Two Books, Two Distinct Takes on Risk

Reviewed by Robert J. Finger

Against the Gods: The Remarkable Story of Risk
by Peter L. Bernstein (John Wiley & Son, 1996, $27.95)

Seeing Tomorrow: Rewriting the Rules of Risk
by Ron S. Dembo and Andrew Freeman (John Wiley & Son, 1998, $27.95)

Actuaries deal with risk, implicitly or explicitly, in most of our professional endeavors. It is likely that dealing with risk will become more important to actuaries in the future, as capital markets consolidate and insurance buyers become more sophisticated. I believe that significant progress remains to be made in the treatment of risk, on both the theoretical and practical levels. Both of these books discuss risk, although in different ways.

Peter Bernstein's Against the Gods is an historical account of the development of the mathematical and statistical ideas underlying what the author terms "risk management." It covers a number of fields, principally the capital markets, where risk concepts are applied today. I think the book is valuable for the historical development and context of risk notions. I do not think, however, that the typical actuary will learn much of a technical nature from the book. I thought the author's explanation of several concepts was either muddled or erroneous. Thus, I believe the book should be read for its history; if you want a technically accurate description of the concepts, other books are more appropriate.

In contrast, Dembo and Freeman's Seeing Tomorrow is an attempt to provide a universal framework for decision-making. It is written for a broad audience, but it provides sufficient technical detail. While I found this book interesting, I do not think its methodology is either as bold or as new as the authors claim, nor as readily adaptable to real decisions.

Bernstein's title, "Against the Gods," is an explanation of why it took so long for western civilization to develop methods for analyzing risk. His explanation is that until about 1200 A.D., virtually all people accepted uncertainty in their lives as "fate," or something over which they had essentially no control. One might think of Homer's Iliad, where the gods and goddesses on Mount Olympus interjected themselves, by whim, into the Trojan War. Slowly, however, a different world view took hold. People began to think in terms of probabilities, to measure variable outcomes, and to postulate that future uncertainties might be related to past variable outcomes.

The first 15 chapters of Bernstein's book, more or less, describe the historical development of relevant mathematical and statistical methods. The final four chapters discuss current issues and current thinking on risk.

Among the historical developments is the Hindu-Arabic numbering system (which was developed about 500 A.D., but largely ignored in Europe until 1200 A.D. and even resisted until the 1500's). Without zero (which wasn't needed for counting purposes) and without a system that readily lends itself to calculations, little progress could be made. (Quick: what is XLVI times MMCDXXIII?)

Other developments, among many, that are discussed include: double entry bookkeeping, games of chance, Pascal's Triangle (binomial expansion), sampling, mortality and annuities (the earliest actuaries), utility, the normal curve, Bayesian analysis (conditional probabilities), the central limit theorem, mean reversion, game theory, and portfolio selection.

The last several chapters in Bernstein's book emphasize behavioral issues. Here there is some overlap with material presented in Dembo and Freeman. For example, most people treat gains and losses differently; the importance of adverse events with low probabilities is often exaggerated; people often set different buy and sell prices on the same items; and most people overweigh newer information.

Bernstein's book presents many ideas and their history. Dembo and Freeman present a structure for making decisions under uncertainty. I will summarize some of their more important ideas, but my treatment is necessarily incomplete.

In Chapter 2, "The Elements of Risk Management," risk is defined as the potential change in value (of some asset) between the current time and some future date. There are four key elements in analyzing risk: (1) selecting the appropriate time horizon, (2) making sure to include all reasonable scenarios (particularly those we want to avoid), (3) selecting a measure for risk, and (4) selecting a relevant benchmark. The third topic is discussed further below. An example of a benchmark would be the Standard & Poor's 500 Index for a portfolio manager of large capitalization U.S. equities.

I think the two most important concepts in the book are the ones discussed in the next two chapters. First, all of the possible scenarios are divided into two groups: those with positive outcomes and those with negative outcomes. The authors say that positive outcomes should be treated like a bet (gamble) and that negative outcomes should be treated like insurance. Thus, there is asymmetric treatment of outcomes, which tends to conform to actual observed behavior. Second, the value of the negative outcomes is based on “Regret,” which I would liken to a nonmathematical type of utility. In other words, how much would you pay to avoid this situation?

The above two concepts are combined into a risk-adjusted value, as follows. It is the value of the positive outcomes less a risk aversion factor times the regret of the negative outcomes. Since individuals will have different regret functions, risk aversion, and benchmarks, in addition to different information, there is a wide range of possible outcomes, for example, “insurance premiums,” that can be negotiated among different people.

There is a great deal of discussion of these concepts and various applications. Although the authors provide an interesting framework, I am not sure that it is particularly practical or that it will lead to better decisions. As I stated above, I believe there is considerable room for improvement in both theory and application.