The Mysterious Letter: A Story about Survivorship Bias

In his book Fooled By Randomness: The Hidden Role of Chance in Life and in the Markets, Nassim Nicholas Taleb tells a story of a mysterious letter that convinces you to invest money in the predictive power of an offshore trading fund. The beauty of the story is that it's a great illustration of survivorship bias that perfectly conveys how fallible we are to it.

You receive a letter from a trading firm informing you that a given market will go up over the course of the next month. Obviously you're suspicious of falling for a scam so you ignore the letter, which actually proves to be correct in its predictions. The next month you receive another letter from the same company stating the market will go down in the month ahead. Again you ignore it and again the prediction turns out to be correct. You receive another letter the third month, and yet another one in the fourth. Each time the predictions come true and you begin to trust the mysterious company that keeps sending them to you. You may even start to feel a little special that you have been singled out to receive this highly valuable market information. So much so that in a moment you would now rather forget, you invest all your savings in the company and you never receive another letter, or see your hard-earned money again.

You go and share your misfortune with a close friend and find out that he too received the same letter, only his letters stopped arriving after the second month. He tells you that the first letter was correct in its predictions, while the second one was wrong. It didn't take you very long to figure out what happened.

The con artist must have started out with a relatively large sample of addresses (or email addresses), say 10,000. He or she divided this initial sample into two groups and sent a bullish letter to the first group and a bearish letter to the second group. When the market proved itself to be bullish the group that received the bearish prediction was abandoned, leaving 5000 in the bullish group. The con artist repeated the process, removing a further 2500 from the second mailing (the market was bearish in month 2 so those that received bullish letters were abandoned). The process was repeated in month 3 (leaving 1250 recipients with correct predictions) and again in month 4, leaving 625. Of those 625 you were one of only a couple hundred victims who were suckered into investing in the fund.

Why did you fall for this trick? The answer is simple, you were compelled by the accuracy of the predictions. Why? Because you only saw the winning predictions!

We are all suckered into believing all sorts of things due to our susceptibility to the survivorship bias, but Taleb's message is not just about helping us to avoid being scammed by con artists, it's about just how much of what we take for granted is merely a phenomenon of randomness.

'I am not saying that Warren Buffet is not skilled;' Taleb says elsewhere in his book, 'only that a large proportion of random investors will almost necessarily produce someone with his track records just by luck.'

So next time you're tempted to use a signal service that claims to have a proven track record of accurate predictions, or to invest in a fund manager who has just beaten the market for the 3rd consecutive year in a row, ask yourself two simple questions:

1. How many signal services or fund managers had to fail for me to stumble across this “winner”?

2. How likely is the success of this signal service/fund manager to be purely a result of random chance?

Remember that more often than not we are only presented with the “winners”, those selected from a far larger pool of possible candidates. The same thing holds for the findings of scientific studies in peer reviewed journals, or the items on the daily evening news. How many studies that you have never heard about didn't find any correlation between eating chocolate and longer life? How many stories that were not deemed newsworthy didn't make the cut on last night's news roundup?

Did you know?

The GBP/USD pair is widely referred to as “cable”. The term dates back to the 19th century, during which the exchange rate between the U.S. dollar and the British Pound was transmitted across the Atlantic via a huge cable that ran across the ocean floor and connected the two countries.

Word of the day
"Broadening Formation" - A chart pattern that is observed when there is significant increase in the price movements of a currency pair, yet without a clear direction.
Pro Tip

Never open a trading account with a non-regulated broker.