Probability-based scam of stock market investors is interesting

imageThe story went that investors in Baltimore were amazed by one stock broker who would always accurately predict the behaviour of stocks in the coming week.

For ten weeks straight, the broker had sent them letters correctly predicting how to invest in a certain stock that week.

The investors, impressed with this evidence of the broker’s skills, invested in him heavily. But there was no broker, and they never saw their money again. They had been duped using simple statistics.

Mathematician Jordan Ellenberg explained this example in a recent Guardian Science Weekly as he spoke about the relevance of basic mathematics to, as it were, real life.

The scammer in the tale simply sent out two template letters by the thousand, one predicting that a randomly chosen stock would rise and the other that it would fall.

With an effectively random chance of either outcome, it was probable that half the letters would turn out to be correct. The other half would be wrong, and be discarded as the useless junk mail failings of a low quality broker.

The key to the scheme though, lay in that probability. Send enough letters and the probability that there will be some recipients who receive nothing but correct predictions – for long enough to make the scam seem worthy of investment – is high.

1000 letters go out in week one, of which 500 are wrong. So of the remaining 500, in week two 250 recipients see another correct prediction. In week three, 125 receive correct letters, and so on, until only a handful of people have received all right letters.

But those few people may now have reason to believe that this is a broker who has accurately predicted the stock market for ten weeks in a row, not to mention people that may have jumped in earlier.

The apparently powerful incentive to move investment portfolios to the broker is nothing but chance and misdirection.

PS. In the podcast Ellenberg also cites another similar example, of something Christian Rudder the founder of OkCupid wrote was revealed by a meta-analysis of the data on that site. Significant numbers of people, he said, use the site by routinely copying and pasting the same text to hundreds of potential partners at once.

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