Zurich Dragon-Kings the nature of extremes, stascal tools of outlier detecon, generang mechanisms, predicon and control Professor of

Professor of Finance at the Swiss Finance Institute

associated with the Department of Earth Sciences (D-ERWD), ETH Zurich

associated with the Department of (D-PHYS), ETH Zurich

Director of the Financial Crisis Observatory

Founding member of the Center at ETH Zurich (June 2011) (www.riskcenter.ethz.ch)

Black Swan (Cygnus atratus)

www.er.ethz.ch

Fundamental changes follow extremes

• Droughts and the collapse of the Mayas (760-930 CE) • French revolution 1789 • “Spanish” worldwide flu 1918 • USSR collapse 1991 • Challenger space shuttle disaster 1986 • dotcom crash 2000 • Financial crisis 2008 • Next financial-economic crisis? • European sovereign debt crisis: Brexit… Grexit…? • Next cyber-collapse? • “Latent-liability” and extreme events 23 June 2016

How Europe fell out of love with the EU ! What is the nature of extremes?

Are they “unknown unknowns”?

?

Black Swan (Cygnus atratus)

32 Standard view: fat tails, heavy tails and Power law distributions const

−1 ccdf (S) = 10 complementary cumulative µ −2 S 10 distribution function 10−3 10−4 10−5 10−6 10−7 102 103 104 105 106 107 Heavy tails in debris Heavy tails in AE before rupture

Heavy-tail of pdf of war sizes Heavy-tail of cdf of cyber

ID Thefts MECHANISMS -proportional growth with repulsion from origin FOR POWER LAWS -proportional growth birth and death processes -coherent noise mechanism

Mitzenmacher M (2004) A brief history of generative -highly optimized tolerant (HOT) systems models for power law and lognormal distributions, Internet Mathematics 1, -sandpile models and threshold dynamics 226-251. (self-organized criticality => fault and earthquakes)

Newman MEJ (2005) Power •critical desynchronization laws, Pareto distributions and •dynamical system theory of self-organized criticality Zipf’s law, Contemporary (coupling of sub-critical bifurcations) Physics 46, 323-351.

D. Sornette (2004) Probability -nonlinear feedback of the order parameter onto the control parameter Distributions in Complex Systems, Encyclopedia of Complexity and System -generic Science (Springer Science), 2004 -mapping onto a critical point (contact processes) D. Sornette (2006) in Natural Sciences, Chaos, , -extremal dynamics Self-organization and Disorder: Concepts and Tools, -sweeping of an instability 2nd ed., 2nd print, pp.528, 102 const figs. , 4 tabs (Springer Series ccdf (S) = µ in Synergetics, Heidelberg) -avalanches in hysteretic loops S Power law-Black Swan story

• Unknown unknowable event ★ cannot be diagnosed in advance, cannot be quantified, no predictability • No responsability (“wrath of God”) • Standard approach: statistical risk and reliability analysis Proposition: Extremes and Crises are not black swans but “Dragon-kings”

Dragon-kings (DK) embody a double metaphor implying that an event is both extremely large (a "king''), and born of unique origins ("dragon") relative to its peers.

The hypothesis proposed in [Sornette, 2009] is that DK events are generated by distinct mechanisms that intermittently amplify extreme events, leading to the generation of runaway disasters as well as extraordinaryBlack Swan (Cygnus opportunities atratus) on the upside. Beyond power laws: examples of “Dragons”

Financial : Outliers and dragons in the distribution of financial drawdowns. Population geography: Paris as the dragon-king in the Zipf distribution of French city sizes. Material science: failure and rupture processes. Hydrodynamics: Extreme dragon events in the pdf of turbulent velocity fluctuations. Metastable states in random media: Self-organized critical random directed polymers

Brain medicine: Epileptic seizures : Characteristic earthquakes? Great avalanches? Floods? Mountain collapses? Meteological events? and so on

Ionosphere and magneto-hydrodynamics: Global auroral energy deposition 2009 dragon-kings

(Spencer Wheatley and Didier Sornette, 2015) time-to-failure analysis

...

H. Nechad, A. Helmstetter, R. El Guerjouma and D. Sornette, Andrade and Critical Time-to-Failure Laws in Fiber-Matrix Composites: Experiments and Model, Journal of Mechanics and Physics of Solids (JMPS) 53, 1099-1127 (2005)

Energy distribution for the [+-62] specimen #4 at different times, for 5 time windows with 3400 events each. The average time (in seconds) of events in each window is given in the caption.

S.G. Sammis and D. Sornette, Positive Feedback, Memory and the Predictability of Earthquakes, Proceedings of the National Academy of Sciences USA, V99 SUPP1:2501-2508 (2002 FEB 19) Cumulative of epidemic fatalities

amplification by (i) hiding and (ii) enhanced connectivity via WWII

1918 spanish flu

dragon-kings

source: http://www.emdat.be Traditional emphasis on Daily returns do not reveal any anomalous events

42 (Courtesy Vladimir Filimonov) Most extremes are dragon-kings Better risk measure: drawdowns

A. Johansen and D. Sornette, Stock market crashes are outliers, European Physical Journal B 1, 141-143 (1998)

A. Johansen and D. Sornette, Large Stock Market Price Drawdowns Are Outliers, Journal of Risk 4(2), 69-110, Winter 2001/02

43 Extreme Risks: Dragon-Kings versus Black Swans

Special Issue EPJ ST SPRINGER D. Sornette and G. Ouillon Guest Editors (May 2012) Dragon-king hypothesis • Most crises and extremes are “endogenous” ★ can be diagnosed in advance, can be quantified, (some) predictability • Moral hazard, conflict of interest, role of regulations • Responsibility, accountability • Strategic vs tactical time- dependent strategy • Weak versus global signals POSITIVE FEEDBACKS

http://www.businessweek.com/the_thread/economicsunbound/archives/2009/03/a_bad_decade_fo.html Michael Mandel Ex. of Dragon-King: the 2008 crisis

Index of over- • Worldwide bubble (1980-Oct. 1987) valuation • The ICT (dotcom) “new economy” bubble (1995-2000)

• Real-estate bubbles (2003-2006)

• MBS, CDOs bubble (2004-2007)

• Stock market bubble (2004-2007)

• Commodities and Oil bubbles (2006-2008)

• Debt bubbles The “perpetual money machine” broke. PCA first component on a data set containing, emerging markets equity indices, freight indices, soft commodities, base and precious metals, energy, currencies...

2003 2004 2005 2006 2007 2008 2009

D. Sornette and P. Cauwels, 1980-2008: The Illusion of the Perpetual Money Machine and what it bodes for the future, Risks 2, 103-131 (2014) (http://arxiv.org/abs/1212.2833) THE GREAT MODERATION

source: U.S. Bureau of Labor . Wheatley, Spencer and Sornette, Didier (2016) Test statistics for DK detection

sum to robust-sum statistic:

max to robust-sum statistic:

issues of (i) swamping vs masking; (ii) inward vs outward

Wheatley, Spencer and Sornette, Didier (2016) MRS: Max-Robust-Sum ratio; SRS: Sum-Robust-Sum ratio Wheatley, Spencer and Sornette, Didier (2016) Wheatley, Spencer and Sornette, Didier (2016) (NAMS: Nuclear Accident Magnitude Scale) CCDF of severity of events. Panel I: The main frame plots the cost of events for the pre- and post- TMI periods according to their CCDFs, in gray and black, respectively. The lower inset figure shows the p-value of a segmentation test of the cost data, identifying TMI (1979) as the change-point in the cost distribution. The upper inset figure shows the estimated parameter α (with ) of a (Equation (3)), for the post-TMI cost data, for a range of lower thresholds (u1). The fit for u1 = 30 (MM USD) is given by the red solid line in the main frame. Panel II: In the main frame, from left to right, are the CCDF of INES scores above 2 (shifted left by 1), the CCDF of NAMS scores above 2, and the CCDF of the natural of post-1980 costs (shifted right by 2). For the center and right CCDFs, the dots with x marks indicate suspected outliers/dragon kings. The dashed and solid red lines are exponential fits to the CCDFs. The inset figure provides the p- value for the outlier test for the upper sample above a growing threshold. The upper curve is for r = 3 outliers, and the lower curve for r = 2 outliers. Spencer Wheatley, Benjamin Sovacool and Didier Sornette, Of Disasters and Dragon Kings: A Statistical Analysis of Nuclear Power Incidents & Accidents, Risk Analysis DOI: 10.1111/risa.12587, pp. 1-17 (2016) DK-detection by breakdown of collapse of pdf’s at different scales

Pdf of the square of the Velocity as in the previous figure but for a much longer time series, so that the tail of the distributions for large Fluctuations is much better constrained. The hypothesis that there are no outliers is tested here by collapsing the Collapse ~of positions and amplitudes for five intensive peaks belonging to the 20th shell. distributions for the three shown layers. While this is a success for small fluctuations, the tails of the distributions for large events are very different, indicating that extreme fluctuations belong to a different class of their own and hence are outliers.

L'vov, V.S., Pomyalov, A. and Procaccia, I. (2001) Outliers, Extreme Events and Multiscaling, Physical Review E 6305 (5), 6118, U158-U166. Mechanisms for Dragon-kings •Partial global synchronization

•Generalized correlated (droplets) percolation

•Transient positive feedbacks leading to singular “finite-time singularity” and changes of regimes/ ruptures/phase transitions

•A kind of condensation (a la Bose-Einstein)

•Forward looking optimisation of consumption/ investment in economic models with heterogenous impatience L. Gil and D. Sornette, Landau-Ginzburg theory of self-organized criticality”, Phys. Rev. Lett. 76, 3991-3994 (1996)

Mechanism: Negative effective Diffusion coefficient

DK for /↵ > 1 56 Mechanisms for Dragon-kings •Partial global synchronization

•Generalized correlated (droplets) percolation

•Transient positive feedbacks leading to singular “finite-time singularity” and changes of regimes/ ruptures/phase transitions

•A kind of condensation (a la Bose-Einstein)

•Forward looking optimisation of consumption/ investment in economic models with heterogenous impatience distribution of percolation cluster sizes above pc Cluster size distribution close to percolation transition for various filament lengths

Raghunath Chelakkot and Thomas Gruhn,Length dependence of crosslinker induced network formation of rods: a Monte Carlo study; Soft Matter 8, 11746)11754 (2012) Scheme of a model system for the rods and linkers Reliability Analysis of Electric Power Systems Using an Object-oriented Hybrid Modeling Approach Markus Schlaepfer, Tom Kessler, Wolfgang Kroeger 16th Power Systems Computation Conference, Glasgow, Scotland, July 14-18, 2008 (PSCC’08)]

L=1.37

L=1.2 L=1

L=1.1

CCDF of blackout energies for four different system loading levels L=1.0, 1.1, 1.2 and 1.37 (circles, stars, triangles and diamonds, respectively) without operator intervention. Mechanisms for Dragon-kings •Partial global synchronization

•Generalized correlated (droplets) percolation

•Transient positive feedbacks leading to singular “finite-time singularity” and changes of regimes/ ruptures/phase transitions

•A kind of condensation (a la Bose-Einstein)

•Forward looking optimisation of consumption/ investment in economic models with heterogenous impatience CREEP Positive feedbacks

Creep strain as a function of time (renormalized by the rupture time tc), for 3 samples.

H. Nechad, A. Helmstetter, R. El Guerjouma and D. Sornette, Creep Ruptures in Heterogeneous Materials, Phys. Rev. Lett. 94, 045501 (2005) ; Andrade and Critical Time-to-Failure Laws in Fiber-Matrix Composites: Experiments and Model, Journal of Mechanics and Physics of Solids (JMPS) 53, 1099-1127 (2005) standard law of supply and demand Positive feedbacks in finance Mechanisms for positive feedbacks in the stock market

• Technical and rational mechanisms 1. Option hedging 2. Insurance portfolio strategies 3. Market makers bid-ask spread in response to past volatility 4. Learning of business networks, human capital 5. Procyclical financing of firms by banks (boom vs contracting times) 6. Trend following investment strategies 7. Algorithmic trading 8. Asymmetric information on hedging strategies 9. Stop-loss orders 10. Portfolio execution optimization and order splitting 11. Deregulation (Grimm act repelling the Glass-Steagal act) 12. Central banks monetary policies

• Behavioral mechanisms: 1. Breakdown of “psychological Galilean invariance” 2. Imitation(many persons) a) It is rational to imitate b) It is the highest cognitive task to imitate c) We mostly learn by imitation d) The concept of “CONVENTION” (Orléan) 3. “Social Proof” mechanism 64 Hong-Kong

Red line is 13.8% per year: but The market is never following the average growth; it is either super-exponentially accelerating or crashing

Patterns of price trajectory during 0.5-1 year before each peak: Log-periodic power law

65 Phase transitions and critical behavior

Order parameter

power law behavior

dragon-kings

Control parameter 66

= µ µ µ c µc Signs of Upcoming Transition

Early warning signals as predicted from theory

• Slower recovery from perturbations

• Increasing (or decreasing) autocorrelation

• Increasing (or decreasing) cross-correlation with external driving

• Increasing

• Flickering and stochastic resonance

• Increased spatial coherence

• Degree of endogeneity/reflexivity • Finite-time singularities Diagnostic of Ariane rocket pressure tanks

• Increasing variance • Increased spatial coherence • Finite-time singularity

Our prediction system is now used in the industrial phase as the standard testing procedure. Prof. Dr. Didier Sornette www.er.ethz.ch D-MTEC Chair of Entrepreneurial Risks Generic Risk Prediction Phase Diagram

Interaction (coupling) strength

SYNCHRONIZATION EXTREME RISKS + 10 + Coexistence of SOC and* Synchronized behavior 1 + + + + * 0.1 + * * 0.01 * SELF-ORGANIZED* * CRITICALITY

0.001 INCOHERENT 0.001 0.01 0.1 1 10 Heterogeneity; level of compartmentalization Financial Crisis Observatory Zurich

•Hypothesis H1: financial (and other) bubbles can be diagnosed in real-time before they end.

•Hypothesis H2: The termination of financial (and other) bubbles can be bracketed using probabilistic forecasts, with a reliability better than chance (which remains to be quantified).

The Financial Bubble Experiment advanced diagnostics and forecasts of bubble terminations •Time@Risk: Development of dynamical methods China stock markets crash June-July 2015 http://tasmania.ethz.ch/pubfco/fco.html

Didier Sornette, Gil Demos, Qun Zhang, Peter Cauwels, Vladimir Filimonov and Qunzhi Zhang, Real-time prediction and post- mortem analysis of the Shanghai 2015 stock market bubble and crash, Journal of Investment Strategies (September issue 2015) (Swiss Finance Institute Research Paper No. 15-32. Available at http://ssrn.com/abstract=2647354) http://www.er.ethz.ch/financial-crisis-observatory.html http://www.er.ethz.ch/financial-crisis-observatory.html http://www.er.ethz.ch/financial-crisis-observatory.html Slaying dragon-kings predictability and control of extreme events in complex systems

possibility to control by small targeted perturbations

Hugo L. D. de S. Cavalcante, Marcos Oria, Didier Sornette, Edward Ott and Daniel J. Gauthier, Phys. Rev. Lett. 111, 198701 (2013) Predictability and control of extreme events in complex systems

Hugo L. D. de S. Cavalcante, Marcos Oriá, Didier Sornette, Ed Ott and Daniel J. Gauthier

•Large class of spatially extended coupled oscillators (physics of earthquakes, biological systems, financial systems, ...) •Most coupled-oscillator systems exhibiting chaos have multiple basins of attraction associated with invariant manifolds. •Generically, riddled basins are found in these coupled-oscillator systems: this that a region of the basin of attraction for one has neighboring intermingled points (“holes”) that connect to one or more of the other . •Riddled basins are always associated with weak attractors, which in turn are associated with attractor bubbling. •A bubble: the system trajectory irregularly and briefly leaves an invariant manifold as a result of occasional noise-induced jump from the dominating stable attractor to a hole in the riddled basin that connects the trajectory to another attractor, eventually followed by reinjection to the dominating attractor in many situations.

•Attractor bubbling in riddled basins of attraction is a generic mechanism

We conjecture this mechanism applies to a large class of spatially extended deterministic and stochastic nonlinear systems. Predictability and control of extreme events in complex systems Hugo L. D. de S. Cavalcante, Marcos Oria, Didier Sornette, Edward Ott and Daniel J. Gauthier, Phys. Rev. Lett. 111, 198701 (2013) Two coupled chaotic systems: master and slave

coupling strength

Synchronization:

power law pdf with exponent -2 invariant manifolds with chaotic orbits

attractor bubbling as well as riddled basins and on-off intermittency

Forecasting of dragon-kings

The unstable saddle-type fixed point at is exceedingly transversely unstable and is the underlying originator of the largest bubbles possibility to control by small targeted perturbations

Control: when , feedback perturbations are applied that are only 3% of the system size (defined as the maximum value of ). Such small perturbation only causes a small change in , yet it has a dramatic change in

control on (both in numerical and laboratory experiments)

dragon-kings

log frequency

Event sizes There is much life beyond power law fluctuations… -Dragon-kings are ubiquitous

-Dragon-kings dominate the long-term organization of complex systems

-Novel robust outlier detection tests

-Prediction of dragon-kings

-Control of dragon-kings Humanity in the Anthropocene => regime shift in 2030-2060 has already started

Barnosky et al. Nature 486, 52-58 (2012)

World human population World GDP

A. Johansen and D. Sornette, Physica A 294 (3-4), 465-502 (2001)

Johan Rockström (Stockholm Resilience Centre) Energy Research & Social Science 8 (2015) 60–65

Humankind is confronted with a “nuclear stewardship curse”, facing the prospect of needing to manage nuclear products over long time scales in the face of the short- time scales of human polities. I propose a super Apollo-type effort to rejuvenate the nuclear energy industry to overcome the current dead-end in which it finds itself, and by force, humankind has trapped itself in. I propose a paradigm shift from a low probability of incidents/accidents to a zero-accident technology and a genuine detoxification of the wastes. A 1% GDP investment over a decade in the main nuclear countries could boost economic growth with a focus on the real world, epitomised by nuclear physics/chemistry/engineering/economics with well defined targets. By investing vigorously to obtain scientific and technological breakthroughs, we can create the spring of a world economic rebound based on new ways of exploiting nuclear energy, both more safely and more durably.

Need for massive risk- taking at the level of societies (similar to WWII efforts) to an INNOVATION POLICY.

(not just monetary policies and fiscal policies) Further Reading D. Sornette, Dragon-Kings, Black Swans and the Prediction of Crises, International Journal of Terraspace Science and Engineering 2(1), 1-18 (2009) (http://arXiv.org/abs/0907.4290) and http://ssrn.com/abstract=1470006)

D. Sornette and G. Ouillon, Dragon-kings: mechanisms, statistical methods and empirical evidence, Eur. Phys. J. Special Topics 205, 1-26 (2012) (http://arxiv.org/abs/1205.1002 and http://ssrn.com/abstract=2191590)

D. Sornette and G. Ouillon, editors of the special issue of Eur. Phys. J. Special Topics on ``Discussion and debate: from black swans to dragon-kings - Is there life beyond power laws?'', volume 25, Number 1, pp. 1-373 (2012). http://www.springerlink.com/content/d5x6386kw2055740/?MUD=MP

D. Sornette and R. Woodard Financial Bubbles, Real Estate bubbles, Derivative Bubbles, and the Financial and Economic Crisis, in Proceedings of APFA7 (Applications of Physics in Financial Analysis), “New Approaches to the Analysis of Large-Scale Business and Economic Data,” M. Takayasu, T. Watanabe and H. Takayasu, eds., Springer (2010) (http://arxiv.org/abs/0905.0220))

D. Sornette and P. Cauwels, 1980-2008: The Illusion of the Perpetual Money Machine and what it bodes for the future, Risks 2, 103-131 (2014) http://ssrn.com/abstract=2191509)

D. Sornette and P. Cauwels, A creepy world, Journal of Risk Management in Financial Institutions (JRMFI) 8 (1), 83-108 (2015)

D. Sornette and P. Cauwels, Financial Bubbles: Mechanism and diagnostic, Review of Behavioral Economics 2 (3) (2015)

Didier Sornette, Why Stock Markets Crash (Critical Events in Complex Financial Systems) Princeton University Press, January 2003

Y. Malevergne and D. Sornette, Extreme Financial Risks (From Dependence to Risk Management) (Springer, Heidelberg, 2006).

S. Wheatley and D. Sornette, Multiple Outlier Detection in Samples with Exponential and Pareto Tails: Redeeming the Inward Approach and Detecting Dragon Kings, (http://arxiv.org/abs/1507.08689 and http://ssrn.com/abstract=2645709)

S. Wheatley, T. Maillart and D. Sornette, The Extreme Risk of Personal Data Breaches and The Erosion of Privacy, Eur. Phys. J. B 89 (7), 1-12 (2016)

D. Chernov and D. Sornette, Man-made catastrophes and risk information concealment (25 case studies of major disasters and human fallibility), Springer (2016),