In his 1996 book, Against the Gods: The Remarkable Story of Risk, financial historian, economist and educator Peter Bernstein traces in narrative fashion the development of probability and statistics in the service of risk management. In the closing chapter, he offers a few overarching conclusions, as follows:
From pages 329-330:
“The effort to comprehend the meaning of nature’s tendency to repeat itself, but only imperfectly, is what motivated the heroes of this book. But despite the many ingenious tools they created to attack the puzzle, much remains unsolved. Discontinuities, irregularities, and volatilities seem to be proliferating rather than diminishing… The goal of wresting society from the laws of chance continues to elude us. Why?”
In partial answer, from pages 334-335:
“The past seldom obliges by revealing to us when wildness will break out in the future… Surprise is endemic above all in the world of finance.
“…[W]e pour in data from the past to fuel the decision-making mechanisms created by our models… But therein lies the logician’s trap: past data from real life constitute a [past-dependent] sequence of events rather than a set of independent observations, which is what the laws of probability demand. History provides us with only one sample of the economy and the capital markets, not with thousands of separate and randomly distributed numbers. Even though many economic and financial variables fall into distributions that approximate a bell curve, the picture is never perfect… It is in those outliers and imperfections that the wildness lurks.
“…[T]he science of risk management sometimes creates new risks even as it brings old risks under control. Our faith in risk management encourages us to take risks we would not otherwise take.”
Nevertheless, in closing on page 337 with a (now triple) nested quotation:
“Opposed though he was to mechanical applications of the laws of probability and the quantification of uncertainty, Keynes recognized that this body of thought had profound implications for humanity:”
…[P]robability is to us the ‘guide of life,’ since to us, as Locke says, ‘in the greatest part of our concernment, God has afforded only the Twilight…of Probability, suitable, I presume to the state of Mediocrity and Probationership He has been pleased to place us in here.’
