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Federer As Probabilist

I am playing quite a lot of tennis these days. Actually, "these days" would more accurately be described as "for the past five years", more or less the period of time ellapsed since I left my derivatives marketing job. Anyway, thanks to my new lifestyle I have managed to hit quite a few backhands lately. I am now playing better than ever, in part thanks to the more habitual practice, but mostly thanks to my new coach ("pro" would be the posher term). Not only is he a great guy to swap volleys with, but he has crucially taught me a completely new perspective about the game. For tennis, you see, is basically all about probability distributions.

What am I saying exactly? Am I implying that you need a PhD to shine on the grass (clay would be more appropriate here in Spain)? Is tennis, a la derivatives, about to be overtaken by quants? No, not really. What I am saying (what my coach tells me) is that real players (read Roger Federer and his peers) are constantly calculating probabilities in their heads prior to hitting the ball. Clearly, these calculations are done at record speed, in an almost intuitive manner. Tennis pros choose each particular stroke to the ball depending on the assumed probability of hitting a successful return. As a rule (so am told) you should never try a selection where odds are worse than 70% (seven out of ten times the ball should get in). Of course, many times you may be forced by your opponent to hit something that usually only works 30-40% of the time. But provided that you are free to choose, only go for the highly probable stroke.

This probability-driven approach bothers me slightly, because I have a tendency to go for the glory-seeking point-achieving applause-arousing difficulty-filled shot, which I only manage to conquer 10-20% of the time. It is a great pleasure when you score, but it is a strategy that in the long run would make you lose a game. Clearly, you can´t win a game of tennis when you are missing 80% of your tries.

The key here is that points obtained through boring, conservative, yawn-causing shots are worth exactly the same as those obtained via gloriously-challenging, beautiful complex ones. Thus the importance of probability distributions. To win, your shots must get in at least 60-70% of the time. Thus, you must select strokes that are assigned by your distribution a probability of at least 60-70%. Here and there you may try the odd low probability sensational shot (especially if you lead 6-0, 5-0), but please make it the exception not the norm.

This probabilistic reality has several implications. First, it deprives fans of the best possible shots. Clearly, few professional players would gamble when there is a trophy at stake. I see it even at the amateur and veterans levels here. Guys who take wild chances during friendly harmless exchanges (resulting in highly exciting play full of extraordinary moments) choose a much more prudent route when it comes to "official" matches.

Second, it makes glory attainable through conservatism, not daring. The best route to winning is for a player to restrain, not encourage, his most creative instincts. Take less of those 40% shots, more of those 80% shots. Of course, by definition the better players are those whose 80% shots are equivalent to others' 40%-shots, but the point is that the point-equivalency reality of tennis heavily discourages everyone from deviating from the path most travelled.

Third, in tennis there is no Black Swan. The rare highly unlike event will NOT have a destabilizing shocking highly-altering impact. The unimaginably impossible return backhand will count no more than one point. Its practial relevance will be absolutely minimal. It won´t be remembered five minutes after it happened. It won´t belong to history (except in the odd chance that it became the match's winning point, at which level its relevance would have been complexity-neutral).

In finance, unlike tennis, the presence of black swans is guaranteed by the fact that the unlikely event counts more than the normal event. A market crash and a 0,1% drop do not count the same. The amounts of money lost are not equal. The payout is not digital, as it is in tennis.

For Federer et al, black swan-searching strategies make no practical sense (apart from the good feeling inside and the round of enthusiastic applause). They would be a certain route to the poorhouse. Looking for the low probability, rare event would get these players nowhere in the grand scheme of things. Those wishing for Wimbledon silver (unlike option traders) have zero incentive to venture into Extremistan.

ptriana@profesor.ie.edu

Country Black Swan

Earlier in the day I was listening to a song by country artist Joe Nichols and couldn´t help thinking about the Black Swan and those who profit from it. Here is country music´s homage to all those who believe in fat tails:

My dad chased monsters from the dark He checked underneath my bed An he could lift me with one arm Way up over top of his head He could loosen rusty bolts With a quick turn of his wrist He pulled splinters from his hand And never even flinched In thirteen years I'd never seen him cry But the day that grandpa died,I realized

Unsinkable ships sink Unbreakable walls break Sometimes the things you think could never happen Happens just like that Unbendable steel bends If the fury of the wind is unstoppable I've learned to never underestimate The impossible

And then there was my junior year Billy had a brand new car It was late,the road was wet I guess the curves was just too sharp I walked away without a scratch They brought the helicopter in And Billy couldn't feel his legs Said he'd never walk again But Billy said he would and his mom and daddy prayed And the day we graduated,he stood up to say:

Unsinkable ships sink Unbreakable walls break Sometimes the things you think could never happen Happens just like that Unbendable steel bends If the fury of the wind is unstoppable I've learned to never underestimate The impossible

So don't tell me that it's over Don't give up on you and me 'Cos there's no such thing as hopeless If you believe:

Unsinkable ships sink Unbreakable walls break Sometimes the things you think could never happen Happens just like that Unbendable steel bends If the fury of the wind is unstoppable I've learned to never underestimate The impossible

Wormholes Exist!

This is what The Economist says in its latest issue regarding last week´s market mayhem: “According to Goldman Sachs, the latest jump in the Vix took it eight standard deviations from its average. If conventional models are correct, such an event should not have happened in the history of the known universe. Then again, the move in energy prices that caused the collapse last year of Amaranth, the hedge fund, was a nine standard-deviation event. Perhaps modellers do not know the universe as well as they would like to think”.

I ain´t no physicist but I think this analysis by the indispensable London-based publication hints on something revolutionary when it comes to the science mastered by Einstein, Feynman and the like. Thanks to wild market movements such as those witnessed a few days ago and thanks to conventional finance theory we are in on a very important secret. An earth-shattering revelation. Possibly the biggest discovery by humankind ever. Now, indisputably, we know. Wormholes do exist.

You are probably asking how dare I make such a daring statement, especially when it comes from a physics-illiterate individual. What allows me to display such inexcusable boldness? Where is my proof?.

I just said it. Real-world market movements and finance theory, that´s my proof. I mean, only the existence of wormholes that allow convenient travel between different universes can explain the fact that certain beings currently present on earth would produce models that assume that the markets behave Normally. Clearly, those beings must be from a different universe. That´s the only possible explanation for their reticence to admit the obvious about our universe, namely that rare events take place so often that perhaps they shouldn´t be dubbed rare anymore (“peculiar” perhaps?). These modellers have to have come from another, wildly dissimilar universe, where apparently Normality does truly rule supreme. Having been raised in such a placid environment it seems only reasonable that they find it very hard to accept the harshly chaotic realities of our world. Rather than adapt to the new universal circumstances, they keep their unwordly assumptions intact, producing models that stubbornly resemble only the realities that they left behind many stars ago. In a way, then, they are like guests who refuse to behave according to the customs of the host.

In the movie Contact, the character played by Judie Foster travels through a wormhole and upon reaching her final unknown destination is greeted by a mysterious alien figure disguised as her beloved father. Once she is back on earth, no one believes her story. No one buys that wormhole stuff. She is almost treated as a lunatic. And yet, after contrasting market realities with conventional market theory, one is very tempted to conclude that that female astronaut was not misleading anyone after all. It certainly looks as if some of today´s finance theorists may have arrived here using the same method of transport that allowed the fictional Dr Ellie Arroway to enjoy one last grasp of her deceased parent.

Probabilistic Prohibition

I am no probability expert (while I did gain a graduate degree where the Statistics department played a key role I haven´t really worked on probability-related issues ever since), but it seems to me that the assumption of Normality when it comes to the financial markets shows strong correlation with that other famously misguided imposition, namely Prohibition in America´s 1920s.

Just like Prohibition forbade regular folks from (legally) drowning down their sorrows, Normality “forbids” investors from taking the markets beyond certain levels. Such probabilistic assumption denies individuals the capacity to cross certain lines, explore certain territories, discover certain realities. It is, thus, a very constraining assumption. A tyrannical one, you might say. Just like with any form of reactionary totalitarianism, individuals are judged to be of limited capabilities, requiring pre-set centrally-imposed stringent regulations. They are assumed to be unable to reach beyond certain limits, forever confined to a restricted existence.

In sum, a financial theory world ruled by Normality is a world where humans (the only ones that can move a market) are prohibited from realizing their full potential, where they are caged in a dull universe of severely reduced possibilities, where freedom is only a word. Perhaps Prohibition isn´t the only historical parallel with the Normality assumption after all. Do I hear .....ism?.

To all those eager to break free from the Normality dictatorship, history may provide a comforting message. Prohibition and ......ism eventually did, of course, spectacularly fail. Why? Simply put, because they run dramatically counter to human nature. People (generally) want to drink. People (usually) want to be free. If one tries to set artificial limits on humans natural desires, ambitions, and capabilities, the eventual end result is bound to be one of failure.

Real-life markets show us with astounding regularity that investors (who, despite occasional evidence to the contrary, are all to human) also want to be free. They want to spread their wings and be able to explore any possible price level, no matter how remote, no matter how inaccesible, no matter how unthinkable. They want to realize their full potential, and invariably do so.

The theoretical straightjacket imposed by Normality seems as much at odds with humanity as were Prohibition and .....ism. Inhumanely unrealistic. Inhumanely unworkable. And yet, all too tempting for certain freedom-denying technocrats.

ptriana@profesor.ie.edu