Gaussian and Paretian

1. Gaussian and Paretian

2. Gaussian – heights of individuals Ratio = 3.7 Tallest man (Robert PershingWadlow) 272 cm Shortest man (He Pingping) 74 cm Source : LadaAdamic - http://www.hpl.hp.com/research/idl/papers/ranking/ranking.html

3. Paretian: city size Largest city (NYC) pop 8 million Smallest city (Duffield, Virginia) pop. 52 Ratio = 150000 Krugman on the Zipf law: “we are unused to seeing regularities this exact in economics – it is so exact that I find it spooky”(1996) p.40 Source: Bak (1996) “How Nature Works”

4. Paretian: word frequency in TV and movie scripts Most frequent word* (rank 1: you = 1222421) Least frequent word (rank 40000: imperious = 6) Ratio: = 203737 * http://en.wiktionary.org/wiki/Wiktionary:Frequency_lists/TV/2006/1-1000

5. Paretian: wealth Wealthiest person (John D Rockfeller) ~ 189.6 billion Poorest (?) ~1000 Ratio =189.000.000

6. Scale-free Networks SEX web scale-free network Routers web Nodes: people (Females; Males) Links: sexual relationships 4781 Swedes; 18-74; 59% response rate. Nodes: computers, routers Links: physical lines (Liljeroset al. Nature 2001) (Faloutsos, Faloutsos and Faloutsos, 1999)

7. 3/4 mistery West and Brown. Life's Universal Scaling Laws West, Brown & Enquist (1997). A General Model for the Origin of Allometric Scaling Laws in Biology Allometric growth – cube-surface law

8. Scaling exponents for urban indicators vs. city size Y(t) = Y0 N(t) β Bettencourt et Al. 2007. Growth, innovation, scaling, and the pace of life in cities, PNAS, vol. 104 no. 17 , 7301–7306¶

9. Cities Traffic jams Coastlines Brush-fire damage Water levels in the Nile Hurricanes & floods Earthquakes Asteroid hits Sun Spots Galactic structure Sand pile avalanches Brownian motion Music Epidemics/Plagues Genetic circuitry Metabolism of cells Functional networks in brain Tumor growth Biodiversity Circulation in plants and animals Langton’s Game of Life Fractals Punctuated equilibrium Mass extinctions/explosions Brain functioning Predicting premature births Laser technology evolution Fractures of materials Magnitude estimate of sensorial stimuli Willis’ Law: No. v. size of plant genera Fetal lamb breathing Bronchial structure Frequency of DNA base chemicals Protein-protein interaction networks Heart-beats Yeast 36 Kinds of “Physical” Power Laws

10. Structure of the Internet equipment Internet links # hits received from website/day Price movements on exchanges Economic fluctuations “Fordist” power structure/effects Salaries Labor strikes Job vacancies Firm size Growth rates of firms Growth rates of internal structure Supply chains Cotton prices Alliance networks among biotech firms Entrepreneurship/Innovation Director interlock structure Italian Industrial Clusters Language—word usage Social networks Blockbuster drugs Sexual networks Distribution of wealth Citations Co-authorships Casualties in war Growth rate of countries’ GDP Delinquency rates Movie profits Actor networks Size of villages Distribution of family names Consumer products Copies of books sold Number of telephone calls and emails Deaths of languages Aggressive behavior among children “No learning” agents (Ormerod) 38 Kinds of “Social” Power Laws

11. We live immersed in an universe surrounded by power laws inside and outside us Why does it matter?

12. We live immersed in an universe surrounded by power laws inside and outside us What happens if we get it wrong and assume a Gaussian world instead of a Paretian one?

13. Exponentials vs. Power Laws Power law y = x -   = constant Exponential y = e – x e = constant Linear axes Log axes Power Law Power Law Bell Curve Bell Curve

14. 1st caseFinancial markets and extreme events

15. Do It Yourself (Financial DIY) • Download Dow Jones index numbers from: http://www.dowjones.com • Take daily variation: take log of each daily index number. Subctract log from following day log • Assume variations fit Gaussian and calculate sample variance s2 or s2 =  (xav –xi )2 / (n-1) • Calculate how typical each crash day is: z = (xi – xav) / s • Using z score calculate probability Mandelbrot & Hudson 2004

16. Probability of financial crushes according to standard financial theory (Mandelbrot, 2004) • August 31, 1998 6.8% Wall Street crush 1 in 20 million • August 1997 7.7% Dow Jones 1 in 50 billion • July 2002 3 step falls in 7 days 1 in 4 trillion And finally • October 19, 1987 29.2% fall 1 in 10-50 “It is a number outside the scale of nature. You could span the powers of ten from the smallest subatomic particle to the breadth of the measurable universe – and still never meet such a number”

17. 2nd caseRisk, Hollywood and skewed industry

18. Budget, revenue and profit in a typical year Budget, Revenue, & Profit in the US Movie Industry in 1999 (Longstaff et al. 2004).

19. Extreme events: outliers support the industry • ‘The Blair Witch Project,’ • Cost = $60,000 • Revenue = 140 million • ‘Waterworld,’ • Cost = $175 • Revenue = $88 million

20. Unrealistic picture of risk (De Vany Hollywood Economics 2003, pp. 219, 284) it masks the importance of the rare events determining the success of the industry and creates a false sense of security ‘(Illusion of Control’ fallacy) Econometric models used for predictions. Results: “predictions of total grosses for an individual movie can be expected to be off by as much as a multiplicative factor of 100 high or low”. (Simonoff and Sparrow, 2000) Consequence: “studio models focus on forecasting expected values and virtually ignore the variance”

21. Assume movie industry is Paretian (De Vany Hollywood Economics 2003, pp. 219, 284) • Risk is unbounded: profit and loss are scalable • Calculate slope. It gives indication of variability and consequently real risk • Scaling property of Paretian distribution allows the statistical calculation of ratios. For instance • Ratio = N10.000/ N100.000 = N100.000/ N1.000.000 = exponent • Practices based on expected results (flat fee distribution, contracting) are damaging. Adopt contingent reward and contract approach • ‘Star system’ doesn’t seem to work

22. 3rd caseManaging niches: Chris Anderson’s Long Tail

23. Two tails of a power law Ricther-Gutenberg Law Small events tail Casti _126 Nc (Earthquakes/Year) Extreme events tail Find gutemberg Earthquake magnitude (mb ) ~ Log E

24. Markets without ends Anderson (2006) The Long Tail

25. Anderson (2006) The Long Tail

26. Anderson (2006) The Long Tail

28. The death of the 80/20 rule of profit Anderson (2006) The Long Tail

29. Fractal markets Anderson (2006) The Long Tail

30. Managing tails as if they were averages Sales predicted by power law model Cut-off point 2nd power law region Latent demand space: new long tail 1st power law region Traditional markets: traditional long tail ……………………. 1.000.000.000 100.000.000 10.000.000 1.000.000 100.000 10.000 1.000 100 10 1 • Long tail of rare, high-impact (‘hits’) events • ‘Economy of scarcity’ • Homogeneous markets • Consumerism • 80/20 rule-inspired management • Long tail of small niches • ‘Economy of abundance’ • Heterogeneous markets • Producerism • Diversity Revenues 1 10 100 1.000 10.000 … 10.000.000 … Product Rank

31. Latent markets Anderson (2006) The Long Tail

32. Google Rhapsody & iTunes Netflix eBay Advertising Music Movies Physical goods and merchants Aggregators Aggregate the long tail of

33. Illycaffe’ Transforming TIEs into positive extreme events Power Law Hollywood The management of risk from Gaussian mean to Paretian tail Anderson From minimum common denominator to niche aggregation strategy Gladwell From management of averages to management of extreme events tail Gaussian Curve

34. Gaussian vs Paretian In a Gaussian world: • Challenge: manage the population • How: reduce population to the representative agent and define variance (of population) • Manage around mean and variance In a Paretian world: • Challenge: manage the frontier • Identify outliers and manage the tail of the distribution • Manage tail

35. The danger of averages Any questions? Thank you