By Michalis Zaouras on March 25, 2009

Where has rational expectations gone

I think this is very typical from a young economist to question. But the latest ponzi scheme that has hit the world financial markets, has raised this question again. To be honest the concept of the credit crunch crisis violates partially the idea of rational expectations, even though the bubble has been rationalized but an adaptation of expectations. To get to my main point, there has been quite a fuss with Madoff's ponzi scheme, 'deceiving' some of the elite in the financial market industry, starting from worldwide bank institutions to celebrities. Some of them pointing out that they were the victims of a plot designed by an ingenious, prestigious trader, excuse me for the abuse of defining Madoff as a trader. But is that all?

To make things clear, Madoff has been widely promising return on investment above 10% and in some cases as much as 47%. In my view there are two cases, these people were honestly declaring that they were tricked or they knew that there is something wrong going on but they were betting that Madoff will not get caught. Someone may believe that these attitudes are fully rational, but not in my view because the probability of this scheme to fail is almost one. It will fail because at some point when a crisis, negative productivity shock or demand driven shock you can call it as you want to, hit the financial market then he would not be able anymore to deliver the excess returns that he promised, because he will attract attention of the regulators and get caught. Also at this point, there will be no arrival of new clients, he will not have enough money to finance his promises to his existing clients, there will be deterioration of his position even further and as a result of that go bust. So why would anyone suspicious of a ponzi scheme join in, that is not rational at all.

To be honest there is a simple answer for my question, a person knowing of this scheme can join for a short time hoping to leave the scheme soon enough. For example, someone that has been promised a return of 15%, she can get the value of her money within 5 years, without reinvesting you will need 7 years. In contrast if you save with interest 5% you will need 15 years for your money to double. So you need the scheme to run successfully for a long period of time to find it worthwhile to join. To be more precise, you will need the scheme to survive into the medium run because we know that in the long run it will fail. But Madoff’s story with his scheme dating from 90’s and according to some from 80’s, points out that this is possible to achieve. It will be interesting though to see if any of Madoff’s clients left the scheme years before, or if they were reinvesting. If the last holds it makes them even more irrational because as the years passes, then the probability to get caught increases.

My answer to the statement above is a simple backwards induction argument, a rational investor who knows about the scheme and knows that it has been running for some time he will not enter because the probability of the scheme to be revealed to financial authorities is too high. This means that Madoff at medium run will have a bigger problem to find new clients even if a crisis is not around and the probability to fail to its promises increases, but then an investor at short run will not invest at all because the probability of failing even at medium run is too high. The backward induction argument holds, if we assume rational expectations.
I would like to close my comment with a great story that a friend of mine told me. During the 80's a guy had a car accident, he survived the accident but it caused him a reasoning problem, he became too rational. This is a true story and psychologists have explored further his case. An example of his reasoning problem is the following, when this guy wanted to have a lunch he had to choose first if he would take it at city centre or not, he would then visit all the places to find the most suitable one and then he would visit all the restaurants to get the best deal and at the end of all these, it was dinner time. So people are not as rational as we believe, based at least on our definition of rationality. Conclusion, are we missing something?

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