How Ponzi and pyramid schemes really work: cash-flow mechanics, why they run for years and the German cases P&R and S&K
Model the cash flow of a Ponzi scheme year by year, see why it can survive for a decade before collapsing, and learn what the P&R and S&K cases teach about warning signs.
What you will learn
- The difference between a Ponzi scheme and a pyramid scheme, and why both must collapse
- How to model the cash flow of a scheme and find the year it breaks
- Why schemes can run for ten years or more without anyone noticing
- What the German cases P&R (containers) and S&K (real estate) looked like from the investor's side
Explanation
A Ponzi scheme (German: Schneeballsystem) is an investment offer in which the "returns" paid to existing investors come from the deposits of new investors, not from real profit. The operator claims a business exists (trading, containers, property, crypto mining), but it is too small or does not exist at all.
A pyramid scheme is different in one detail: participants earn mainly by recruiting new participants, and each entry fee flows upwards. There is often no investment story at all. Recruiting-based schemes are banned in Germany under the law against unfair competition (UWG), while Ponzi schemes are prosecuted as fraud (Betrug) or breach of trust (Untreue).
Why both must collapse
A pyramid fails because of arithmetic. If each member must recruit six new members, the levels are 6, 36, 216 and so on. Level 12 would need about 2.2 billion people and level 13 about 13 billion, more than the population of the Earth. Everyone in the last two or three levels loses.
A Ponzi scheme fails because of cash flow. Every euro of promised return and every euro of redemption must be paid from new deposits. As long as new money grows faster than the payout obligations, the scheme pays reliably, which is exactly what builds its reputation. When inflows slow, which always happens because the pool of possible investors is limited, the cash balance falls and collapse follows within one or two years.
Why they run for years
- Payouts are modest and regular. Many schemes promise 6–15% per year, not 100%, which attracts cautious savers.
- Reinvestment. If most investors let their "profits" roll over, little cash leaves the scheme.
- A real business as cover. P&R really owned containers and S&K really owned buildings. Nobody counted whether the assets matched the sales.
- Respected intermediaries. Independent advisers earned commissions on each sale and had no incentive to ask hard questions.
The German cases
P&R (Munich, insolvency 2018). P&R sold shipping containers to private investors with a buy-back promise and fixed rental income. About 54,000 investors had claims of roughly €3.1 billion. The insolvency administrator found that around 1.6 million containers had been sold but only about 618,000 existed, a gap of about 980,000 containers or roughly 61%. He stated that the group had effectively been insolvent since about 2010 and had paid old investors with new money until March 2018. The founder died in 2019 before a verdict. By 2025 creditors had received about 20–21.5% of their claims.
S&K (Frankfurt, raid 2013). S&K sold participations in real-estate funds. After a raid in February 2013 the two founders were arrested; in 2017 the Landgericht Frankfurt sentenced each to eight and a half years in prison for breach of trust, with damage of about €240 million for roughly 11,000 investors, about €22,000 per person. Investor money was moved between funds and companies and spent on the founders' lifestyle.
In both cases the documents looked professional, payments arrived on time for years, and the sales channel was trusted advisers.
Worked example
Hypothetical example: a scheme promises 12% per year, paid in cash. Assumptions: the operator keeps 15% of every new euro for commissions and lifestyle; 20% of the capital outstanding at the start of each year is redeemed by investors; fees, taxes and interest on cash are ignored. New deposits per year: €1.0m, €2.0m, €3.0m, €3.0m, €1.5m, €0.5m.
| Year | New money | 12% payout | Redemptions | Operator take | Cash at year end | Investor balances |
|---|---|---|---|---|---|---|
| 1 | €1,000,000 | €0 | €0 | €150,000 | €850,000 | €1,000,000 |
| 2 | €2,000,000 | €120,000 | €200,000 | €300,000 | €2,230,000 | €2,800,000 |
| 3 | €3,000,000 | €336,000 | €560,000 | €450,000 | €3,884,000 | €5,240,000 |
| 4 | €3,000,000 | €628,800 | €1,048,000 | €450,000 | €4,757,200 | €7,192,000 |
| 5 | €1,500,000 | €863,040 | €1,438,400 | €225,000 | €3,730,760 | €7,253,600 |
| 6 | €500,000 | €870,432 | €1,450,720 | €75,000 | €1,834,608 | €6,302,880 |
Year 2 step by step: payout €1,000,000 × 12% = €120,000; redemptions €1,000,000 × 20% = €200,000; operator take €2,000,000 × 15% = €300,000; cash = €850,000 + €2,000,000 − €620,000 = €2,230,000.
Year 7 with no new money: obligations = €6,302,880 × (12% + 20%) = €2,016,922, but only €1,834,608 is in the bank. The scheme defaults in year 7, and investors believe they own €6.3 million against €1.8 million of real cash.
Common mistake
Practice activity
On paper: a scheme promises 10% per year and has €4,000,000 of investor balances at the start of a year. Investors redeem 25% of balances during the year, the operator keeps 10% of new money, and the cash at the start of the year is €600,000. How much new money must arrive this year so that the cash does not fall below zero?
Show solution
Obligations: payout €4,000,000 × 10% = €400,000; redemptions €4,000,000 × 25% = €1,000,000; total €1,400,000. Cash covers €600,000, so €800,000 must come from new deposits net of the operator's 10%: 0.9 × N = €800,000, N = €888,889. The scheme needs about €0.9 million of fresh money just to stand still, and more every year.
Limitations: real schemes have irregular redemptions and often stop paying selectively before the final collapse.
Key takeaways
- Ponzi schemes pay old investors with new money; pyramids pay recruiters with entry fees. Both are mathematically certain to fail.
- Modest, regular returns and high reinvestment rates let a scheme survive for many years.
- P&R sold about 1.6 million containers of which only about 618,000 existed; S&K caused about €240 million of damage. Both used real assets and trusted advisers as cover.
- Only independent verification that assets exist and produce the cash can distinguish a real business from a scheme.
Next step
In the next lesson you will study pump-and-dump campaigns, where the fraud happens in a public market and leaves a visible footprint in volume and price.
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