Summary—The Nature of Risk essay discusses the four moments of risk found in my Camus distribution, Monte Carlo simulation, time-series modeling, my advanced Bernoulli model—and what I have to offer organizations.
Albert Camus (1913–60) was one of the creators of existential philosophy—which asserts that individuals have total freedom and total responsibility. Camus was a French Nobel Prize winning writer, philosopher, journalist, playwright and novelist. He was born in Algeria to a Spanish mother and a French father who was killed in World War I—whereupon Camus was raised in poverty by his illiterate mother. Tuberculosis plagued Camus from early in life and forced an end to his soccer career and his studies at the University of Algiers. He was also a theatrical playwright, director and actor. After university he turned to journalism and his reporting of Muslim problems brought action—and also marked the beginning in which he never ceased to fight against injustice. When I read Camus it is as if he is speaking to me in the same way that my own writing speaks to me. Camus’ brother was named Lucien. His uncle, whom he lived with, was named Étienne. And his wife was named Francine. My father is named Lucien. My grandfather was named Étienne. And my aunt, who introduced me to Camus, her name is Francine. I also had a great dog named Camus. I believe I am the reincarnation of Albert Camus.
The Normal Distribution. A probability distribution identifies the range of possible outcomes for a given set of data. Consider the normal distribution which is shaped like a bell. The top of the bell represents the highest probability. The normal distribution is completely defined by the first two moments (ie. mean and standard deviation). It is a cornerstone of risk management that brings together all moving parts into a single distribution. Closed-form is a method that can be solved with a pencil and paper. Open-form is a method that can be solved iteratively with a computer. The central limit theorem is a closed-form method of aggregation that combines distributions into a normal distribution. Normal distribution values can be simulated in Microsoft Excel as follows =normsinv(rand()).
The Camus Distribution. If one wishes to include higher moments (ie. skewness and kurtosis) then a more robust distribution is required. Monte Carlo simulation is an open-form method for bringing distributions together. It is able to handle any degree of complexity from distributions and probabilistic processes like time-series modeling. The Cauchy distribution is the counter allegory to the normal distribution and can be simulated as follows =normsinv(rand()) / normsinv(rand()). While the normal is characterized by very short tails, the Cauchy has very long tails. Consider a simulated denominator being extremely close to the mean of zero. The value of the simulated Cauchy then shoots off to the moon (eg. =1 / 0.0001). In order to develop the four-moment Camus distribution, I had to truncate the Cauchy’s tails and choose weighted averages between it and the normal. The Camus distribution is a hybrid of the normal distribution and the Cauchy distribution.
Time-Series Risk Modeling. Time-series risk modeling is a situation where each epoch is dependent on the previous epochs (eg. daily temperatures). I developed time-series risk models when I was consulting to TransCanada Pipelines and Canadian Pacific Limited. The process involves deconstructing rates into signal, wave and noise components. The components are forecasted individually and then reconstructed in a Monte Carlo simulation environment. The simulation parameters are selected by best-fitting the first four forecasted moments (ie. mean, standard deviation, skewness and kurtosis) with the realized moments. The forecasted moments are based on historical data while the realized moments are based on both historical and future data. The ideal time-series parameters are selected so that the forecasted moments best predict the realized moments. Garch is an advanced class of time-series algorithms that estimate parameters for the variability of the second and fourth moments. For example, if there were a spike in rates, they would tend to remain excited for several epochs.
The Bernoulli Model. The Bernoulli model is a sophisticated realization of portfolio theory that I developed with the hope of becoming a universal standard for business, education and government. Unlike other risk management practices, the Bernoulli model is built from the ground-up and uses a top-down strategic approach. The essence of portfolio theory is forecasting, integration and optimization. It forecasts the four moments of distributions using either a closed-form or open-form method in order to integrate the distributions into a single portfolio distribution. The method then recommends decisions that optimize risk-reward efficiency. The Bernoulli model employs the complementary principle on multiple levels. The complementary principle was defined by Niels Bohr (1885-1962) as two fundamentally different perspectives of the same phenomenon. For instance, the Bernoulli model has two sets of valuation parameters that serve to contrast paradigms. The Bernoulli model is based on a standardized approach that uses Microsoft Excel and the Microsoft VBA programing language. This methodology gives access to all the Excel and VBA functions and methods. An underlying database then provides access to the exposure and rate data.
Executive Risk Management. The idea behind executive risk management is to take a fundamentally different viewpoint of risk that helps prepare for impending paradigm shifts. The complementary principle also applies here to risk management by having two profoundly different perspectives (ie. existing practices compared to the Bernoulli model) of the same phenomenon—in this case, risk. Peter Bernstein argues in his 1998 book Against the Gods—The Remarkable Story of Risk that the primary objective of executives is forecasting. Forecasting must also include forecasts of the associated risk (ie. standard deviation, skewness and kurtosis). The Bernoulli model is ideally suited for executive risk management.
Insurable Risk Management. I developed insurable risk models when I was consulting to PetroCanada and Nexen. Insurable risk management includes the risk factors of property, business interruption and liability. Potential losses are modeled with Monte Carlo simulation by breaking down into frequency and severity. The frequency is modeled with the Poisson distribution for property and liability. Severity is modeled with the lognormal distribution for property and business interruption, while severity is modeled for liability with the Pareto distribution. The Pareto distribution has a much longer tail than the lognormal distribution thereby accounting for the potential for very large liability losses. The lognormal distribution is the one-tailed version of the two-tailed normal distribution. The Pareto distribution is the one-tailed version of the two-tailed Cauchy distribution. Business interruption frequency losses are modeled with the Bernoulli distribution. For example, for each property loss, there might be a sixty percent probability of the associated business interruption loss. Simulation then brings all risk factors together into a single distribution.
Making Hard Decisions. We have difficult decisions to make all the time. The basic premise behind risk management is that with low risk one expects a low return. While with high risk one expects a high return. This is the essence of efficiency analysis. We must strive to make decisions that optimize risk-reward efficiency. It is important that executives have access to a straight-forward approach to decision-making without the need for a strong mathematical background. By applying utility theory one is able to link gut-feel with risk-reward. For example, one may be happy with a ten percent return, but not be ten times happier with a hundred percent return. Utility theory takes this preference into account. Another crucial component of decision-making is sensitivity analysis, which is the calculation of how valuation parameters are sensitive to change. With the Bernoulli model there are two complementary paradigms. This allows users to see the sensitivity between paradigms by making the parameters equal except for one. Good decision-making also provides an audit trail of the decision-making process, which the Bernoulli model provides.
Christopher Bek. FS Northrop said that if one makes a false or superficial beginning, no matter how rigorous the methods that follow, the initial error will never be corrected. Just like Descartes founded modern Western philosophy by tearing down the medieval house of knowledge and building from the ground up, I also offer the same service of building from the ground up. I am a philosopher and scientist who offers the realization of scientific management practices. I am not well versed in the day to day workings of existing risk management practices which, I would argue, is a great strength of mine in that I have much less tendency to fall prey to common sense notions. Einstein said that common sense is nothing more than the collection of prejudices acquired by the age of eighteen. Based on my mathematical and actuarial science designations, I bring forth a new perspective on risk and reward.
Conclusion. The four-moment Camus distribution could be described as the perfect actor. Time-series modeling includes series such as oil prices that breakdown into signal, wave and noise. The Bernoulli model is an advanced application that offers an independent perspective on forecasting, integration and optimization. The addition of insurable risk aims to combine all risk factors together into a portfolio distribution. While existing risk management practices could be described as tactical, I offer strategic risk management practices.