Next to being a successful trader, Taleb has written several highly influential books in the field of statistics, philosophy and finance. The first book he has written is Fooled by Randomness, in which he presents the idea that modern human beings are in general unaware of the existence of randomness. Instead of being aware of randomness, they tend to explain random outcomes as if they are non-random. He states that people overestimate causality, e.g., they see elephants in the clouds instead of understanding that they are in fact randomly shaped clouds that appear to our eyes as elephants. Furthermore, we look for explanations even when there are none and thereby tend to view the world as more explainable than it really is.Perhaps the most well-known book by Taleb is his bestseller The Black Swan, The Impact of the Highly Improbable. This book focuses on the extreme impact of certain kinds of rare and unpredictable events, the so-called outliers, and the human tendency to find simplistic explanations for these events. The origin of the Black Swan theory is the story that in history, mankind was sure that black swans did not exist and that all swans were white. When the Dutch explorer Willem de Vlamingh discovered the existence of black swans in Australia, the term became metamorphosed to connote that a perceived impossibility might later be disproven. According to Taleb, a Black Swan is an event with the following three attributes. First of all, it is an outlier, as it lies outside the realm of regular expectations since nothing in the past can convincingly point to its possibility. Second, it carries an extreme impact. Third, in spite of its outlier status, human nature makes us concoct explanations for its occurrence after the fact, trying to make it explainable and predictable. Examples of Black Swan events are 9/11 and the financial market crisis in 2008.
One of Taleb’s fables regarding Black Swan type events is that of the turkeys that are raised and fed for Christmas. Only judging from past events, the turkey can consider itself to be lucky, since its owner feeds him every day. There is no indication from these past events whatsoever that suggests that one day the turkey will be slaughtered. In fact, the turkey grows more confident every day that he is safe. However, there will be a moment in time just before the turkey is slaughtered that it will become obvious why the owner cared for him so well (see figure below). Hence, the narrative becomes clear after the event. The turkey’s belief that every day would be fantastic, would be reinforced by the fact that every day was fantastic. The accumulation of supporting information does not just reassure the turkey, but also actively destroys its ability to think about what it does not know. The moral of the story is, do not be a turkey! Alternatively, do not trust constantly rising house prices or burgeoning stock markets. Hence, focus on what you do not know, which is far more relevant to the Black Swan problem.
Taleb’s latest book was published in November 2012 and is called Antifragile. In the introduction of the book, Taleb describes the term antifragility as follows: “Some things benefit from shocks; they thrive and grow when exposed to volatility, randomness, disorder, and stressors and love adventure, risk, and uncertainty. Yet, in spite of the ubiquity of the phenomenon, there is no word for the exact opposite of fragile. Let us call it antifragile. Antifragility is beyond resilience or robustness. The resilient resists shocks and stays the same; the antifragile gets better.” Hence, robustness is insensitive to Black Swans, while antifragility is what gains from disorder (Black Swans) and thus likes volatility, in contrast to fragile systems, in which every error makes the system weaker. This is exactly how Taleb views our current economy. Instead of trying to regulate the economy against a crash, we should create one that improves by failures and hence make it antifragile. In order to do so, he advocates for a strong safety net for individuals, to ensure entrepreneurs will take the risks, but not a corporate safety net that bails out bad banks. Hence he opts to bound the size of the banks, let banks fail and to abandon economic stabilization practices.
Upon being asked what his future writing plans are, he answers: “I am planning to consolidate the books Fooled by Randomness, The Black Swan, Bed of Procustes and Antifragile into one book called Incerto, which will come out during Christmas. I will smooth out the topics, in order not to have too much overlap. The rest of my life, I will add to mathematical explanations. I will put the Technical Incerto, which is the more technical companion of the books, on the internet for free, so you can all read it.”
Nassim Nicholas Taleb originally comes from Lebanon and now lives in the USA. His parents are both Lebanese and both have a French citizenship. Coming from a good family with politically important positions in Lebanon, Taleb had the opportunity to attend a French high school. However, due to the Lebanese Civil War, his family suffered and lost quite some wealth and political prominence. Later on, he received his bachelor and master in science degrees from the University of Paris. Moreover, he holds an MBA from the University of Pennsylvania and a Ph.D. in Management Science from the University of Paris.
Taleb proceeded his career in both the business world as in the academic world. In the financial world he is a successful hedge fund manager and derivatives trader. As a trader, his strategy has been to safeguard investors against crises while reaping rewards from rare events (the so-called ‘Black Swans’). Taleb is considered to be a pioneer of tail risk hedging (‘Black Swan protection’), through which investors are insured against extreme market moves. In times of crises, Taleb earned lots of money. He made a multi-million dollar fortune during the financial crisis that began in 2007 by speculating that a crisis (a Black Swan) would occur. He attributes this development to the mismatch between statistical distributions used in finance and reality. The strategy he uses is the so called ‘Barbell strategy’. Taleb tells us about this: “Instead of having securities with medium risk, I have a linear combination of α% zero risk (cash adjusted for inflation) and the remaining (1-α)%, I invest in the highest risk securities (take for example, α = 0.8). My overall risk would be medium risk, which is much more robust in the left tail. Hence the central idea of barbell is to invest in a convex linear combination between two classes of risk.“
As a nice side note, Taleb mentions that he does not only use a barbell-strategy for his investments, but also for training his body. He believes the human body is antifragile and prospers by randomness. Instead of lifting small weights very often, Taleb applies the strategy of ‘maximum lifts’ training: every now and then he takes an extremely heavy barbell and tries to lift it once or twice. Preferably he chooses a barbell which is heavier than the one he used last time. In this manner he is able to lift very heavy weights, without spending boring hours in the gym.
Although Taleb is very successful as a trader and is still active in this field, he has expressed quite some criticism towards the business world. In his book The Black Swan he states that he decided to stop reading newspapers and says about this choice: “It was initially a great excuse to avoid keeping up with the minutiae of business, a perfect alibi since I found nothing interesting about the details of the business world – inelegant, dull, pompous, greedy, unintellectual, selfish, and boring.” Upon being asked why he is still active in this world, he answers in a much more positive way than in his book: “Why am I still in the business world? I do not hang around with business people. The reason I am in finance, is because I want to be independent. I do not have rich friends, but instead all my friends are intellectuals. Finance allowed me to be free and become a scholar independently. It is better than having a career as a professor, because now I work until 3 or 4 pm and the market closes, and then I am free to read and I have no obligations until the market opens again the next morning. Trading was a great life during which I spent 20 years conducting much research and reading many books, which is something I would not have been able to do in academia. I lived in both the academic and the business world and I can say that in general the academic world is rather corrupt. In the medium-business world, everyone is happy when someone makes some money. However, in academia, everyone wants honor and is upset if they do not get any honor, but someone else does. Therefore it becomes a zero-sum game. In general, when the businesses are not too large, people are happier in the business world since they compare themselves less to others.”
To sketch the problems of econometrics, Taleb asks us to use our imagination: “Imagine you have boarded a plane with destination Siberia. Just before the plane is leaving the pilot announces that he does not have a map of Siberia; he proposes to use a map of Alaska instead, because this also is a cold territory close to the North Pole. Would you leave the plane?” This would never happen in a real plane, because the pilot has ‘skin in the game’, i.e., if the plane crashes the pilot dies as well. Therefore, investment advice should be ignored if the advisor did not invest in the advised portfolio himself, the advisor does not have ‘skin in the game’. In many cases econometricians and economists have a lack of ‘skin in the game’ and fit reality to their models instead of the other way around.
Taleb does not only defend his philosophical points with words, but also with pure mathematics and statistics. During the interview, he discusses a paper with us in which he backs the points made in his books. Besides pure mathematics, Taleb also uses Monte Carlo simulation in the paper. These simulations have the advantage that they provide more insight into complicated problems. Moreover, it gives the possibility to learn more about problems that cannot be solved technically.
As was stated before, Taleb worked many years of his life as a trader. As we all know, the distribution of assets often has fat tails. To measure fat tails, economists use the concept of kurtosis, i.e. the variance of the variance. According to Taleb it is extremely difficult to measure the kurtosis of a distribution. He has collected data over a time period of 50 years of the US stock market and found out that 80% of the kurtosis was determined by only one single observation, the crash of 1987. This means that we cannot tell how stable our estimated variance is, even though some claim they can. So the problem is not that there are fat tails since most people are aware of that (though they often try to forget it). However, the problem is that we cannot determine how fat the tails are within standard methods. Never.
Unfortunately, also other risk measures are unreliable estimates according to Taleb: “Correlation is so unstable that it kills Markowitz”. The point here is not just that it is difficult to estimate the correlation coefficient (the estimation of a covariance matrix is more unstable than the estimation of the variance), but also that the estimation errors have a big impact on the outcome: the portfolio in which you want to invest.
Taleb not only criticizes models that simply assume some distribution, but also non-parametric methods to test the distribution of a sample. For example, the Kolmogorov-Smirnov test often does not reject fat tailed distributions. Taleb simulated a normal distribution and a fat tailed distribution with the same mean and variance and both 1000 observations. The result was very remarkable; the fat tailed distribution passed the test better than the thin tailed (normal) distribution (see figure below). However, in another simulation of the same experiment the Kolmogorov-Smirnov test did reject the fat tailed distribution. The reason that it is possible to fool this test, is that these tail events are not always in your sample and therefore the null hypothesis of a normal distribution often cannot be rejected. This is the problem of induction: absence of evidence ≠ evidence of absence. Or to put it differently, if you have seen ten thousand white swans and no black swans, you cannot say that black swans do not exist. However, if you see a black swan you know that black swans exist. The conclusion is that the Kolmogorov-Smirnov test is good at rejecting, but that a sample that passes the test is not necessarily normally distributed.
It is not possible to estimate small probabilities according to Taleb, even if you have the right model. This is because small estimation errors (of parameters of the model) have a big impact on the estimators of small probabilities. Take for example a normal distribution. The probability of a 10 sigma event is approximately 170,000 times higher than estimated, if the real sigma is 15% higher than your estimate of sigma. When using non-parametric methods you cannot estimate these small probabilities either for the obvious reason of sample insufficiency in the tails.
Taleb: “Fat tails are not about the incidence of low probability events, but about the contribution of events away from the ‘center’ of the distribution to the total properties.” Why is it a problem that we cannot estimate these small probabilities? This is because rare events often have a big impact, so underestimation of small probabilities in the left tail could lead to severe overestimation of the expected payoff. Furthermore, the probability of bankruptcy could easily be underestimated.
Another problem of econometrics, according to Taleb, is the use of asymptotic theory. Obviously we only have finite samples, so it is important to be sure which results of asymptotics we can use and which we cannot. For example, the Central Limit Theorem converges very slowly in case of fat tailed distributions. In fact, the distribution of the sample mean has fat tails itself. The main problem of asymptotics is that convergence goes slowly in the tails due to the low number of observations.
Advice for Econometricians
Perhaps, you as an econometrician have started to wonder what to do with your life after having read all this criticism on econometrics. But please do not be disheartened, since Taleb is a financial mathematician himself and has a lot of advice for us. “Be an econometrician, but do not be a turkey! The rule I applied to myself is that I never did anything in trading or academia that was not recitable into general scholarship. I have a test for this; never read or do anything that you cannot remember 20 years from now. When reading a newspaper, you know it is not relevant in 20 years. However, when you are a trader, you study probability theory and you deal with random events. When reading probability theory, you know that the material is still valid 20 years from now. Therefore I picked option trading as my profession, since it allowed me to practice probability theory. I consider statistics to be epistemology and for me decision theory is philosophy of actions. In trading I was never bored with what I was doing. So please choose a profession that you like to do and that does not bore you. Moreover, it should be relevant to you 20 years from now, otherwise it is a waste of time.”
As was already stated before, Taleb holds an MBA from the University of Pennsylvania. However, he is rather critical about this study program: “You meet a lot of smart people and the atmosphere is nice, but you hardly learn anything. The only useful things you learn are institutional finance, accounting and computer sciences. Unfortunately, everything linked to portfolio theory is bullshit. The less theoretical the subject matter, the more useful it is. It is good to do math and re-derive all theorems you learn. While doing that, I found out that the Central Limit Theorem did not apply to fat tails. However, someone who studies it in the textbook will say that it works for n to infinity, but that does not apply to the real world. Hence, when you try to derive the mathematical theorems yourself you will find the flaws. Therefore it is good to have a barbell strategy of institutional stuff and mathematical stuff.”
As a final advice we learn the following from Taleb: “One lesson I learnt is that you should not be nice to the ones above you, but be nice to the ones below you. To me, an asshole is someone who is arrogant to the people below him and nice to the people above him. In general, I am not nice to people that have power, such as journalists and government officials. In return, I have to be ten times as nice towards children and students, since they are not corrupt yet. Furthermore, do not deal with people who do not have ‘skin in the game’. This is a necessary, but not a sufficient condition. People who do not have skin in the game, become a crux of randomness. People who have skin in the games are fools of randomness.”
Let us end with a promising and interesting quote from Taleb: “Statisticians and econometricians are the most important professions, but also the most dangerous ones. As an econometrician, you have more power than anyone, since everything, ranging from the economy to medicines, depends on probability theory.”
We would like to thank Nassim N. Taleb for his precious time and for sharing his thoughts with us.
Text by: Suzanne Vissers
Co-writer: Floris van Loo