investor has limited gains or losses to $10. If the index rises above $510, the investor has been paid in advance for his commitment to sell it for $510 if asked, or to allow another investor to "call" it away at $510. If the stock falls below $490, the investor has paid someone to agree to buy it for $490, or to allow the investor to "put" the stock to the counterparty at $490. Therefore, capital gains on this strategy are limited to $10 if the stock rises to $510 or above, and losses are limited to $10 if the stock falls to $490 or below. In addition, the strategy captures any dividends that might be paid on the index before the option expires, plus the net payment (if any) from selling the upside "call" and buying the downside "put" protection.

There are a few ways a strategy like this can make money over time, but the potential profits can be traced to two different sources: riskless profits from market mispricing or return from exposure to risk.

The profit opportunities from mispricing are:

• Getting paid more for the upside protection than you pay for the downside protection.
• Collecting dividends paid on the stock that aren't fully reflected in the option prices.
• Collecting the bid/ask spread on the options as a market maker while paying a lower bid/ask spread on the underlying stock.

The profit opportunities from exposure to risk are:

• Selling the upside closer to the market price than the downside protection purchased (for example, selling the upside from $510 limiting gains to $10 but only buying protection below $480 allowing losses of up to $20). This is akin to selling insurance with a low deductable but buying insurance with a high deductable.
• Trying to pick exactly when to enter the investments (market-timing).
• Expecting that the index rises on average more frequently than it falls over the life of the strategy (the magnitude of the increase doesn't matter as much since the strategy has sold the upside).

In short, the strategy can generate profits either by taking small arbitrage profits or taking calculated timing and index exposure risk.

An Extra Layer of Complexity
Now that we understand that Madoff's strategy can be simplified to buying a security, selling much of the upside gains, and buying downside protection, we can add the one extra level of complexity that Madoff claimed to be using. Madoff was buying baskets of individual stocks representing part of an index, selling the upside exposure on the entire S&P 100 Index, and buying downside protection using options on the entire S&P 100 Index. Because the diversification inherent in 100 stocks makes indexes less volatile than underlying stocks, the index options are less expensive than individual stock options on the same 100 stocks. Therefore, any income generated from the net sale of options would be diluted by the lower price of the index options, but any net hedging costs would also be lower. Another possible reason for using index options to hedge is the greater liquidity in the index option market relative to the underlying stock option market, theoretically allowing more money to be put to work using the strategy. However, it is quite odd that he claimed to use the S&P 100 Index when the far more liquid S&P 500 options were available for his multibillion-dollar fund.

By hedging using index options, the strategy is exposed to an additional risk and an additional potential source of profit from exposure to risk: The subset of stocks purchased can change price differently than the options used to hedge them over the life of the options. For example, if one owned more Enron than was represented in the index on which the option was used to hedge, one would have lost a bunch of money when Enron suddenly went bankrupt. But the index used as a hedge didn't decline as drastically, so the put options didn't spike in value. However, the exposure to stock concentration could also be a source of profit. If the basket of stocks picked outperformed the underlying index on average, the exposure to risk could generate large profits.

Reasonable Expectations
If we take all of the small market inefficiencies out of the equation, the strategy Madoff claimed to be using should have generated small profits in up markets from the limited upside return, small profits in down markets from the limited downside return, plus a small amount from inefficiencies, and possibly a little upside or downside over time from the performance of the basket of stocks relative to the index. However, if we examine the claimed returns on the first page of this fact sheet we can see that the returns were clearly different from reasonable expectations.

Net Net
Overall, the strategy Madoff claimed to have been using was simply a mechanism for capturing small potential inefficiencies in the options market, and taking some limited investment risks. The strategy could have been pursued in a viable investment hedge fund to generate returns, but likely the returns wouldn't have been as spectacularly positive and smooth as Madoff had claimed, and there was a distinct risk of a material loss from an Enron-like scenario as described above. Certainly, if we compare how this strategy should have behaved in up and down markets, the results he was claiming would not have passed the sniff test.

Forgive me for hammering the point home, but what brought Madoff's fund down was not the use or misuse of options, it was allegedly the use of a classic Ponzi scheme. If the allegations are true, he likely took few option positions at all. Again, a Ponzi scheme is simply a fraud that pays old investors the cash contributed by new investors, producing the false appearance of investment returns. Ponzi schemes blow up when funds start flowing out of rather than into the fund, and deleveraging has caused capital to pour out of all investments like a waterfall. Had the market correction not happened on a grand scale, Madoff's alleged scheme could well have persisted for many more years.