In his book, Against The Gods, the remarkable story of risk, financial analyst and asset manager, Peter Bernstein, begins with the creation cosmic creation. He mentions that “the recognition of risk management as a practical art rest on a simple cliché with the most profound consequences: when our world was created, nobody remembered to include certainty.” Indeed, the Greek gods rolled the dice to decide who would rule the heavens, the world, and the underworld. While they did recognize that much in the world was accidental and unexplainable, they failed to develop a science of probability. In fact, the use of the Hindu numbering system and the concept of zero proved crucial in developing a science of probability.
Blaise Pascal and the invention of statistics
Mathematical prodigy, Blaise Pascal, a Frenchman, relied upon probabilistic thinking to prove the existence of God or at least prove that believing in God was eminently rational. He thought up of 2 scenarios :
- Scenario 1: if one were to live an orderly life in the hope of making it to heaven in the afterlife, then, those that lead a moral life endure limited sacrifices in this world in exchange for infinite satisfaction in the world beyond, assuming that God does exist and that there is a life after death.
- Scenario 2 : On the other hand, a man unwilling to live a moral life may indulge in earthly satisfactions. But, if God does exist and there is, indeed a life after death, he may fail to make it to heaven and suffer infinite dissatisfaction.
- To put it differently, there is a 50% chance that God exists and agreeing to make finite sacrifices for infinite satisfaction is very rational.
In the United Kingdom, John Graunt applied to statistical sampling to a problem of financial risk. He recorded the causes of death in London and realized that the most feared causes of death were actually not the most likely causes of death. In doing so, he pioneered the use of averages. In Germany, Edmund Halley calculated the odds of a person of a given age dying in a given year. These calculations provided the basis of life insurance policy although, governments at this time were selling annuities and generally ignored the rigorous approach pricing risks and sold annuities to all comers at a uniform price.
Later on, in 1738, Daniel Bernoulli wrote that the value of an item must not be based on its price but rather on the utility it yields. Bernoulli meant something beyond expected value which is the calculation of relative probabilities of various outcomes. He knew that different people may have different risk preferences. The odds of being struck by lightning may be small, but a person terrified of lightning would place a high value on protection against it—perhaps higher than the probabilities would justify. Bernoulli also realized that the satisfaction that people derive from increase in wealth diminishes as they get richer. This perception carries crucial implications for risk management, since people generally fear losses more than they yearn for gain.
In 1801, Carl Frederick Gauss, a young math prodigy accidentally discovered normal distribution also known as the bell curve. This provides a mapping of how probabilities may be distributed in a given sample. A concept that is critical to risk management and assessing probabilities.
Regression to the mean
Francis Galton, the pioneer of eugenics, discovered that the principle of regression to the mean prevailed. In other words tall or exceptionally gifted parents tend to produce slighter shorter slightly shorter or less gifted children who are closer to the average than the outstanding. Galton’s principle of regression to the mean matters greatly when forecasting market prices. Regression to the mean actually makes it is advisable to fire a money manager who has been doing extraordinarily well and to hire one who has been doing quite poorly. Odds are that the high performer will have a period of low performance and a poor performer world will experience high performance. That’s regression to the mean.
Defining risk with a number
In doing so, people starting defining risk with a number. But regression to the mean cannot anticipate extraordinary events. For example, when President Herbert Hoover reassured the US that prosperity was almost at hand, he wasn’t lying. He was making a reasonable forecast based on his experience with prior recessions and depressions. Nothing like the Great Depression had ever occurred before so it wasn’t part of his database for calculating the mean.
The author also talks about Nobel Prize winner Markowitz applied advanced mathematics to selecting stocks in a portfolio. His most important discovery was the role of diversification in reducing risks. He proved that an investor could hold a portfolio of securities that were, treated separately and distinctly, quite risky—and yet have a reasonably low risk portfolio. How could this be? The individual stocks risk offset one another. But critics object that his use of variance as a reasonable expression of risk.
Finally, Israeli psychologist Daniel Kahneman recognize that people make decisions that seem to be founded on rational analysis. For example, investors are likely to arrive at a different decision about the right course of action if the problem before them is framed differently.
In his book, Against The Gods, the remarkable story of risk, financial analyst and historian, Peter Bernstein shows that when the world was created, no one thought about including certainty. The Greeks rolled the dice to decide who would rule the heavens and the underworld but failed to develop a theory of risk and probability. In fact, using the Hindu numbering system prove crucial in developing mathematics of probabilities that Lavelle developed by math prodigy Blaise Pascal, who uses probabilistic thinking to prove the rationality of believing in God, Carl Frederick Goss who turned to mathematics to invent the bell curve, John grande who looked at the causes of death
John Graunt and Edmund Halley looked at the causes of death to calculate life insurance policy based on the average probability of dying of a given individual at a given age. Regression to the mean also proves critical in assessing how outcomes are distributed. But it cannot anticipate extraordinary events like the Great Depression of 1929.
Nobel Prize winner, Markowitz shows that asset managers may build low-risk portfolios made up of very risky components if other components nullify or compensate one another. But many object that using variance to measure risk is perhaps not the best. According to Israeli psychologist Daniel Kahneman, investors don’t make decisions based on a rational process but rather on how information is presented to them and how it’s framed.
What I find very interesting in the book is that there’s a thorough analysis of what is risk and how to measure it. It shows that our understanding of risk has changed over time and that even today the use of volatility in variance to assess and measure risk does not free from error. Also, most of the book has to do with applications of risk in finance. But there is also risk in other fields including innovation, cybersecurity, war, geopolitics, and even project management.