Mathematical proof Ponzi, pyramid schemes will fail
Fin24
Cape Town - Faced with empty wallets and rising costs, thousands of South Africans are placing their faith in “get rich quick” schemes that lure desperate consumers with promises of unrealistic investment returns.

However, whether a Ponzi or a pyramid scheme, it can be mathematically proven that such schemes will eventually collapse and leave investors with nothing.

Ponzi and pyramid schemes are essentially the same, with both relying on contributions from new investors to pay existing investors the promised returns. These are usually totally unrealistic and not comparable to returns achieved by legitimate savings and investment products.

While investors in a pyramid scheme know that they need to recruit new members to maintain the flow of funds, Ponzi schemes claim to make legitimate investments but instead use the funds to enrich founders rather than for any legitimate business purposes.

Given the current furore around MMM, described as a social financial network, Mike McDougall, CEO of the Actuarial Society of South Africa, was motivated to do some number crunching to show in simple, yet no uncertain terms, why such schemes are destined to fail.

“It can be stated with absolute certainty that these schemes will eventually collapse, leaving many people financially destitute, while only the founders and a few early participants make considerable gains,” he said.

“There are essentially two reasons for this. Firstly, if a scheme is paying out more than is being earned, it will run out of money. Secondly, such schemes need continuing growth in new members to sustain payments to existing members, and the reality is that they will ultimately run out of new investors,” he said.

“The only uncertainty is when the collapse will happen, which depends on how quickly the fund is growing and how much bigger the declared yields are than the actual investment earnings on the funds invested.”

Example of scheme

To demonstrate, McDougall points to the simple example of a scheme that begins with 100 members who each invest R1 000 with a promised return of 30% per month. Every month 100 additional members join the scheme and each invests the same amount until the scheme collapses. Members receive their first payment the month after they make their investment.

In this example, the scheme begins with 100 members and total funds of R100 000. In the second month, there are 200 members and the fund closes with R170 000 after paying dividends of R30 000 to the founding members.

The total dividends paid rapidly escalate each month as the membership base increases, until the scheme reaches its seventh month. In its seventh month, the scheme begins with R70 000 and receives an additional R100 000 from new investors. However, the scheme must now pay total dividends of R210 000 to its numerous members, leaving it in debt of R40 000. Instead of R300 each investor only gets R243 and the scheme collapses.

Table: From hero to zero

Month Investors Starting fund balance (R'000) New money (R'000) Dividends (R'000) Closing fund balance (R'000)
Inception 100 0 100 - 100
1 100 100 100 30 170
2 100 170 100 60 210
3 100 210 100 90 220
4 100 220 100 120 200
5 100 200 100 150 150
6 100 150 100 180 70
7 100 70 100 210 -40

Propping the scheme up

“With more rapid growth in members or lower pay-outs, the scheme would continue for longer, but the result would ultimately be the same,” notes McDougall.

As pyramid schemes rely on snaring new members, he emphasised that you should be wary of being dazzled by testimonies of high returns by people already in a scheme.

“The reality is that by the time you join a scheme, you may just be propping the scheme up so that early joiners can profit at your expense. You and other new investors may never recoup even your initial capital amount, let alone make a return on your investment,” he warns.