Monday, December 15, 2008

The Impossible Economics of a Ponzi Scheme

Bernard Madoff will be the Guinness Record Holder for running the largest Ponzi scheme. However, he will not hold the record for being the best Ponzi schemer of all time. To be the best, you need to time your exit and get out of town before the inevitable collapse. The economics of this house of cards is illustrated in the following table. It is linked to a spreadsheet that estimates the best time for grabbing your passport and making a hasty exit.

The numbers in the table are based on the following assumptions. You can change the growth rates in the linked table and see how the date of inevitable collapse changes.
  • The beginning contribution is $1 million. Each year thereafter the amount contributed by the unsuspecting investors increases by 5%
  • The expected amount that investors think they have in the fund each year is equal to the amount from the previous year compounded at the fictitious return (12%) plus contributions less withdrawals for the current year.
  • Withdrawals each year are equal to 5% of what investors think they have in their accounts based on the assumed fraudulent returns.
  • The actual amount in the fund consists of net contributions for the given year plus last years real balance compounded at the after-Ponzi rate of return. For example, if the actual amount earned on the fund is 3% and the Ponzi manager takes 6% then the after-Ponzi rate is -3%.
  • The criminals take-home pay is equal to a given percentage of the actual amount in the fund in the previous year. In this case a 6% Ponzi tax is assumed.

Assuming there are no expert financial analysts who might get suspicious, and given recent history that seems unlikely, this scheme could last 26 years. You can try out your own parameters and calculate your own get of of town date. One interesting insight is that a higher promised return can reduce the cumulative take-home pay for the criminal. A promised return of 20% will break the bank in the 19th year and and almost cut in half the cumulative profits. Because of a wealth effect created by the higher fictitious return withdrawals increase, cutting the life of the scam. Given that too high a promised return will also decrease credibility, the best promise seems to be an above normal but not exorbitant return. This is likely what Madoff promised.

The obvious factors that hasten the collapse during a recession include a decline in contributions, an increase in withdrawals, and a reduction in the underlying real rate of return.

Google Spreadsheet

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