Black Swans in the eyes of a White Swan

The more I study mathematics of finance, the more I feel that what I learn does not make the life easier at all. The whole study of financial mathematics is based on the assumption that what happened in the past will repeat in the same way in the future. If a stock had high volatility in the past, then the price of the option for this underlying stock will be high because it carries high risk. However, no matter how complex mathematics we use to analyze the world of finance and economics, our predictions do not go beyond predictions simply because we do not know the future. However, with the help of complex mathematical jargon and intellectual arrogance, we can easily be convinced that some people with special skills have power to estimate the future movements of the market and can help you make money from betting against the improbable ones.

Nassim Nicholas Taleb’s book “The Black Swan: The Impact of the Highly Improbable” is all about the criticism of over-mathematisation of the finance and economics. He starts his book with some autobiographical stories; a childhood in Lebanon, war time stories, advantage of having a Levantine heritage and ending up at prestigious Wharton Business School. Of course, he criticizes his formal schooling as it is largely based on Gaussian Bell Curve and Markowitz Portfolio Theory. His main attacking point in the entire book is Gaussian Distribution (Normal Distribution) which is not capable of catching the black swans (extreme rare events) therefore it is useless because history is made of black swans, not the white ones. Revolutions, uprisings, natural disasters, wars, economic recessions are all examples of these black swans which cannot be predicted through conventional statistical tools. Predicting the normal is nothing according to him as it can be done by everyone and it does not give any edge to anyone who can do it. Plus, normal events does not cause any change in the history. They are left to the oblivion shelves of the past.

In one part he writes “Those who spend too much time with their noses glued to maps will tend to mistake the map for the territory.” meaning that our models should not be mixed up with the reality itself. They are only models and should not give us over-confidence. In fact, the book basically reveals that the biggest problem in today’s financial world is the overconfidence on the mathematical models and graphs as if they are really saying something about future. The scientific expressions and mathematical jargon make outsiders intimidated and ultimately keep them away from understanding the black swans.

I cannot say that Normal Distribution should be accused of the market failures or the mathematicians who help building all those financial formulas can be blamed. The problem is the profit-hungry brokers and CEOs who do not understand the assumptions behind all those theorems. In the world of mathematics, we need to platonify everything so that simplified versions can give us simple results. For example, infamous Black&Scholes option pricing formula is nothing but a one-page derivation of option price under the assumption that arbitrage-free and complete markets, efficient markets, constant volatility and interest rates etc. There are at least 10 assumptions for B&S to work efficiently and we all know that this is impossible to happen. Then the decisions which are heavily based on these mathematical formulae will eventually fail. But should we than blame the mathematicians for this? Or the men who take all those assumptions granted without considering that randomness is far from our comprehension and it cannot be tamed with a simple formula.

Besides this, normal distribution is a perfect tool to understand the normal events in our lives. Taleb talks about standard deviation with dismay but never mentions other risk measures which are much more useful to evaluate the risk of loss in the world of finance. For example, expected shortfall with a reasonable confidence level can easily catch the possible black swans in the normal set of events. Naturally, no one can predict the earthquake or the consequences of an earthquake. We can perhaps have large disaster reserves in insurance companies so that in the event of a big disaster the losses will be compensated without making people suffer for long time.

After reading the book, I can only conclude that today’s financial system which allows making huge profits through transferring risk is only a sham but nothing else. I can understand transferring the risk in the time of a loss as it does not benefit anyone but just covers the loss. This is why I think insurance companies should be strictly controlled by the government and should not be allowed to invest their reserves into risky portfolios in search of profit. At the end of the day, the reason for the existence of the insurance company is simply to help people who lose their property/loved one/vehicle/business etc so that society will keep moving without getting interrupted. Therefore, they are not supposed to make huge profits from the money they collect from people who are simply apprehensive about their futures.

I also found his comments on capitalism versus socialism very naïve and ill-informed. His defense for capitalism was nothing but a childish aphorism. Here it is:

“Capitalism is, among other things, the revitalization of the world thanks to the opportunity to be lucky. Luck is the grand equalizer, because almost everyone can benefit from it. The socialist governments protected their monsters and by doing so, killed potential newcomers in the womb. “

Well, here what he says is let the world live in its own luck, let the lucky ones make billions and the rest can live with the income under a dollar a day. He forgets that being unlucky brings suffering, brings tears and blood, brings misery to those unlucky people’s lives. So shouldn’t a responsible government think a solution for these unlucky people and elevate their life standards? If you live the entire world to the luck, what happens is 3% of world population will own more than 80% of the wealth and 97% will share the remaining 20%. Despite some social democracies in some countries, we still have an ongoing injustice and turmoil is most parts of the world. Imagine, when we leave it to mere luck (meaning pure greed) and watch it.

Here is another naive aphorism from the writer: “If people were rewarded strictly according to their abilities, things still be unfair –people don’t choose their abilities. Randomness has the beneficial effect of reshuffling society’s cards, knocking down the big guy.”

But he forgets that it is not the randomness, it is the anger of people which knocks down the big guy. We should neither support the big guy nor knocking him down (it costs lives of innocent people too) as we should only be against the existence of the big guy because by the time he is being knocked down (Think about Egypt: how many years did it take to dethrone Mobarek? How many people, journalists, intellectuals, writers have suffered under his regime?) so many would be perished in one way or other. What we need is not ups and downs, we need happy people with happy futures. We don’t need innovations of iphones or ipads to be happy. We need a secured future in which children can grow up without the fear of nuclear disasters or the toxics of e-waste. The world keeps dumping the e-waste to Africa now (I just watched a documentary about these children who collects copper and steel to burn in the garbage and sell for a few pennies, unlucky ones! huh?).

I would like to imagine if Mr Taleb was not a son of privileged Lebanese family, was not able to attend privileged schools to learn many languages and the tricks of stock markets, was not lucky enough to write books on unlucky people, then would he be thinking in the same way? Yes, he is lucky in his own terms but does this mean that he needs to be blind towards those who are not as fortunate as him. People who are born to poor families, born to an African tribe or to a family in a Libyan desert cannot see the world as he sees and definitely cannot agree with him. How unlucky Mr Taleb is that he cannot be with majority of the people but only supports a few privileged lucky ones. Changing his definition of the black and white swans, I can call him a lucky white swan who thinks that the unlucky black swans need to exist forever and interrupting nature's randomness will make things worse. Therefore, one should ask "why do we have empathy, why do we need to help others, why do have the feelings like mercy, compassion, tolerance? If nature made us greedy -I don't believe it despite the avalanche of discovery channel documentaries on wild animals- then why do we need to have peaceful societies, international rules, sports events? At the end, the book is full of aphorisms of a white swan on why black swans should stay as black. I agree with the criticism of epistemological arrogance of finance minded people but since the book does not offer any solution to the problems of the world other than the writer's over confidence on mathematics and statistics, I consider it as a failure, yet it sold millions of copies. So what? Harry Potter sold even more!!!

PS: He seems he does not know anything about Central Limit Theorem as he never mentions it. The reason Gaussian Bell Curve is used largely in today's world is not the variables fit to normal distributions. The reason is when we take a large sample from any set of data, the sum of the values in any possible sample can be approximated by a normal distribution. Therefore, nature does not need to be normal for us to communicate through normal distribution. I think, he is not a mathematician and he just learnt the formulae of financial mathematic to apply to his portfolio, I can forgive him. However, talking about great Mathematicians like Gauss, Galileo, Russell in a way he is better than them makes me angry. I am sure it will make any decent mathematician angry to hear those comments from a man who is only a stock broker and a rich man, yet calling himself philosopher.