Against The Gods

Peter Bernstein’s masterpiece Against The Gods is without a doubt one of the great works in business literature. It’s an insightful and illuminating investigation into the meaning of risk and the ideas and techniques humans have developed over centuries to quantify and manage the unknown. Through a comprehensive collection of history and philosophy Bernstein investigates the controversy between two groups that take different approaches to decision making

  1. Those who believe the best decisions are based on numbers
  2. Those who base their decisions on more subjective beliefs about the uncertain future

The genesis of risk management comes from the Renaissance–a time of exploration and discovery when individuals began to think more openly about how the future is determined. Work of the earliest thinkers revolved around games of chance: dice, casino games and the like. One of the more interesting problems was posed by a Franciscan monk named Luca Paccioli. Suppose two teams agree to play a game until one team has won six rounds. However, the game is stopped when team A has won five and team B has won three. With the game ending prematurely, how should the stakes be divided?

Initially this situation doesn’t appear to be worth investing much effort. But from a risk management perspective the question possesses something much greater. Both teams still have the possibility of winning. However, the probability that each team has to win may be quite different. Frenchmen Blaise Pascal and Pierre de Fermat were among the first to dabble in this area by developing a procedure to determine the likelihood of future outcomes. These early pioneers of probability theory accounted for the number of possible outcomes–the combinations of wins and losses that result in completion of the game. The key assumption in their work, and much of probability theory, was that the outcomes had to be measured mathematically.

While measurement seems straightforward enough it poses one of the great problems in the real world. Not every single possible scenario or instance can be measured for the simple reason that we don’t have the time or resources to do so. One way to get around this problem is to measure a representative portion of the population. The concept of sampling was a giant step forward in risk management. Insurance companies such as Lloyd’s of London and the Insurance Company of North America in Philadelphia were (and still are) highly dependent on sampling populations to determine their exposure to financial loss. The idea of using probability to define risk was advanced by another French mathematician named Abraham De Moivre

The Risk of losing any sum is the reverse of Expectation; and the true measure of it is, the product of the Sum adventured multiplied by the Probability of the Loss. [1a]

Following De Moivre’s prescription–multiplying a sum by the probability–gives rise to a distribution of possible outcomes that we recognize today as the normal distribution or bell curve. The early exploration of statistical concepts such as this provided tools for quantifying the likelihood that something may occur. However, the real world presents many situations that are not strictly games of chance with a statistical, numbers-based outcome.

Probability has always carried this double meaning, one looking into the future, the other interpreting the past, one concerned with our opinions, the other concerned with what we actually know. [1b]

Often times the information we need to make a mathematically informed decision is limited or incomplete, whether we realize it or not. Pierre-Simon Laplace and Jules-Henri Poincaré recognized that sometimes we have too little information to apply the laws of probability. It is difficult to get all the pieces of necessary information together to make a decision and we never know for sure how good our sample is. This gives rise to uncertainty. As a consequence we have to fall back on our reasoning and make an attempt at guessing the odds.

While facts are intended to provide a single answer reasoning and subjectivity can introduce many potential answers. Furthermore, the real world often presents situations and outcomes that people have never contemplated before. In some circumstances events can–often surprisingly–occur more frequently than the normal distribution would suggest. Economist Frank Knight argued that surprises are likely to occur in a system where decisions are based on forecasts. If everyone had all the information that they needed then the outcome would be strictly based on probability. He was cautious that anything about the future could be learned from the frequency of past occurrences.

In a similar manner, John Maynard Keynes suggested that objective probabilities of future events do not exist. Our lack of knowledge about future events denies us the certainty of knowing what the probability of a future occurrence actually is. There is no event that is identical to an earlier event. Uncertainty, rather than probability rules in real world decision making. In The General Theory of Employment, Interest and Money Keynes commented

[Most of our decisions] to do something positive…can only be taken as a result of animal spirits…and not as the outcome of a weighted average of quantitative benefits multiplied by quantitative probabilities. [1c]

By acknowledging the unknown, Keynes and Knight made a radical departure from other economist and mathematicians of the time. John von Neumann, the inventor of game theory, takes issue with Keynes treatment of expectations. Von Neumann collaborated with German economist Oskar Morgenstern to write The Theory of Games and Economic Behavior, which reverts back to a rigorous mathematical treatment of economic decision making. Game theory, as their work came to be known, posits that the source of uncertainty lies in the intentions of others.

almost every decision is the result of a series of negotiations in which we try to reduce uncertainty by trading off what other people want in return for what we want ourselves. [1d]

Despite the in-depth mathematics of game theory, Morgenstern brushed aside the idea that economics could be used for predicting business activity. No one can know what everybody else is going to do at any given moment.

The concept of Keynes’ “animal spirits” was not lost to history books. In the mid twentieth century psychologists Daniel Kahneman and Amos Tversky ushered in a new era of risk management by investigating human behavior as it relates to decision making. Collectively their work is referred to as Prospect Theory and pins decision making behavior on two shortcomings

  1. Emotion destroys the necessary element of self-control that is needed to make rational decisions
  2. Humans possess an inability to fully understand the events that they are dealing with

One of the more well known concepts of Prospect Theory is that of risk aversion. The manner in which we make decisions involving gains and decisions involving losses is asymmetrical. We focus our energy on events with low probability and high drama while ignoring those with high probability and more mundane outcomes. We do this because losses hurt emotionally–a lot. We are much more sensitive to losing a given amount than we are to gaining the same sum.

The ways in which we measure, understand and deal with risk have evolved greatly over many centuries. The science of probability theory developed by early philosophers and mathematicians has a high degree of merit in providing a framework of how to think about risk. The more modern ideas proposed by Kahneman and Tversky–that decision making has a subjective and emotional base is inherently new, but spread from the rigorous mathematics that preceeded. Bernstein closes with the insightful idea that the science of risk management creates new risks while simultaneously controlling others. Food for thought indeed.

Bernstein, Peter L. Against The Gods. John Wiley & Sons Inc. 1998.
(a) p. 126
(b) p. 48
(c) p. 216
(d) p. 232

NOTES – Against The Gods.pdf

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