Charles Ponzi, Bernard Madoff and the exponential function

The Ponzi scheme is a fraudulent investment scheme named after Charles Ponzi. The idea is simple. Investors are promised fabulous returns on money. A few investors cautiously bring in small change, and the money is returned with interest as promised. Reassured, these investors bring in larger amounts. Other investors join them. People ask questions on how the money can grow so fast. Answers range from gold and diamonds mines in Africa to philanthropic donors who crave anonymity. In reality, there is no investment. Money from new investors is paid to old investors, while the organizers of the scheme help themselves to some of it. As long as the returns are coming, few questions are asked. People who ask too many questions are even censured by others who have invested money in the scheme, and are reveling in their imaginary returns.

Ponzi schemes tend to be short-lived, with a few exceptions. One important exception may be Bernard Madoff, and we will get to him. In order to thrive, a Ponzi scheme requires a growing inflow of new investment, and to get this inflow, the returns have to be be large enough to induce greed. Charles Ponzi, for example, promised to double money in 90 days. At that rate, money grows to 16 times in a year, and 4000 times in 3 years - exponential growth. To be truthful, all investment at fixed interest rate grows exponentially. Money kept in a bank at 7% interest would double in 10 years, 16 times in 40 years and 4000 times in 120 years. Exponential growth is the norm. What is not normal is the fabulous rate promised by the Ponzi scheme. I suspect that a lot of Ponzi schemers lack an appreciation of the exponential function. Anyway, if Ponzi's scheme were to go on for three years, an investor who brought in a thousand dollars on the first day would be entitled to four million in three years. So long as the investor does not demand his money, all is well. But chances are that the investor of a thousand dollars, now thinking himself a rich millionaire, would want to spend a modest few hundred thousand of his millions. At this point, paying the investor becomes a challenge because inflow of investment money can never keep up with the rapid exponential growth of accounts payable. The game winds up.

It is not hard to see that the longevity of a Ponzi scheme is inversely related to the promised rate of return, but the rate of return must noticeably exceed that obtainable through legitimate sources so as to attract new investors. In this regard, Bernard Madoff took the game to the next level. His returns were consistent, and always better than the market, but not like Charles Ponzi's. His scheme lasted over a decade in the complete absence of investments, and swallowed over 50 billion dollars. His story carries a bold warning: A smart enough Ponzi schemer may get away with a lifetime of fraud. Madoff had no investment whatsoever. A combination of a mediocre investment scheme with fraudulent accounting that shows consistent returns could last many decades. The idea is similar to what Enron and other firms charged with accounting fraud did. Somehow, productive and deceptive activities tend not to co-exist harmoniously over time, which is a great blessing for investors. Still, it pays to be cautious.

There is only one effective antidote to the Ponzi bug - transparency. Never put money into an investment that hides information, whatever the excuse may be. Madoff hid information for decades claiming that his techniques were proprietary trade secrets - sounds legitimate, but no reason is legitimate enough. Another partially effective cure is diversification. There is something pitiful about people who lament the loss of their life's savings in a Ponzi scheme. It is as if they have failed to evolve in a fundamental manner. Not only were they naive or greedy or both, they never understood the eggs and baskets principle either. The law can and should punish predators, but it is impossible to protect those who willingly set themselves up as prey.