I admit that it may sound a bit ludicrous, but I have been thinking for a while on how to devise mathematical models of Ponzi schemes and pyramid schemes. I assume that most of you know what a Ponzi scheme is, but for the ones who don’t here’s a concise definition from Wikipedia:
A Ponzi scheme is a fraudulent investment operation that involves paying abnormally high returns (”profits”) to investors out of the money paid in by subsequent investors, rather than from net revenues generated by any real business.
It is clear that a Ponzi scheme is unsustainable and that it will (sooner or later) collapse due to its own weight. The scammer promoting such a scheme will be owing ever-increasing amounts of money to the investors, and as soon as the influx of new investment capital is not enough to pay off the debt plus interest, the scheme will collapse. By the way, Ponzi schemes have happened for a long time, but the scheme bears the name of its most “illustrious” scammer, Charles Ponzi (1882–1949) , who ran a huge fraudulent operation in the U.S. in 1919 and 1920.
[ Charles Ponzi in 1920 - photo courtesy of the U.S. government ]
From the July 16, 1974 edition of the San Diego Daily Transcript:
At the height of his success in Boston in 1920, Charles A. Ponzi was hailed by those he was cheating as the greatest Italian who ever lived. “You’re wrong,” he said modestly, “there’s Columbus, who discovered America, and Marconi, who discovered radio.” “But, Charlie, you discovered money,” they told him.
Note that:
- the early investors in a Ponzi scheme will make money if they drop out before the whole thing collapses. On the other hand, the later investors will lose money.
- there’s a money transfer from the later investors to the scammer promoting the scheme and the earlier investors, so to say. As such, one has the incentive to be an earlier investor provided that the fraud lasts long enough for one to profit.
- an investor might be aware that there’s fraud going on and still invest if he thinks that the scheme will last a bit longer before it collapses so that he can get his money back and earn the interest.
This is interesting.
The question is how to devise mathematical models of Ponzi schemes. Which variables to choose? Which assumptions to make? It is not nearly as easy as one might think at first glance, I must say. An over-simplistic model is easy to devise, but it will tell us little. I have been building some models, and I will most likely write about them in future posts.
For the time being, if you are curious about this topic, here are a couple of papers I found at SSRN:
- The Optimal Design of Ponzi Schemes in Finite Economies (by Utpal Bhattacharya)
- Dynamic Efficiency, the Riskless Rate, and Debt Ponzi Games Under Uncertainty (by Olivier Blanchard and Philippe Weil)
Tags: Charles Ponzi, Finance, Fraud, Ponzi schemes
February 3, 2008 at 5:52 pm |
I suspect that most of the potential readers who are lured to this post by the word “modeling” in the post’s title will be utterly disappointed when they realize that we are discussing mathematical models here, and NOT the kind of models that show up on the cover of Sports lllustrated’s famous swimsuit issue ;-)
February 3, 2008 at 7:10 pm |
We call it Gaidar or Chubais scheme in Russia, sorry for offtopic :)
As for the topic, I’ll be eager to see your solution and results.
February 3, 2008 at 8:12 pm |
Are those Yegor Gaidar and Anatoly Chubais, the ones responsible for the “shock therapy” of the wild post-USSR times in the early 1990s?
February 4, 2008 at 12:29 pm |
Yes i think you are right Rod, Chubais is pretty well known for his role in some scandals..
though i don’t think it can be called a Ponzi scheme if you put it in parallel with the original Charles Ponzi scheme (i call it original for the sole reason that the term is derived from his name, i acknowledge that there must have been such frauds very often from the time cash and trade is in existence) and compare it with how financial professionals these a days define a Ponzi scheme..but this is just a preliminary opinion..i am not very sure.
but i guess Vladimir can give a better elaboration on that part..
and i have been thinking of modeling them as well! and you are right..it is not as easy as it looks like in the first look!
February 7, 2008 at 7:05 am |
[...] Ponzi Schemes II As I wrote a few days ago, one of ongoing projects is to devise mathematical models of Ponzi schemes. In my [...]