What the odds of a start-up billionaire being eaten by a shark?

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Warning: No Sharks Here

Jersey City, US: A new trading software is installed on the servers of a global financial services firm. A technician forgets to copy a piece of code to one of the eight servers used to automatically route equity orders. New commands passed through this eighth server produce very unexpected results. For about 45 minutes, the system rapidly buys and sells millions of shares in 148 quoted companies. By the time the company identifies the glitch and liquidates all the unwanted trading positions, it has a loss of $440 million on its hands. This is more than its entire revenue from the previous quarter. Its shares sank by 32 percent. On a subsequent day, they fell another 62 percent. The firm never recovers from the setback. Within four months, it agrees to be acquired by a rival.     

How high would you estimate the chances of a chain of events so remarkable? Well, the above is a true story. It all took place on August 1st, 2012 and it involved a firm called Knight Capital Group. Yet, I guess that whatever probability you attached to that outcome, it was too high.

In our daily lives, we are constantly faced with uncertain situations about which we must make a probability estimate. Investors face such situations more frequently than most. Participating in any risky venture involves an estimation of the likelihood that it all goes horribly wrong – swimming at a beach where sharks have been spotted, buying an out-of-favor security program, or launching a start-up in the hope of becoming a billionaire. Although we might be able to estimate the probabilities, research suggests that we do not perceive probabilities in line with their stated values. Instead, we tend to see low probabilities as being more likely than they really are.

This tendency was first described by the Nobel-Prize-winning psychologist, Daniel Kahneman, and his long-standing research partner, Amos Tversky. They observed the tendency of experimental subjects to attach exaggerated weights to very low-probability outcomes. Consequently, subjects perceived rare events as being much more likely than they really were.

Who's afraid of a stock market crash?                    

In the case of positive events, like winning the lottery, subscribing to ‘the next Google’ in an IPO, or betting that a few lines of missing computer code bankrupt a trading firm, we consider them to be more likely than they are and tend to overpay for the opportunity to participate. In the case of negative outcomes, like shark attacks and stock market crashes, the overweighting of low probabilities causes us to be more fearful than we need to be. Here the tendency is to overpay for protection from the negative outcome, in the form of insurance or option premiums. In both cases, the misperception of probabilities diminishes investors’ returns over the long-run.


The media doesn’t help to improve our probability estimations. Over thousands of years of human evolution, we have learned a useful rule of thumb: things that we commonly see often are more probable than things that we rarely see. So, if we base our probability estimates of an event on the ease with which it comes to mind, then we ought to fare rather well, as common events come more easily to mind than rare events. Modern media, however, disrupts this rule of thumb. As everyday events are not particularly newsworthy, the media bombards us instead with a series of interesting, but ultimately rare stories. It is the plane crash, not the safe landing, that makes the news; the smiling jackpot winner holding an oversized cheque, not the dismayed punter tossing a losing ticket into the trash. Hence, our rule of thumb encourages us to attach high probabilities to rare outcomes.

Base rates: Boring, but bountiful

Avoiding the disappointment and costs associated with the probability of mis-weighting requires that we are all better calibrated. To do this we must constantly remind ourselves of the base rate, the underlying probability of an event occurring without intervention, also known as the prior probability. Admittedly, attending to base rates is not much fun, not least because they tend not to move too much. It is especially tedious in the immediate aftermath of a rare event, i.e., just after a market meltdown or a blow-out IPO. Yet it is precisely these situations that present opportunities for the shrewd investor. While others overweight the low probabilities of a repeat, the base-rate-attentive investor might find some mispriced securities.