Risk Latte - Small Probabilities and Rare Events - What the Lehman Bozos didn't Understand

Small Probabilities and Rare Events - What the Lehman Bozos didn't Understand

Rahul Bhattacharya
September 15, 2008


In June 2008, if you had asked anyone other than, perhaps, David Einhorn, as to what was the probability of Lehman Brothers going bankrupt he or she would have said very small. Very, very small indeed! In 2007 the bank's net profit had set a record of $4.2 billion. The bank, until June this year, had not even reported a single quarterly loss ever. But then within three months the bank went bust.

How rare is this? Some would call it bizarre but it is nothing other than a truly rare event. And this is what those bozos - the so called exotic traders and Ph.D.-turned-quants - on the Manhattan dealing floors didn't understand.

In finance, just as in life, the probabilities don't matter. In fact, we are not even sure if the concept is a sound one. It doesn't matter whether an event has a 99% chance or a 1% chance of happening. What really matters is if the event happens what is the payoff? That is what motivates option traders, investors, short sellers, hedge fund mangers, and in the broader context, scientists, engineers, entrepreneurs and explorers.

If Christopher Columbus had calculated the probability of his finding westward route to Asia in 1492, American wouldn't have been discovered. If scientists and medical researchers today and in the past centuries were to be guided by the probability of making new discoveries and inventions then this world of ours would not have emerged from the Dark Ages.

David Einhorn, the prescient hedge fund manager, realized early on this year that Lehman was going to fail, and fail pretty soon. What were the chances of that happening, the so called "probability"? We are sure he didn't have a clue; in his mind it could have been anything, 0.5%, 1% 10% or even 30%. But he didn't care simply because if that happened, if Lehman were to indeed go bankrupt soon, he would make a killing if he shorted the stock at those levels. And he did.

The possibility of a payoff, and in fact, a disproportionate payoff, is what matters in the financial markets and in life. If a future payoff is "disproportionate" to the existing state of an economy then speculators will engage in that act. What we term as "disproportionate payoff" can also be called a "non-linear payoff" in math terms. It is the non-linearity of the payoff - that if an event happens in the future, the payoff will be far greater that than the efforts that we make to get to that event in the future - that give the financial options their value, their convexity.

You don't need a Ph.D. to understand that. If you are dumb and make a living earning a salary and skimming bonuses off a company's balance sheet then you need to spend ten minutes with Nassim Taleb to understand this concept. The Lehman bozos, including the Big Dick should have spent ten minutes with Nassim Taleb on the first Monday of every month.


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