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Thomas Bayes (1701-61) was an English minister who initiated evolutionary advances in the field of statistics by constructing a mathematical model for blending new and old information. Bayes’ theorem is applicable when prior knowledge or beliefs are available regarding future events. The method sheds light on the process of how probabilities and forecasts change as new information emerges. A simple example might involve tossing a coin to determine its bias towards heads or tails. One’s prior opinion might be that the coin is unbiased. Using Bayesian analysis, each successive coin toss provides an updated probability as to the validity of the original belief. The power of the method can be found in the framework that helps make risk-related decisions based on incomplete information.

The Doctrine of Chance. Bayes did not publish a thing in his lifetime and was virtually unknown in scientific circles. He left two papers to fellow minister Richard Price who Bayes held in high regard. After he died, Price sent one of Bayes’ papers entitled—Essay Towards Solving a Problem in the Doctrine of Chance to the British Royal Society. It became a scientific landmark and forever immortalized Bayes in the eyes of statisticians, economists and social scientists. During the 1800s, several mathematicians refined and clarified Bayes’ somewhat sketchy ideas—resulting in more usable forms. From there, Bayesian-style statistics came to reign supreme until the end of the century. Early in the 1900s, the English statistician Sir Ronald Fisher developed a simpler, objective procedure for analyzing data, which by the 1920s was being used to the exclusion of Bayesian analysis. Fisher’s method allowed researchers to determine whether analytical results were significant or not without the influence of Bayesian subjectivity. Many believed that subjectivity does not belong there in the first place. Their bumper stickers read “Objectivity or Nothingness.”

Back to Bayes. In 1995, James Brophy (a cardiologist) and Lawrence Joseph (a biostatistician) from Montreal, Canada published a widely read article in the Journal of the American Medical Association entitled—Placing Trials in Context Using Bayesian Analysis. The article centered on the long-running debate regarding the choice of two clot-busting drugs given to heart attack victims as they arrive at the hospital. Both drugs worked well, although the more expensive drug ($1,500 vs $200) had been determined in a comprehensive study to be one-percent more effective in saving lives. This type of drug is administered hundreds of thousand of times a year. The authors contended that the study, which essentially used the traditional methods of Fisher, had a built-in, unspoken bias to prior beliefs. Brophy and Joseph believed that a Bayesian approach would compel the researchers to formally account for their previous opinions. They concluded that the original study was prejudiced in favor of the more expensive drug—and that there was no meaningful difference between the two drugs. Their findings removed the potential for malpractice liability.

The Founding Father. Richard Price, the custodian of the Bayesian revolution, was not just a minister, but also a mathematician, human rights advocate and nonconformist. He was friends with Benjamin Franklin and Adam Smith and even provided editorial input into Smith’s classic work The Wealth of Nations. In 1765, a life insurance company hired Price to construct a series of mortality tables for the company to use in setting premiums for insurance and annuities. After studying the work of Edmund Halley and Abraham de Moivre, Price published a book on life contingencies that became the bible on the subject for the next hundred years. The work earned Price the title of the founding father of actuarial science.

The Math of Life. Although Price represents the actuary in the traditional sense, the ideas of Bayes embody actuarial science in a truer sense in that his approach facilitates the meaningful coalescence of mathematics with real life. And as such, actuaries are said to do the math of life. All actuarial students are required to pass a difficult set of exams—half of which are mathematical. The Jobs Rated Almanac says that the actuarial profession regularly tops the list of 250 professions ranked on the criteria of work environment, income, job outlook and stress. Microsoft Encarta defines, “An actuary as a person who applies the theories of probability and statistics and the principles of finance to problems of insurance, pensions, population studies, and other related fields.” Another definition might be one who manages portfolios with the intention of optimizing wealth subject to risk exposure constraints.

Actuaries of the First Kind, known as life actuaries, deal with issues of life and health risk. Insurance companies employ actuaries to determine premiums and manage reserves for insurance and annuity products. Actuaries are sometimes thought of as the engineers of the insurance business. Pension actuaries consult to companies regarding the management and funding of pension portfolios used to provide employees with retirement benefits. In this role, actuaries offer expert advice on issues like plan design, funding, investment and portfolio risk management. Actuaries of the first kind are the most common type.

Actuaries of the Second Kind, known as casualty actuaries, deal with issues of property and casualty risk. Whereas the mathematics of life contingencies is central to life actuaries, credibility theory is the primary analytical tool used by actuaries of the second kind. Bayesian analysis is part of credibility theory. Casualty actuaries work in insurance or function as consultants addressing questions of ratemaking and loss reserving for property, liability and workers’ compensation risk factors. I have also modeled earthquake and hurricane risk factors.

Actuaries of the Third Kind, known as corporate actuaries, deal with issues of corporate financial risk management. Corporate actuaries bring to companies something offered by no other profession—a rigorous, theoretical and applied expertise in the areas of risk modeling and decisionmaking. Expertise of this nature would seemingly be indispensable to corporations. Yet, there are very few actuaries employed in this manner. Upon reflection, it would seem in many ways that actuaries are not aware of what they really are—which is risk managers. As such, it is understandable that corporations have not recruited actuaries.

Corporate Risk Management. All companies are portfolios of risk. The ability to effectively manage these portfolios becomes stronger with the number of risks under consideration. So whereas the treasury department provides a centralized source of cash management, so too should the risk management department provide a centralized source of risk management. Companies could use actuarial expertise for modeling hedgable, insurable and investment risks—and in the closely linked field of economic forecasting. In fact, actuaries have much to offer in regard to the formulation of debt and dividend policies as well. It is the same process of modeling market factors that is the engine which ultimately drives operational, investment and hedging decisions. That engine could logically be located in the risk management department under control of a professionally trained actuary. Companies would be well advised to consider the broad and deep skill set that actuaries have to offer. It is entirely possible that corporations will soon wonder how they ever got along without actuaries.

The Bernoulli Model takes portfolio theory to another level by bringing together the corporate moving parts into a single portfolio distribution like the normal distribution. I spent nine months developing The Bernoulli Model. It uses a top-down, strategic management approach to scientific management and combines the processes of forecasting, integrating and optimization. The Bernoulli Model employs the forecasting method of Monte Carlo simulation along with the four-moment Camus Distribution that I developed to model the full spectrum of risk factors. Monte Carlo simulation rolls the dice over and over in order to calculate the four moments of the distribution. Optimization algorithms then search risk-reward space in order to determine optimal decisions subject to Delphi constraints. The Delphi method is an iterative questionnaire for officers and directors to define corporate values. The Bernoulli Model is destined to be the favorite toy in the CFO’s toy box. It dares to apply the wholistic concepts of risk and reward to the entire corporation.

Conclusion. The great American sea captain Nathaniel Bowditch (1773-1838) spent the first part of his life at sea gaining the legacy of a marine navigation master. His book The American Practical Navigator is still used as a standard sailing text today. Bowditch spent the second part of his life as an actuary working for an insurance company. So too may the advancement of the actuarial profession be as wide-ranging as the adventurous life of Bowditch—and see actuaries of the third kind playing meaningful corporate roles as we sail into the Third Millennium. Personally, I am willing and able to assume the role of corporate actuary for any thoughtful organization.