# Against the Gods | Peter L. Bernstein

Summary of: Against the Gods: The Remarkable Story of Risk

By: Peter L. Bernstein

## Introduction

In ‘Against the Gods: The Remarkable Story of Risk’, Peter L. Bernstein unfolds the fascinating historical progression of understanding and managing risk. The summary delves into the development of probability, statistics, and various sciences that lay the foundation for modern risk management. The book offers a journey from ancient Greek philosophy to the Renaissance, the Industrial Revolution, and now the digital information era. The summary reveals how the actions of pioneers like Fibonacci, Blaise Pascal, Pierre de Fermat, and others have led to the conception and use of complex financial instruments like derivatives in the modern world.

## The Development of Probability and Mathematics

The book delves into the history of probability and mathematics. Starting from the Greeks and the Hindu numbering system, the book takes you through the developments that led to the modern-day use of numbers in modern society. The book talks about the time when much of the Western world relied on Roman numerals and how the Fibonacci ratio mathematically expresses the balanced proportion that the Greeks called “the golden mean.” It also explains how the invention of zero allowed people to calculate using merely 10 symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. During the Renaissance period, thinkers turned their attention to developing the mathematics of probability. They converted risk-taking into one of the prime catalysts that drive the modern Western world. The book tells the story of these remarkable visionaries whose work revolutionized our understanding of risk, how to measure it, and weigh its consequences.

## The Pioneers of Probability

The article delves into the history of probability and its pioneers. It begins with Luca Paccioli and his puzzle about dividing stakes in a gambling game, which led to the study of risk. Girolamo Cardano made progress in probability calculation, and Galileo studied dice. However, the most significant pioneers were Blaise Pascal and Pierre de Fermat, who worked together to solve the puzzle of Fibonacci’s ratio. Pascal developed the argument for belief in God based on probability theory and argued that faith is the only rational response to the universe.

## Revolution of Statistical Sampling

John Graunt’s Natural and Political Observations Made Upon the Bills of Mortality revolutionized the field of statistical sampling in 1660. Graunt, a dealer in commodities, applied statistical sampling to the problem of financial risk. He tabulated the causes of death in London and various aspects of demography, being the first to recognize that the most feared causes of death were not the most likely. Moreover, he saw the value of averages. Edmund Halley used data from Breslau, Germany, to calculate the odds of a person of a given age dying per year, which established the basis for the life insurance industry. However, governments selling annuities to raise money ignored this approach and sold annuities at a uniform price to all comers. Statistical sampling is essential to the use of statistics, probability, and risk management. But where do these numbers come from? Graunt and Halley’s groundbreaking work pioneered the measurement of the unknown through odds and probabilities.

## The Value of Utility

In his 1738 commentary, mathematician Daniel Bernoulli asserted that the value of an item should not be based on its price, but rather on the utility it yields. He introduced the concept of diminishing marginal utility and the idea that people have different risk preferences. Bernoulli recognized that even beggars possess skill and outlined how to measure the price of that ability. He also saw that people derive less satisfaction from increasing wealth as they get richer. Bernoulli’s notions have crucial implications for risk management, as people tend to fear losses more than they seek gain. His asymmetric view of decision-making has become one of Prospect Theory’s most notable discoveries. Although people are not as rational as Bernoulli had anticipated, his concepts highlight how people’s perceptions of wealth affect their decisions.

## Discovering the Bell Curve

Carl Friedrich Gauss, a renowned mathematician, inadvertently stumbled upon the ‘normal distribution’ or ‘the bell curve’ at the age of 18. He made this discovery while conducting a geodesic survey to improve geographic measurements. Gauss found that he could measure the accuracy of his observations by comparing them to the mean of all the readings and calculating their distance from it. Although he didn’t realize the significance of his discovery at the time, it proved to be a crucial concept in risk management. Despite his many mathematical and astronomical contributions, Gauss’s accidental discovery of the bell curve remains one of his most enduring legacies.

## Galton’s Principle and the Real World

The book delves into Francis Galton’s explorations of the normal distribution and the principle of regression to the mean. He used this to prove that heredity was destiny but discovered that particularly tall or gifted parents slightly tended to produce more average offspring. The principle of regression to the mean is essential when forecasting market prices, as it advises against expecting extraordinary performance to continue and firing money managers who have been doing well. However, research shows that people do not take a rational view of performance, assigning too much value to recent occurrences. While powerful, a word of caution is in order as times do change, and the world today is different from the world of the Industrial Revolution.