Discussion Paper

No. 2013-11 | February 06, 2013
Black Swans, Dragon Kings, and Bayesian Risk Management


In the past decades, risk management in the financial community has been dominated by data-intensive statistical methods which rely on short historical time series to estimate future risk. Many observers consider this approach as a contributor to the current financial crisis, as a long period of low volatility gave rise to an illusion of control from the perspectives of both regulators and the regulated. The crucial question is whether there is an alternative. There are voices which claim that there is no reliable way to detect bubbles, and that crashes can be modeled as exogenous ‘black swans’. Others claim that ‘dragon kings’, or crashes which result from endogenous dynamics, can be understood and therefore be predicted, at least in principle. The authors suggest that the concept of ‘Bayesian risk management’ may efficiently mobilize the knowledge, comprehension, and experience of experts in order to understand what happens in financial markets. 

Paper submitted to the special issue
Economic Perspectives Challenging Financialization, Inequality and Crises 

JEL Classification

C11 G32 D81 G18

Cite As

Armin Haas, Mathias Onischka, and Markus Fucik (2013). Black Swans, Dragon Kings, and Bayesian Risk Management. Economics Discussion Papers, No 2013-11, Kiel Institute for the World Economy. http://www.economics-ejournal.org/economics/discussionpapers/2013-11


Comments and Questions

Tony O'Hagan - Invited Reader Comment
February 19, 2013 - 09:03

see attached file

Armin Haas - Uncertechnologies
March 20, 2013 - 13:30

Dear Prof. Hagan,

Thank you very much for your inspiring and encouraging comments.

We very much like your notion of uncertechnologies, and are proud to call ourselves uncertechnologists.

Indeed, the Bayesian approach sees all uncertainties within a single coherent, and we would add, comprehensive ...[more]

... framework. As it is a powerful approach, it can also become dangerous when used by unskilled hands, or when misused intentionally. This is exactly the reason why we made our concept of Bayesian Due Diligence the central pillar of BRM.

Basically, we agree that the concept of heavy-tailed distributions is a powerful one, but we see a fundamental challenge when it comes to Black Swans. Please mind that our concept of Black Swans differs from that of Taleb. For us, a Black Swan is an event that people cannot imagine, or refrain from imagining. This relates to cognitive and psychological constraints, respectively. If, however, an analyst cannot image a specific event, for whatever reason, how can he address it by using heavy-tailed distributions? We do not suggest that we have an answer for this question. We just want to raise awareness for this issue.

Anonymous - Referee Report 1
March 11, 2013 - 09:25

see attached file

Armin Haas - A Conceptual Paper
March 20, 2013 - 13:38

Dear Referee,

Thank you very much for your report that raises import questions.

Our short and crisp paper aims at introducing the concept of Bayesian Risk Management. We did not aim at a survey of concepts or tools for dealing with uncertainty in economics or finance ...[more]

... in general. We neither aimed at discussing how financial risk management dealt with systemic risk before the contemporary financial crisis hit, and how the financial risk community reacted to the outbreak of the crisis. Because we wanted to be short and crisp, we refrained from giving details how we developed our concept. As we thought that giving one or two examples of applying our concept would compromise its generality, we haven chosen the format as it stands.

Our paper is not a standard economics paper. A standard economics paper follows the status quo plus epsilon approach: it builds on an established concept, and adds a little to it. Typically, it uses a well-established formal apparatus. Obviously, it is at the discretion of the editors whether they want to confine their journal to publishing such papers. The discipline of economics badly needs platforms for sharing innovative concepts. We think that one of the reasons of the financial crisis is that economists stuck too long to inappropriate concepts.

As subjectivist Bayesians we argue both on the descriptive and the normative level. We think that humans often actually behave like Bayesians. And we think that they have good reasons for this behavior. To what extent our empirical hypothesis is valid, is an important research question. We would, however, remark that in empirical research one should discriminate between whether someone claims to be a frequentist, and whether he actually is. It is our understanding that formally, the Basel II regulations are neutral concerning frequentist or Bayesian approaches, but actually gave rise to the dominance of frequentist techniques in bank risk management. We would not be surprised to find that a considerable share of the actors who applied these frequentist tools were well aware of their shortcomings but had substantial incentives to ignore these shortcomings. At least we encountered quite some managers who pretended to believe in the efficient market hypothesis but actually thought differently.

We did not want to write a paper on the Basel regulations. We could, however, exemplify the need of our BRM approach in general, and of our Bayesian Due Dilligence in particular, when discussing possible future Basel regulations. Running practically all banking risk management on frequentist tools that look five years back at maximum is not a really convincing approach given the history of financial markets. It is a stylized fact of financial markets that at least once a century, speculative bubbles burst. This was well known even before Reinhart and Rogoff published their monograph. BRM offers a concept for including expert knowledge into risk management, and the knowledge of economic historians is but one example. This, however, creates the risk that expert input is used to provide arguments for even higher leverage. A reasonable regulation must keep this risk in check. Bayesian Due Diligence is the conceptual frame for this as it asks the risk managers to document and be able to defend their necessarily subjective choices.

Anonymous - Invited Reader Comment
March 11, 2013 - 09:45

see attached file

Armin Haas - Reply
March 20, 2013 - 13:41

Dear Reader,

Thank you very much for your useful comments that will help us improve our paper.

@1: Priors should be informed by expertise. Existing expertise actually is the easy case. Non-existing expertise is formally tricky, as it is not trivial to come up with a non-informative ...[more]

... prior.

@2: We would love to discuss the issue of BRM and plurality, but this would leave us deeply into philosophical ground. If the editors encourage us to do so, we are fine.

@3: We would exemplify it by contrasting the inability of established financial risk management models to mobilize the expertise of economic historians with BRM, which gives room for mobilizing it. Cf. the last paragraph of our answer to referee report #1.

@4: Whenever there is sufficient data, we are fine with frequentist methods. Typically, frequentist methods ask for many, but not too many data, which is exactly their problem when in many real life situations only few data are available. The big danger of BRM is that its potential can be misused by intentionally selecting biased expertise. For addressing this danger, we made our Bayesian Due Diligence the central pillar of our concept.

@5&@6: This is a misunderstanding. We do not present a specific model but a general concept. In our own work, we used a rather diverse set of models and methods, which have only in common that they were subjective Bayesian approaches. We could talk about these models, but this would no longer be a short and crisp conceptual paper. Cf. paragraph 1 of our answer to referee report #1.

Anonymous - Referee Report 2
May 23, 2013 - 08:38

see attached file

Anonymous - Choice of Format
July 18, 2013 - 10:20

Dear Referee,

Thank you very much for your report that raises further import questions.

In light of your report, and the feedback given otherwise, we think it is fair to say that we encounter a problem with the format we have chosen for our paper. We ...[more]

... intentionally wanted to be short and crisp. We neither aimed at a paper sketching the history of Bayesian thinking, nor at a technical paper presenting our quantitative work. We also refrained from discussing the scope, merits, limits, and complications that come with notions like Black Swan or Dragon King. We thought we had good reasons for our choice.

Sometime, we may write a paper highlighting the philosophical and historic background of BRM. We would probably start with Socrates and Confucius, and give American philosophical pragmatism quite some room. Of course, de Finetti is one of our heroes. His statement that “probability does not exist” is still intriguing. Ramsey is a good choice, but then Keynes should also come in with his “animal spirits” and his conviction that investment choices are generally not made on the basis of expected values. So yes, your respective lines very well resonate with our thinking – but this should go into a different paper and, we would guess, into a different journal.

Another time, we may want to come up with a paper targeting the community of Bayesian epistemology. Historically, subjectivist definitions of probability were well in use before Bayesianism took off. Currently, however, it is the subjectivist Bayesians who dominate the field of subjective probabilistic reasoning. As we acknowledge in our paper, there is an objectivist Bayesian community. For us, being an objectivist Bayesian somehow is a contradictio in adjectio as we think that it is inconsistent to use Bayesian techniques while claiming that probabilities are objective. For us, it is one of the great advantages of Bayesianism to have both a concept and a toolbox for dealing with informative priors. Sometimes, we have to deal with situations in which we indeed have not a clue about what is going on. But it is an indication of perplexity to strive for such a state of affairs as ideal, instead of perceiving it as a challenging complication.

A further technical paper might contain our work on a Bayesian Value at Risk measure.

In the present paper, we intended to target a wider community of economists and risk managers who not necessarily are familiar with, or interested in, the subtleties of Bayesian epistemology and its historic developments. We consciously referred to Taleb and Sornette because we assumed this would resonate with a wider audience, compared to Ramsey and de Finetti. We also refrained from becoming too technical because we did not want to detract from the fundamental challenge that sticking to the frequentist mindset poses for financial risk management.

Explaining how the frequentist mindset that dominated and still dominates risk management interacted with all other determinants of the current financial and economic crises is a challenge of its own, and deserves at least a paper on its own. We totally agree that greed and fraudulent behavior played a prominent role for bringing about the crisis, but even the greediest financial manager had the obligation to comply with financial regulation, and comply he did. This was only possible, we think, because the risk management establishment, which insisted that the tools they used were sufficient for meeting the challenge, easily dismissed any critique of actual practice in the financial sector that was based on an understanding of the financial system routed in historic expertise. Practically, these tools exclusively rested on the frequentist mindset, although the choice of these tools can conveniently be described by BRM. To put it bluntly: They did not see the risks because they did not want to see the risks. And they did not need to look at the risks ahead, because they relied on tools that allowed them look back. And the regulators let them prevail.

Concerning your item 1, we have two issues. First, you attributed to us the statement that data-intensive statistical methods rely on short historical time series to estimate future risks. We indeed think that there are data-intensive statistical methods that rely on short historical time series to estimate future risks. Others may use long historical time series, and still others may additionally use a prioris. The point we intended to make was that data-intensive statistical methods that rely on short historical time series to estimate future risks have dominated risk management in the financial community.

The second issue concerns your statement that it is possible to estimate future risk based on historical time series using Bayesian methods. We are unsure about how to interpret this statement. Are we supposed to read it as your opinion, or do you suggest that we have voiced it as our opinion in our abstract?

If we are supposed to read it as your opinion, we just want to note that we agree.

If, however, you suggest that we voiced this statement as our opinion in our abstract, we must admit that we are not aware of having done so, simply because we neither object this statement nor focus it.

Concerning the principle “no measurement without theory”, you are of course right that this belongs to the field of epistemology. Interestingly, none of us ever received this teaching from philosophers, but some of us received it several times from physicists. We find this intriguing as many people, laymen and academics alike, still think that discriminating between facts and theory would be possible, and that physics as hard science is a paradigmatic field in which such discrimination is daily practice.

Anonymous - Referee's Reply
July 29, 2013 - 11:38

Now, I read the authors' reply as well as all the related comments. I think the authors have not properly taken into account referees' suggestions; in fact, they are not available to modify their paper even if referees as well as readers made several comments pointing to a similar direction ...[more]

... (essentially, clear examples of the proposed method are missing). As it stands, this document is good for a discussion paper, but it is not suitable for publication. Therefore, I suggest rejection.