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Against the Gods cover

Against the Gods

Peter Bernstein

 4/5

read: 2021-08-19

non-fiction · #mathematics #history

A brief history of risk, and how we became so scientific in analysing it

Pre 1200: Beginnings

  • Probability and risk was borne out of gambling
  • It begun in Greece, when their philosophers were at the forefront of intellectual discussion
  • Counting and numbers were needed before probability could be known
  • Fibonacci and his series
  • The golden ratio
  • The abacus
  • The number system was developed by Hindus
  • The centrepiece of the Hindu number system was the invention of the number 0

1200 - 1700: A Thousand Outstanding Facts

The Renaissance Man

  • Girolamo Cardano
    • Extracted the first ideas of probability from gambling
    • Was also a gambling addict
    • Did a lot of work on combinations of numbers
  • Luca Paccioli
    • Came up with the “problem of Balla”, in which two players are playing a game of balla and it is cut short.
    • The question is, how do you divide the pot among the two players?
    • Evenly? But what about the player who is clearly winning?
    • How much more should you give the winning player?

The French Connection

  • Blaise Pascal & Pierre de Fermat
  • Spoke about Paccioli’s problem of Balla
  • How should the pot be split?
  • Very famous sets of letters were echanged between them
  • Pascals triangle
  • Pascals wager
    • If hell is as bad as it is described and heaven as good, then no matter how small the probability of it being real, you should beleive just in case
    • This is a probabilistic view of religion

The Remarkable Notions of the Remarkable Notions Man

  • Invariance
  • Demographic data
  • John Graunt’s “observations”
    • Compiled insurance data
    • Aggregated the first “statistics”
  • Edmund Halley’s “Life tables”
    • Predicted the occurence of a comet (Halley’s comet)
    • Created an age distribution of the population
  • Edward Lloyd’s coffee house -> Lloyds of london

1700 - 1900: Measurement Unlimited

Considering the nature of man

  • Daniel Bernoulli (Jacob’s nephew)
  • Utility theory (thinking of utility as a function of value)
  • St Petersberg paradox
  • Human Capital
  • Loss aversion
  • Differing levels of risk aversion
  • “Exposition of a new theory of the measurement of risk”

The Search for Moral Certainty

  • Jacob Bernoulli
  • Abraham de Moivre (first observed and documented the bell curve)
  • Thomas Bayes
  • Moral certainty = Statistical Significance
  • Inference & Bayes’ theorem
  • Assumes that events happening in the future will follow the same pattern (distribution) as in the past
  • Law of large numbers (Jacob Bernoulli)

The Supreme Law of Unreason

  • Carl Freidrich Gauss
    • Built on de Moivres observations of the bell curve
  • Marquis Laplace
  • Bell curve
  • Stock market randomness
  • Independence <—> Normal distirbution

The Man with the Sprained Brain

  • Francis Galton
    • Obsessed with measurement
  • Lambert Quetelet
  • The “average man” (L’homme moyen)
  • Regression to the mean
  • Average (“standard”) deviations
  • Correlation

Peapods and Perils

  • Regression to the mean
  • Stock market overrreaction
  • Dangers of expecting regression to the mean all the time
  • What mean should be regressed to?
    • At what point has normal shifted to a new location?

The Fabric of Felicity

  • Utility
  • Which risks should be taken?
  • Preferences and tradeoffs
  • Daniel Bernoulli -> Jeremy Bentham -> William Jevons
    • Bernoulli built the groundwork
    • Bentham invented utility theory
    • Jevons built on it

1900 -> 1960: Clouds of Vagueness and the Demand for Precision

The Measure of our Ignorance

  • Louis Bachalier: The theory of speculation
  • Acceptance of uncertainty
  • Birth of risk management
  • Kenneth Arrow
  • Practicality is introduced
  • Risk management becomes more pragmatic
  • There is so much randomness that nothing can be that precise
    • The gravitational pull of an electron in the milky way can affect a game of billiards on earth

The radically distant notion

  • Frank Knight
  • John Maynard Keynes
  • Moving away from probablity theory and toward practical applications and risk
  • Historical evidence cannot predict the future
  • Keynes: Intervention from government removes uncertainty

The Man who counted everything except calories

  • John von Neuman
  • Game theory
  • Oskar Morgenstern
  • Rationality
  • Other’s decisions as the cause of uncertainty

The Strange Case of the Anonymous Stockbroker

  • Harry Markowitz: Optimal portfolio selection
  • William Sharpe: CAPM model
  • Max return sub to risk
  • Min risk sub to return
  • Variance may not be a good proxy for risk

Degrees of Beleif: Exporing Uncertainty

The failure of invariance

  • Kahnemen and Tversky
  • Prospect theory
  • Behavioural biases: Humans dont always act rationally
  • Loss aversion
  • Ambiguity aversion
  • Paradox of choice
  • Experimental economics

The Theory Police

  • Behavioural biases
    • Decision regret
    • Loss aversion
    • Risk aversion
    • Endowment effect
  • Market rationality
  • Market efficiency
  • Risk management in the 1970s
  • DeBondt & Thaler

The Fantastic System of Side Bets

  • Derivatives (financial options) reallocate risk
  • Black Scholes Merton model
  • Volatiliy & risk vs direction
  • 1987 portfolio insurance crash
    • Aimed to replicate a put option
    • Sold stock on way down
    • Bought as it came back up
    • Problem was too many people were doing in, so as stock prices began to go down they crashed really fast
  • 1990s companies speculating in derivatives
    • P & G

Awaiting the wildness

  • The future of risk management
  • Models of the future
    • Chaos theory
    • Neural networks
    • Genetic algorithms
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