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Unformatted text preview: Risk Management in the Real World Lecture 2 Introduction to Power Laws The supreme law of Mediocristan Imagine a 1000 persons standing on a stadium. Think that the heaviest conceivable man you know is among them. How much of the total does he represent? .3%? The supreme law of Mediocristan : as the number of observations becomes very large, not a single element can be consequential to the total. 2 The Supreme Law of Extremistan Imagine the same stadium, the same people. Include the wealthiest person you know in there –say Bill Gates. How much does he weigh compared to the total? 99.999%? Economic variables do not work like weight, height, calories consumed, etc. 3 N N Taleb © 2008 Odds of Exceeding with a Gaussian • 3 sigmas: 1 in 740 times • 4 sigmas :1 in 32,000 times • 5 sigmas :1 in 3,500,000 times • 6 sigmas :1 in 1,000,000,000 times • 8 sigmas :1 in 1,600,000,000,000,000 times • 10 sigmas:1 in 130,000,000,000,000,000,000,000 times • 20 sigmas: 1 in 3600000000000000000000000000 • 00000000000000000000000000000000000000000000000000 00000000000 times Notice the acceleration 4 N N Taleb © 2008 Richer than 1 million: 1 in 62.5 Richer than 2 million: 1 in 250 Richer than 4 million: 1 in 1,000 Richer than 8 million: 1 in 4,000 Richer than 16 million: 1 in 16,000 Richer than 32 million: 1 in 64,000 Richer than 320 million: 1 in 6,400,000 5 N N Taleb © 2008 Wilder Randomness • Richer than 1 million: 1 in 62.5 • Richer than 2 million: 1 in 125 • Richer than 4 million: 1 in 250 • Richer than 8 million: 1 in 500 • Richer than 16 million: 1 in 1,000 • Richer than 32 million: ? 6 Where the Gaussian Comes From N N Taleb © 2008 7 8 9 40 steps4020 20 40 2 ´ 10 10 4 ´ 10 10 6 ´ 10 10 8 ´ 10 10 1 ´ 10 11 1.2 ´ 10 11 1.4 ´ 10 11 Numbers of Wins ? Losses 104020 20 40 0.01 0.02 0.03 0.04 0.05 0.06 A more Abstract Version :Plato 's Curve 11 Law of Large Numbers How the Law of Large Numbers Works N N Taleb © 2008 Look around you Wealth concentration “Google e f ect” Size of cities Harry Potter phenomenon Size of HF Academic citations 80/20 … turning into 99.99/.01 12 N N Taleb © 2008 Only a Few Days 13 N N Taleb © 2008 Graph series0.250.20.150.10.05 0.05 0.1 0.15 1 317 633 9491265158118972213252928453161347737934109442547410.20.150.10.05 0.05 0.1 0.15 1 308 615 9221229153618432150245727643071337836853992429946064913 14 N N Taleb © 2008 Equities 50 100 150 200 250 3004.8%4.2%3.6%3.0%2.4%1.8%1.2%0.6% 0.0% 0.6% 1.2% 1.8% 2.4% 3.0% 3.6% 4.2% 4.8% Series1 Series3 SP500 Theoretica 15 N N Taleb © 2008...
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 Spring '09
 Taleb,NassimN
 Taleb, Fractal, fractals

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