D. SORNETTE

ETH-ZurichChair of Entrepreneurial RisksDepartment of Management,Technology and Economicshttp://www.mtec.ethz.ch/

Shocks, Crises and Crashes in Nature and the Economy

Man-madeTerrorism, Global Warming,Pollution, Financial Crises,Riots, Overpopulation

EntrepreneurialOperational, Market,Credit, Cultural,Economic, Political

TechnologicalNuclear Meltdown,Aircraft Crashes, OilSpills, ComputerFailure, Explosions

NaturalEarthquakes, hurricanessnowstorms, floods,locust plagues, meteoriteimpacts, volcaniceruptions, forest fire

Heavy tails in pdf of earthquakes

Heavy tails in ruptures

Heavy tails in pdf of seismic rates

Harvard catalog

(CNES, France)

Turcotte (1999)

Heavy tails in pdf of rock falls, Landslides, mountain collapses

SCEC, 1985-2003, m≥2, grid of 5x5 km, time step=1 day

(Saichev and Sornette, 2005)

Heavy tails in pdf of Solar flares

Heavy tails in pdf of Hurricane losses

1000

104

105

1 10

Damage values for top 30 damaging hurricanes normalized to 1995 dollars by inflation, personal

property increases and coastal county population change

Normalized1925Normalized1900N

Dam

age

(mill

ion

1995

dol

lars

)

RANK

Y = M0*XM1

57911M0-0.80871M10.97899R

(Newman, 2005)

Heavy tails in pdf of rain events

Peters et al. (2002)

Heavy tails in pdf of forest fires

Malamud et al., Science 281 (1998)

0

200

400

600

800

1000

1200

1 2 3 4 5 6 7 8 9 10

After-tax present value in millions of 1990 dollars

DBC

1980-84 pharmaceuticals in groups of deciles

Exponential model 1dataExponential model 2

OUTLIERS OUTLIERS

Heavy-tail of Pharmaceutical sales

Heavy-tail of movie sales

Heavy-tail of price financialreturns

Heavy-tail of Firm sizes

Heavy-tail of pdf of war sizes

Levy (1983); Turcotte (1999)

Heavy-tail of pdf of health care costs

Rupper et al. (2002)

Heavy-tail of pdf of book sales

Heavy-tail of pdf of terrorist intensityJohnson et al. (2006)

Survivor Cdf

Sales per day

Market Risk + Intrinsic NON-diversification RiskHeavy distribution of firm’s capitalizations, lack of diversification and the pricing anomalies

Most risks can be diversified away but NOT the MARKET RISKS(CAPM, APT, Factor models…)

Yannick Malevergne and D Sornette (2006)

(Axtell, Science, 2001)

P(S)~1/S1+µ µ=1

(Axtell, 2001)

⇒ New Internal consistency factor (ICC)

Market factor

Market Factor +

f

Market Factor +

EW

Market + Under

Diversified

Market factor

Market Factor +

f

Market Factor +

EW

Market + Under

Diversifiedµ=2 94% 94% 95% 94% 99% 99% 99% 99%µ=1 80% 95% 95% 86% 88% 99% 99% 93%µ=0.5 56% 97% 97% 79% 56% 99% 99% 83%

N=1000 N=10000

P(S)~1/S1+µ µ=1

Simulation on Synthetic stock markets

Group 1 Group 4

CAPM ICC Cap Value GrowthValue +

Cap ICC + CapICC + Value

All Four Factors

Consumer Non Durables 75.9% 94.1% 88.4% 79.7% 91.8% 94.1% 94.3% 94.3%Consumer Durables 74.4% 92.3% 87.9% 76.9% 90.2% 92.4% 92.3% 92.4%Manufacturing 82.2% 96.7% 92.0% 85.9% 95.4% 96.8% 97.0% 97.1%Energy 58.3% 67.8% 63.7% 63.4% 68.5% 68.1% 69.3% 69.3%Business Equipment 74.5% 87.4% 86.2% 74.8% 86.6% 88.0% 91.6% 91.8%Telecom 62.7% 68.2% 68.1% 63.9% 69.4% 68.6% 72.6% 73.0%Shops 71.8% 90.1% 86.7% 72.8% 87.6% 90.3% 90.4% 90.5%Health 65.1% 74.5% 75.9% 66.4% 77.4% 76.2% 80.5% 80.5%Utilities 58.3% 60.8% 58.9% 65.9% 66.5% 61.7% 66.3% 66.5%Others 71.9% 92.8% 83.6% 81.6% 92.7% 93.4% 95.2% 95.2%

Average 69.5% 82.4% 79.1% 73.1% 82.6% 82.9% 84.9% 85.0%

Best of the groupWorst of the group

10 equally-weighted industry portfolios

Group 2 Group 3

Comparison with Fama-French three-factor model

• Self-organization?Extreme events are just partof the tail of power lawdistribution due to“self-organized criticality”?(endogenous)

•“Catastrophism”: extreme events require extreme causes that lie outside the system (exogenous)

•A mixture? How would it work?

Origin of LARGE RISKS?

Guidelines from Physics: perturb and study the response

Problem: Fluctuation-dissipation theoremfar from equilibrium is not expected to hold

Fluctuation-dissipation theorem far from equilibrium is not expected to hold

Externally imposed perturbations may be different from spontaneous fluctuations (external fluctuations lie outside the complex attractor)

Attractor of dynamics may exhibit bifurcations

D. Ruelle, Physics Today, May 2004

Endogenous versus ExogenousExtinctions -meteorite at the Cretaceous/Tertiary KT boundary -volcanic eruptions (Deccan traps) -self-organized critical eventsFinancial crashes

-external shock-self-organized instability

Immune system-external viral or bacterial attack- “ internal” (dis-)organization

Brain (learning)-external inputs-internal self-organization and reinforcements (role of sleep)

Recovery after wars?-internally generated (civil wars)-externally generated

Aviation industry recession-September 11, 2001-structural endogenous problems

Volatility bursts in financial time series -external shock -cumulative effect of “small” news

Commercial success and sales -Ads -epidemic network Social unrests -triggering factors -rotting of social tissue

Discoveries -serendipity -maturation

Parturition -mother/foetus triggered? -mother-foetus complex?

Earthquakes -active triggered seismicity -passive "witnesses"?

Multifractal scaling of thermally activated rupture

Example for the Landers

aftershock sequence

(1992, M=7.3, California)

Temporal decay of the rate N(t) of aftershocks

after a mainshock at t=0

N(t) = K/(t+c)p

p is in the range [0.3, 2], often close to 1

[Omori, 1894; Utsu, 1960]

Landers28 june 1992M=7.3

Big-Bear, M=6.4 28/06 8:05

Big-Bear, M=6.4 28/06 8:05

Joshua Tree, 22/04 M=6.1 Joshua Tree,Joshua Tree, 22/04 M=6.1 22/04 M=6.1

Krau

sz a

nd K

raus

z, 19

87

Mechanics of Triggered Seismicity

A B

One class of models to explain triggeredseismicity is slow crack growth : under theeffect of applied stress and thermal agitation,cracks within rocks grow subcritically bybreaking successive atomic bonds (representedby springs). After they reach a critical length,they propagate critically : this is the seismicevent.

σNτ

The second class is state and rate-dependent friction, which predicts atime shift between a stress perturbationand the possible slip instability. Thisprocess is also activated by stress andtemperature.

λ0 ~ mean seismicity rate

λ(t) : seismicity rate

σ0 : strength

σ(t) : applied stress

V : activation volume

T : temperature

k : Boltzmann’s constantTime

Cumulative nb of EQ

slope ~ λ0

The Physics of Stress-Aided Thermal Activation of Rupture

( ) ( )

−−= VkT

tt σσλλ 00 exp

Poisson Intensity (average conditional seismicity rate) At position and time t

(Zhurkov, 1965)

p(M) = aM + bN(t) ~ 1/tpPrediction:

V

Σ

D. Sornette and G. Ouillon, Multifractal Scaling of Thermally-Activated Rupture Processes, Phys. Rev. Lett. 94, 038501 (2005)

Multifractal hierarchy of Omori laws N(t) ~ 1/tp

Rib eir o e t al, 2 00 6

For Southern California (SCEC catalog):

p(M) = 0.10M + 0.37

For Japan (JMA catalog):

p(M) = 0.07M + 0.54

For the World (Harvard catalog):

p(M) = 0.14M + 0.11

p(M) = aM + bN(t) ~ 1/tp

Southern California

Macro signature of kBT amplifiedby exponential of long-memoryprocess and multi-scaleheterogeneity

Financial shocks and Forecast of Financial Volatility

(Sornette, 2003)

scale

time

Arneodo, Muzy and Sornette (1998)

Causal cascade of volatility from large to small time scales

The Multifractal Random Walk (Bacry, Muzy, 2000)

D. Sornette, Y. Malevergne andJ.F. Muzy,Volatility fingerprintsof large shocks: Endogeneousversus exogeneous,Risk Magazine (2003)

Response to an external shock

Real Data and prediction of Multifractal Random Walk model

D. Sornette et al., Phys. Rev. Letts. 93 (22), 228701 (2004); F. Deschatres and D. Sornette, The Dynamics of Book Sales: Endogenous versus ExogenousShocks in Complex Networks, Phys. Rev. E 72, 016112 (2005)

PREDICTING COMMERCIAL SALES

20:00 4 March. 2005

Updated every hourAMAZON BOOK SALES

The Original “Crisis”

• On Friday January 17, 2003,WSMC jumped to rank 5 onAmazon.com’s sales ranking (withHarry Potter as #1!!!)

• Two days before: release of aninterview on MSNBC’sMoneyCentral website

(2003)

Epidemic branching process of word-of-mouth

endogenous

Exogenousrelaxation

Exogenous precursor

θ=0.3±0.1

Real data averaged over +100 books

Exogenousrelaxation

Exogenous precursor

endogenous

Predicting the rise and fall of social and economic interactionsby monitoring and modeling internet activities and commercial sales

• Book, CD music sales…

• Internet searches

• YouTube

• Open source software projects

• Ethical Hacking security

• NATO (National Association of Theatre Owners)

Survivor cdf

Nb views

(R. Crane, G. Daniel, Nov 06)

R. Crane, G. Daniel, G. Harras, Y. Malevergne, DS + ….

Predicting Financial Crashes

Each bubble has been rescaled vertically and translatedto end at the time of the crash

time (~2 years)

price

A. Johansen and D. Sornette, Stock market crashes are outliers, European Physical Journal B 1, 141-143 (1998)Johansen, A. and D. Sornette, Large Stock Market Price Drawdowns Are Outliers,Journal of Risk 4(2), 69-110, Winter 2001/02

Outlier or King effect -material rupture-hydro turbulence-finance…

Drawdown Drawup

Ln(Survival CDF)

950C

1Kg

1cm

97

1cm

1Kg

99

1Kg

101

The breaking ofmacroscopiclinearextrapolation

?Extrapolation?

BOILING PHASE TRANSITIONMore is different: a single molecule does not boil at 100C0

Simplest Example of a “More is Different” TransitionWater level vs. temperature

(S. Solomon)

95 97 99 101

Example of “MORE IS DIFFERENT” transition in Finance:

Instead ofWater Level:-economic index(Dow-Jones etc…)

Crash = result of collective behavior of individual traders(S. Solomon)

Mechanisms for positive feedbacks in the stock markets

• Technical and rational mechanisms for positive feedbacks1. Option hedging2. Insurance portfolio strategies3. Trend following investment strategies4. Asymmetric information on hedging strategies

• Behavioral mechanisms for positive feedbacks1. It is rational to imitate2. It is the highest cognitive task to imitate3. We mostly learn by imitation4. The concept of “CONVENTION” (Orléan)

Feedbacks: negative but also POSITIVE

Herding in finance

Disorder : K small

OrderK large

Critical:K=criticalvalue

Renormalization group:Organization of thedescription scale by scale

Scale invariance

Our prediction system is now used in the industrial phaseas the standard testing procedure.

J.-C. Anifrani, C. Le Floc'h, D. Sornette and B. Souillard "Universal Log-periodic correction to renormalization group scaling for rupture stressprediction from acoustic emissions", J.Phys.I France 5, n°6, 631-638 (1995)

Strategy: look at the forest ratherthan at the tree

Red line is 13.8% per year: but themarket is never following the averagegrowth; it is either super-exponentiallyaccelerating or crashing

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

Psychology of Investors and EntrepreneursThe “principle of Galilean invariance” in human psychology

Results: In worldwide stock markets + currencies + bonds

•21 endogenous crashes•10 exogenous crashes

1. Systematic qualification of outliers/kings in pdfs of drawdowns2. Existence or absence of a “critical” behavior by LPPL patternsfound systematically in the price trajectories preceding thisoutliers

Endogenous vs exogenous crashes

+C

Demonstration of universal values of z and ω across many different bubblesat different epochs and different markets

ω

z z

z

Probability of crashes; alarm index–Successful forward predictions: Oct. 1997; Aug. 1998, April 2000–False alarms: Oct. 1997

The bubble andCrash of Oct. 1987Continuous line:first-order LPPLDashed line: second-order LPPL

Transversal analysis of credit risk, firm network risk,asymmetric information risk and bubble risk:

towards a "Crisis Observatory"

• Added-value strategies / expected returns1. Asymmetric information between managers and investors2. Reverse engineering of hedge-funds and derivative strategies3. Combining portfolio and investment strategies

• Risk measure and control1. Scenario and crises analyses2. Robust statistical methods to address model error

• Bubbles, crashes and extreme risks of unsustainable regimes1. The “Crisis Observatory” and crash alarm index2. Robust multivariate scanning of world assets3. NL models with positive and negative feedbacks

• Macro and micro economic analyses1. Separating information from “noise’’ and false consensus2. Endogenous vs exogenous extreme risks

G. Daniel, G. Harras, S. Hu, Y. Malevergne, V. Pisarenko, DS, A. Saichev, S. Yukalov ….