ECON484-Topic #1: Implications of Black Swans and Mathematical Economics

Nassim Taleb’s lecture at JMU on Black Swan events has many implications for mathematical economics and economics in general. Black Swans are defined by Taleb to be events that are outside “the realm of our expectations,” have extreme impacts, and can be explained after the fact. Aside from the obvious financial market and crisis examples, try to think of how a black swan event has altered our perceptions of an economic theory. Do Black Swan events apply only to financial markets and macroeconomics, or should we consider them in fields like health economics, public finance, monetary theory, and other fields? How has the “Gaussian” or “normal” error shaped other fields of economic theory, and how do you think we can adapt any models to account for Black Swan events?

Taleb’s website can be found at, and some of his more technical work can be found at a broken link on his page (correctly routed here)

14 thoughts on “ECON484-Topic #1: Implications of Black Swans and Mathematical Economics”

  1. Black swan events alter our perception of economics and finance in several ways. The most relevant change that must be made is within risk management. Taleb’s definition of a black swan causes risk management to become more complicated than ever before [1]. However, if an investor truly believes in the possibility of a black swan there is really only one way to invest. An investor should allocate a large amount of his or her resources into very low risk, low reward investments. Basically, an investor is looking at having about 95% of their portfolio in cash and treasury bonds, while the remaining 5% can be invested in extremely risky financial derivatives [2]. This type of financial portfolio insures the investor that on the chance of a black swan, their portfolio either does extremely well, or they just lose around 5%. The primary problem that arises with this portfolio structure is that black swans are by definition rare [3]. Therefore, for a financier to invest like so, they are looking at a long time (if not eternity) of minimal loses and even smaller gains for this portfolio. This portfolio is essentially betting on the assumption that there will be at least one black swan. Since a black swan is prospectively unpredictable, this sort of betting is probably ill-advised, which brings up another concern; the financial portfolio described above could be perceived as riskier than one which leaves out the possibility of black swans, simply because the investor is basically only losing. So, the black swan theory has merely made risk management more complicated than may be necessary.


  2. At the core of Mr. Taleb’s lecture at JMU is the idea that we don’t know enough about the world to make any definitive claims; our attempts to do so driven by our idiosyncratic hubristic nature has led us down the path of fragility. He argues that optimization is a double-edged sword; a trade-off between higher average growth rate and higher exposure to “blow-ups” or Black Swan events. Mr. Taleb claims that this trade-off is not worth making in the mystified “extremistan” domain because large deviations are not only unpredictable, they are also unquantifiable; suffice to say that they will be astronomically greater in magnitude.

    To combat fragility, Mr. Taleb advocates, is to become more robust in the face of Black Swans through redundancy. This reasonably valid but vague suggestion borders on contradiction and meaninglessness; because it is thus implicitly hinted that the method to maintain efficiency and survivability in the long run is to maintain inefficiency in the short run. This begs the question of just how redundant one must be in the short run in order to build a sufficient barrier against large deviations while retaining adequate competitiveness to survive in the short run. But due to the suggested unquantifiable nature of Black Swans, a satisfactory answer to the previous question is impossible give.

    On a philosophical note, if the whole point to the Black Swan movement is to be humble against uncertainty, acknowledging there are many things in the world we do not understand or are not understandable, with Black Swan phenomenons being one of them; why is Mr. Taleb so adamantly certain of his understanding of the world? In a sense exclaiming to the world that he is absolutely convinced that he is unconvinced by anything. Is Mr. Taleb immune to the perceptual biases that he so steadfastly critics? In his turkey analogy, the actions of the butcher is totally exogenous to the turkey, where as in the real world deviations are endogenously influenced by the decisions made by economic agents. Even if you keep 95% of your portfolio in low risk, low return, liquid assets; and the other 5% in high risk assets, you are still incurring the exposure to hyperinflation, which in of itself could be characterized as a Black Swan event, carrying extremely high expected losses.

    In my opinion as a student of Mises and the Austrian school, debt is not the problem in and of itself, the underlying problem resides within the fractional reserve banking system and the institutionalized monopoly on money. A dollar lent ought to be from a dollar saved. When you borrow a dollar it ought to represent that someone somewhere else forewent using that dollar so that you have the ability to use resources that aren’t currently being used elsewhere. When you have a monetary system that encourages an expansion of credit not backed by savings or flat out increases it sporadically and arbitrarily on its own discretion, it grants the illusion of greater savings than actually exist, in real terms. This in turn encourages lower savings, increased consumption, increased production of all manner of goods, both in length of structure of production and breadth, which then leads to bubbles.

  3. The advent and continual evolution of the Internet and its uses serves as one, if not the most significant Black Swan events in recent history. For sellers and firms, the Internet provides an almost limitless forum for those who wish to put their goods and services on a market that reaches anybody with an Internet connection. For consumers, the almost uncensored flow of information to hundreds of millions of people worldwide through indexes like Google that allow for smarter comparison-shopping in an instant (literally). With relation to economic theory, we can see how the Internet established what is essentially a worldwide meeting place of ideas and information that benefits both firms and consumers. We can see the principles of supply and demand embodied vividly because of the Internet –increased number of buyers and producers in a market for a good and constantly changing tastes and preferences due to viral marketing, to name a few. In this case, we can validly see how a Black Swan event reinforces an economic theory such as supply and demand basics and their impact on price and quantity.
    But in relation to financial markets and the Black Swan market crash, we can see how an economic theory was turned on its head. During his speech at JMU, he points out the fallacies of economists who use misguided principles to measure risk and esoteric mathematics to bolster and rationalize their leverage behind their models. On face, this is a valid argument. To reason what might happen in the future by looking at the past is to account for only a small portion of the picture of what could occur.
    But how do we account for shocks in the system that by definition cannot be foreseen and have implications that affect the course of the future? He writes:

    Black Swans being unpredictable, we need to adjust to their existence (rather than naively try to predict them). There are so many things we can do if we focus on anti knowledge, or what we do not know. Among many other benefits, you can set yourself up to collect serendipitous Black Swans by maximizing your exposure to them[1].

    From this, I would reason to say that Taleb doesn’t necessarily advocate a pre-empted approach to measuring volatile things like uncertainty in financial markets (i.e. trying to include every and any little significant factor that might happen into a model). Rather, looking at the big picture at all angles and at the margins can help put us at a better position to anticipate and adjust to Black Swans. However, doesn’t this reasoning water-down the very nature of Black Swans? It wouldn’t matter if we force ourselves to think outside of the box and embrace “anti-knowledge” to help alleviate any negative impact of a Black Swan. Black Swans are unforeseeable due to their outlier characteristic, have immense impact, and can only be reviewed retrospectively. Wouldn’t a car with a million airbags still be crushed if a boulder lands on it?


  4. As mentioned above, and during the lecture, the utter neglect of the possibility of these Black Swan events occuring has produced pervasive effects in the financial world, trickling down affecting both borrowers and lenders in almost every industry. This neglect has bolstered the habit of credence in forecasts and projections built on faulty assumptions, which, at many times, are used to irresponsibly place large sums of money. Dr. Naseem Taleb ridiculed many of these heavily utilized economic and financial institutions as lacking robust nature due to the increasing complexity of the financial environment and recommends downsizing from an ‘extremistan’ type society, which consists of upper and lower extremes of wealth and power, to a more ‘mediocristan’ state of the world, where the playing field is more level in many aspects.
    Regarding economic theory, the introduction of the concept of “Black Swan” events has incurred many implications on economic theory. For example in econometrics, unbiased estimators, uncorrelated independent variables and the absence of heteroskedasticity (homoskedasticity) are usually always assumed in models and are, for the most part, the reason why these models are trusted. Without them, they are no longer robust and are as good as guesses. Although to a certain extent, econometric models and those like it, do provide certain insight to effects on dependent variables if constructed carefully, they should not be trusted blindly. Two of Dr Taleb’s characteristics of this type of event are that they are outside the realm of predictability and have large consequences. This definition implies that no financial model can take them into consideration, and implicitly, that no one takes them into account. If this is true, then people will continue to behave as such until another one occurs, incurring massive damages, or until financial players begin taking less risk, so that when one does occur again, there will be less detrimental effects. Due to the destructive nature of these events, I believe that the possibility of these events should be taken across the board because after all, they are outside the realm of predictability.

  5. A black swan event will always be lingering and always has the potential to have a huge impact on the economy. Nassim Taleb makes a good point when he says a black swan event is just like a turkey being fed just to be butchered one day. The turkey never accounts for the event to occur just like financial models today. A lot of financial and economic models that we have today do not account for a very unlikely, but very costly event like a black swan. However, I feel that without these models we would be worse off than with them because they do model the other part of the economy that is likely to happen. It is also important to have these models because it gives people a basis to work off of so the market is less chaotic. Markets work in a way that recognizes black swan events, but also realizes they are unlikely so aren’t given much attention [1]. Nassim Taleb gives a good analogy on his website that if a bus driver blindfolds himself and crashes the bus he should never be allowed to drive that bus again. This is what is happening to the economy though because these black swan events are not being accounted for. Although I feel like black swan events will never be predictable, I think they could be hedged at least in the financial market. Taleb talks about buying options that are out of the money to hedge against large changes in the stock market. While this cannot always work to help soften the impact the effect of a possible black swan event in the economy, it is a good first step.

    To discount all financial and economic models is going too far because there’s no way to tell what shape the economy would be without them. I agree with most of what Taleb is saying because it makes sense that a small probability of risk can turn into something disastrous when that probability becomes a reality. So long as important financial models are using a normal curve to predict probability these unforeseeable improbable events will likely keep happening [1]. However, I do not feel like he gives enough advice on how to go about fixing this. For the time being it is probably best to learn from the mistakes that have caused previous black swans and try to be more ready for them in the future. The key is not to try and prevent them, but to prepare for them and hedge against them.


  6. The existence of black swans is not restricted to financial markets alone. The three criterion listed by Taleb can be met in a host of other socioeconomic sectors. In the arena of health economics, for example, it’s not difficult to imagine a new type of epidemic or a catastrophic natural disaster that leaves a lasting impact on the market for health services. The existence of illnesses like AIDS, H1N1, or SARS may become obvious to scientists after they have become widespread, but it would be impossible to predict their coming before outbreaks had occurred. This, as Taleb states, leads to backward rationalization.
    If black swans are only visible in retrospect, the question is, do they really matter? Jane Kim writes in the wall street journal “Because black-swan events are so unpredictable, the markets’ reactions to them can be equally unpredictable. Just because an approach worked last time doesn’t mean it will work in the future.” It may be possible to prepare yourself for types of swans that have been seen in the past, but a new type cataclysm is always looming. The only thing you can control is your reaction to such events but not necessarily the catastrophe itself. If you are to be executed the next day, make sure you still shave (Taleb).

  7. I’ll focus here on Taleb’s assertion that because the models of statisticians, economists, and financiers are ineffective in predicting randomness, these respective fields are useless [1]. I find two significant flaws with this theory.

    First, he bases this criticism of “empty suits” largely on the Gaussian distribution’s difficulty with predicting events that are rare –there’s a 99.73% chance that an event will not fall outside of 3 standard deviations from the mean of a normal curve. Trouble is, as Columbia’s Andre Gelman notes, Gaussian models are rarely used on their own – much more complex, multilevel Bayesian models that were created for the explicit purpose of correcting the limitations of the normal distribution are the vehicle of analysis for trained statisticians [2]. If Taleb wants to discredit entire fields of academia, he would be advised to directly engage their best models. By ignoring the entire subfield of Bayesian statistics, as the editors of The American Statistician note, the only logical conclusion is that Taleb is attacking a straw man [3].

    Second, Taleb’s attack against economic models – that they’re worthless because they cannot predict Black Swan events — misses the point of the field as a whole. As NYU’s Thomas Sargent explains, macro models in particular are designed to describe aggregate economic fluctuations when markets work well, not to predict the future [4]. Taleb’s view – that we abolish the Nobel Prize and shun economists – is unfounded, as it would require us to discard concepts that have been proven time after time by both theory and empirical data, ranging from the micro work on the tradeoff between labor and leisure to the macro analyses of the factors that drive development.

    Taleb is doing what’s easy – pointing out the flaws in fields that are inherently imperfect – but he doesn’t offer anything close to alternative models. I’ll side with those he derides – academics on the cutting edge of economic and statistical research – and trust that they will continue to make adjustments in their models where necessary in their attempt to better understand how our world works.

    [1] Outlined in James Ian Gow’s review of The Black Swan published in The Public Sector Innovation Journal in 2008.
    [2] Andrew Gelman, statistician at Columbia University, on Taleb’s The Black Swan.
    [3] Westfall, Peter H and Joseph M. Hilbe “The Black Swan: Praise and Criticism” in The American Statistician August 2007.
    [4] The Federal Reserve Bank of Minneapolis, September 2010 Interview with Thomas Sargent.

  8. Taleb Challenges us to find new robust financial instruments in measuring the risks we face under any economic climate. These Black Swan events he speaks of may be rare but during an occurrence they become a significant in our economic world. When the expression “Black Swan” was first introduced, no one had ever seen a black swan just as no one had ever seen a pig fly. Ironically amongst the discovery of Australia we had discovered the black swan as well. Taleb uses this as the title of his theory in order to stress the point that we cannot rule out the sighting of a black swan just because we have not experienced one, just as we cannot throw out possibilities of major outliers in our economic and financial modeling. He stresses the dangers of not accounting for the possibilities of these outliers, which I believe it would be extremely difficult to include. Most financial models include factors such as risk free investments. These models including these risk free events obviously don’t take into account the possibilities of “Black Swans.” The risk free rates in these models are related to treasure bills and other government related bonds. Just as many people said AIG was to “big to fail” during the financial crisis of country there is always a “Black Swan’s” chance that our treasury bills are not as risk-free as we suspected.
    A few list of Taleb‘s “TEN PRINCIPLES FOR A BLACK-SWAN-ROBUST WORLD” is a very interesting list that I encourage any reader’s to take a look at. It is a quick list full of many interesting points. Here is the link

  9. When we discuss Taleb’s ideas, I think it is important to keep in mind that Taleb is a philosopher at heart. He generally just has a problem with induction and the way people value information or knowledge obtained through induction.

    As his problem with scientific inquiry is concerned with economics and finance, he distrusts models that are built upon relatively small data sets using assumptions that he believes cannot accurately predict the probability of a “Black Swan” event occurring [2].

    Referring to Jared’s post, I think he would say that statistical applications grounded in Bayes’ Theorem are still flawed if the prior distribution of a data set used in a Bayesian statistical analysis is Gaussian. Amongst his peers, Taleb is not the only academic who understands the shortcomings of these models. His ideas are just so far out of the mainstream, that people are unsure what to think. Robert Schiller is quoted in one of his papers saying “you may have a point but you go too far” [1].

    If many academics understand that the math we use to assess risk, value assets, or otherwise predict economic variables is suspect, then why are these tools taught to students? Taleb believes it is a desire to, and I’m paraphrasing, “give students something” [1].

  10. @Eddie Mifflin
    I took particular note of your paraphrasing Taleb’s analogy that a bus driver who blindfolds himself only to crash the bus should not drive the bus again. After reading a bit of Taleb, I cannot help but think that he would apply this metaphor to his frequent target, Ben Bernanke.

    I would be the first to admit that Bernanke’s tenure has been far from flawless – he’s received plenty of valid criticism from both the left and the right – but I’d also add that if the bus has already crashed, I’d want someone who’s one of the world’s foremost thinkers on fiscal and monetary policy and their history helping to rescue the survivors. Bernanke fits that description perfectly, and I think it would be interesting to see Dr. Taleb suggest a candidate who could have done any better given the same circumstances.

  11. Taleb is a philosopher, more so than he is a financier or economist. He has problems with people and the sciences reliance on induction for knowledge and how we value knowledge obtained through induction. Even if we are going to rely on induction, the data sets used in our models are so small that they cannot accurately represent the probabilities with which Black Swan events will occur (since Black Swans, by definition, are rare anyway).

    Referring to Jared’s post, I think Taleb would still say statistical work grounded in Bayes’ Theorem is still unreliable if the prior distributions of the sample data being used in the Bayesian analysis are Gaussian.

    Although, I do agree that Taleb’s arguments leave us wanting more, as he doesn’t seem to offer corrections to these allegedly faulty models. For instance, in one paper, he argues that optimization isn’t wealth maximizing in a Black Swan world, because we are not adequately protected in the event of the unexpected [2]. With the case of financial institutions, he offers redundancy in the form of capital buffers as a way to guard against Black Swan events, that is far short of a new or improved way to value risk or model asset prices [2]. But hey, this is a philosopher we are talking about.

    But, even if currently accepted models, though perhaps flawed, are the best tools we have to predict the future or estimate real world phenomon, Taleb would still disagree that the use of these tools is warranted; he likens the “this is the best we can do” argument to the same reasoning as medieval doctors [1].

    That being said, I think we have to use these tools, but be understanding of their shortcomings.

  12. I apologize for posting twice, I was just trying to reply to the original post so I could put my sources in. But, somehow it posted my comment twice. Here are the papers I referenced.

    1. Taleb, N.N.(2011), Why did the Crisis of 2008 Happen? forth. New Political Economy
    2. Taleb, N. N. (2010), Errors, Robustness and the Fourth Quadrant, International Journal of Forecasting

    Again, I apologize for posting all of this.

  13. Black Swan is really unpredictable and it is the reason of the financial crisis. one of the risky measurement is VaR(Value at Risk). VaR is supposed to measure expected losses from a trading portfolio at a given statistical confidence level. It is calculated by looking at past data and then inferring future market behavior. If markets are stable, VaR will say that there´s no risk ahead. But actually it isn’t. The reason of the financial crisis was underestimate of the risk. VaR also underestimated the risk of sub-prime mortgage asset. VaR is good measurement when economic is stable but not good measurement when economic got depression time. The VaR figure will be small, resulting in small capital charges, allowing banks to have to pay just a little upfront about 1% in order to devour monstrous amounts of those “non-risky” assets. This is valid both for liquid and illiquid stuff since VaR, incredibly, does not discriminate like a Treasury Bond and a CDO; all that matters is what past data says, potentially resulting in the obscene conclusion that a T-Bond may incur a higher capital charge than a CDO. That is, VaR can make it easier (cheaper) for you to gorge on deleteriously lethal stuff than on staid safe alternatives.

  14. @Brad Reeser
    I would very much like to see what Taleb would say in a debate with a trained statistician who fully understands the theory about how Beyesian models adjust and improve on the normal distribution (which I surely do not). I doubt that will ever happen, though, as he appears to be on “permanent media blackout.”

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