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Bell Curve Loathing


Humans are saddled with the instinct to oversimplify. To ignore risks or overestimate knowledge.


A few months have elapsed from the article in which I wrote about the distinct and everlasting danger of selling a cheap tail – "selling the probability that something terrible will not happen and only get mere pennies for the contract."

I suggested that in order to engage in such a strategy for anything more than an Olympic cycle; you must involve the recognition that one's investment edge must be very nearly flawless. "Let that investment edge be quantitative, qualitative, experiential, fundamental, macroeconomic…let it come from the stars' alignment with the sun, or over your neighbor's picket fence, or in a dream. Whatever your style – whatever the basis for that edge – you better have every confidence in the world that your conclusion is the right one if, on the other end of that analysis, you decide to sell cheap vol."

Inevitably, the world has mocked this free advice ever since I first gave it. In markets, what has worked will continue to work. Simple as that. Any ridicule I have received is almost certainly my own fault, anything free is worth nothing.

In life, as in investment portfolios, one's submission to the above dimension reduction, simplification - can lead (will likely lead) to hardship, penury, pain, and disability even, all with some describable probability. To walk around thinking that we are invulnerable is to court such risks. It is to invite them.

Such simplification finds its very basis in our physiology. Our ancestors' choices multiplied over and over again, producing evolutionary returns to our forebearers who, in turn, were able to quickly recognize the difference between having a meal and being a meal. All the Cro-Magnon scholars who dithered and debated the stripes in the bush as being a feral pig and not a lion; they are no longer with us, nor is their DNA. Thus we find ourselves, modern man, limited in our ability to grasp reality. We are unable to recognize that short straws are there to be drawn.

By admiring the mathematics, and limitations, of options pricing theory; we can gain perspective on the not-intuitive concept of selling cheap tails. This practice takes time and a not-trivial amount of previous mathematical training. Perspective can be found by practicing the craft of options arbitrage. This will take even more time, along with an effort to unlearn the mathematics of options pricing theory.

But it can also be had by misfortune, which is both less and more costly all at once.

Over the course of several years my first born son became inflicted, known now in hindsight, by a rare form of meningitis. Slowly paralyzed and literally consumed by this pathogen; we sought out all the best medical insight available to help diagnose the condition. It had zero effect.

Each expert, bell curve in one hand and stethoscope in the other, could only look within the confines of his own experience and his own written and read literature in an attempt to explain the symptomology . But such attempts revealed the limits of their experience , my son's case simply fell outside of their bell curve. Exhausting one medical specialty, we moved to the next, seeking answers from diagnosticians using the same mistaken tools and achieving the same terrifying non-answer each time. With these 'experts,' we exhausted every possible probability that fell within the heart of the medical bell curve; thinking that if we just continued to look for experts with yet another pediatric sub-specialty, we might strike upon the diagnosis. And by focusing on the defined – on the known – probabilities which by definition reside in the heart of the diagnostic bell curve, we were implicitly selling a tail.

Only now do we know that contracting such meningitis is a function of several highly independent, individually improbable events taking place in a specific series. It's the equivalent to winning life's anti-lottery three weeks in a row. It is decidedly not the type of diagnosis that comes from theorizing – not the type of diagnosis that comes from collecting a series of symptoms and comparing it against the 'literature.'

We concentrated on the heart of the diagnostic bell curve at first. We were wrong and that cost us time. Delaying the identification of the pathogen – delaying the diagnosis - made it worse. Who is to say precisely what that decision has cost? But selling that tail and focusing on the heart of the diagnostic probabilities was – is – a haunting mistake.

In my firm's past explorations of probability theory, complexity, and the role of rare 'tail' events in financial markets, our focus has always been on the potential loss to income, to assets. But tails, too, can have a personal expense incalculable on a monthly P&L; an expense that is incurred with ferocious constancy; an expense that has a face, a personality, a name.

Humans are saddled with the instinct to oversimplify. To ignore risks or overestimate knowledge. Such intellectual anchors have cost; whether you understand those costs viscerally or theoretically matters little. So long as you understand them ahead of time.

No positions in stocks mentioned.

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