Applying The Bernoulli Model

Summary—This essay describes the process of putting into play an executive risk management, decisionmaking and forecasting system.

Quotation—A successful business executive is a forecaster first—purchasing, production, marketing, pricing and organizing all follow. —Peter Bernstein

Jewish religion stresses the fact that Scripture can be interpreted on many different levels.  Christ’s teachings encompassed themes that were already central to Jewish thought—for example, love and the importance of helping the unfortunate.  But he also taught the unorthodox thesis that Jewish law could be summarized in terms of loving God with one’s whole heart.  Christ sharply criticized those who made a great show of their holiness but who failed to show compassion—a theme again borrowed from the Hebrew prophets.  Muhammad (570-632) was a merchant in Mecca who became the central prophet and founder of Islam.  The term Islam derives from slam and means peace and surrender—namely, the peace that comes from surrendering to the will of God’s sovereignty.  Before Islam the religions of the Arabic world involved the worship of many gods—Allah being one of them.  Muhammad taught the worship of Allah as the only God, whom he identified as the same God worshipped by the Christians and the Jews.  And Muhammad also accepted the authenticity of both the Jewish prophets and Christ—as do his followers.  It is then accordingly clear that there is but one God.

The Bernoulli Model.  The Bernoulli Model uses a top-down, strategic management approach to scientific management.  It combines the processes of forecasting, integrating and optimization.  The act of forecasting produces not only estimates of outcomes but also estimates of uncertainty surrounding outcomes.  In addition to the basic closed-form method of integration involving the two-moment normal distribution, The Bernoulli Model also employs the method of Monte Carlo simulation along with the four-moment Camus Distribution in order to generate, capture and integrate the full spectrum of heterogeneously distributed forecasts of outcomes and the uncertainty surrounding outcomes.  Optimization algorithms search risk-reward space in order to determine the optimal set of decisions subject to Delphi constraints.  Closed-form optimization algorithms include linear programming while open-form methods include hill-climbing and genetic algorithms.

The Method of Prototyping.  The method of prototyping involves developing a series of micro-models which eventually become macro-models.  In this case these micro-models are designed for use by the treasurer.  The Bernoulli Model further adds the Delphi program to more specifically define organizational values—utility theory to translate external values into internal values—Monte Carlo simulation to integrate heterogeneous risk components—the Camus Distribution to four-dimensionally represent risk—the Bernoulli moment vector for tracking forecasts—and an alternative hypothesis to serve as the loyal opposition to the null hypothesis.  The model also includes very stylish and highly-advanced Excel charts, VBA code and RoboHelp files.

Financial Indicators.  A financial indicator designates a pointer of value—eg. VaR—Value at Risk, EaR—Earnings at Risk, CFaR—Cash Flow at Risk, UaR—Utils at Risk.  It is important to understand that each indicator includes a statistical distribution.  Here The Bernoulli Model utilizes the Bernoulli moment vector—each of which vector contains fourteen elements.  Financial indicators are the cornerstone of risk management.  These financial indicators emphasize what organizations hold of value.  The officers and directors designate the expected financial indicator values as well as the uncertainly or risk surrounding the chosen values.  Theses values are chosen by the officers and directors using the Delphi program.  The financial indicators expand on the definition of risk and reward.

Expanded Definition of Risk and Reward.  Financial indicators are the objects by which risk and reward are measured.  Exposure (ie. Exp—M0) measures the initial exposure to change in value.  While the four-moment The Bernoulli Model provides an expanded definition of risk from the two-moment normal distribution to the four-moment Camus Distribution (ie. Mu—M1, SD—M2, Skew—M3, Kurt—M4) and fractal scaling (ie. Frac—M9) provide an expanded definition of risk.  Utility theory provides an example of an expanded definition of reward by changing external market values into internal Delphi values.  For example, a 100 percent external return (ie. Mu—M1) becomes a 50 percent internal return (ie. VaL—M5) while a –20 percent internal return becomes a –30 percent internal return.  While a 100 percent return is obviously desirable, undue emphasis on trying to achieve such a result may produce erratic outcomes and the missing out on more conservative opportunities.

Utility Theory.  In 1905 Albert Einstein wrote one of the most profound documents ever written entitled Special Relativity Theory.  In 1952 Harry Markowitz wrote one of the most profound documents ever written entitled Portfolio Selection Theory.  In 1738 Daniel Bernoulli (1700-82) wrote one of the most profound documents ever written entitled Utility Theory—the full name of the theory being—The Exposition of a New Theory on the Measurement of Risk.  The central theme of Utility Theory being that the value of an asset is the utility it yields rather than its market price.  His paper delineates the all-pervasive relationship between empirical measurement and gut feel.  The utility function converts external, market returns into internal, Delphi returns.

       The Bernoulli Moment Vector.  The Bernoulli moment vector tracks risk and return forecasts via a fourteen-element vector.  The Markowitz Model uses the mean to represent the forecast or reward and the standard deviation to represent the dispersion or risk—thus laying the groundwork for risk-reward efficiency analysis.  The method of moments is a simple procedure for estimating the statistical moments of a distribution.  The mean is the first moment of a distribution and is calculated as the average value—and the standard deviation is the second moment and is calculated as the average deviation about the mean.  The Bernoulli Model also employs an expansion on the method of moments with the Bernoulli moment vector relating to the aggregate portfolio distribution.  The zero moment in the Bernoulli moment vector represents exposure.  The Camus Distribution represents the first four moments.  The fifth moment is VaL and represents a utilitarian translation of reward and thus an expanded definition of reward.  The sixth moment is VaR and represents the confidence level and thus an expanded definition of risk.

The Complementary Principle.  Niels Bohr is one of the founding fathers of quantum theory who also defined the complementary principle as the coexistence of two necessary and seemingly incompatible descriptions of the same phenomenon.  One of the first realizations dates back to 1637 when Descartes revealed that algebra and geometry are the same thing—ie. analytic geometry.  The Bernoulli Model allows for the separation of the null and alternative hypothesis.  This ability to compare paradigms represents an invaluable feature of The Bernoulli Model.  The Bernoulli moment vector represents the tabular depiction of the Bernoulli portfolio while the Excel charts represent the graphical form of the Bernoulli portfolio.

The Delphi Program.  The Delphi program is the overriding guidance system for The Bernoulli Model.  It employs the iterative Delphi method designed to draw out fundamental values from officers and directors.  The purpose of the Delphi process is to streamline decisionmaking for all concerned.  The Delphi program is named after the Socratic inscription—Know Thyself—at the oracle at Delphi in ancient Greece.  The primary Delphi value pertains to the confidence level and value for allowable downside risk exposure of the portfolio distribution—using a financial indicator like VaR.  Secondary Delphi value pertains to the utility translation function and risk-reward efficiency analysis.

The Actuarial Valuation Process.  The actuarial valuation worksheet shows the progression of the financial indicators through the valuation process.  The actuarial valuation worksheet shows the end result of the technical development.  The worksheet contains the Bernoulli moment vector for both the components and the portfolio.  It also contains advanced Excel charts that are broken down into the null configuration and the alternative configuration.  Anything that is not made clear from the actuarial valuation worksheet can be found in the technical analysis worksheet.  This worksheet shows the development of the actuarial valuation process.

The Treasurers’ Perspective.  The Bernoulli Model is a top-down strategic management, forecasting and risk management system that is mathematically accessible to executives.  It is designed for use by the treasurer showing the actuarial valuation Excel worksheet illustrating a storyboard that demarcates the same six Excel charts for all organizational financial indicators used in the actuarial valuation process.  The worksheet also presents both the null and alternative valuation parameters and the null and alternative Bernoulli moment vectors.  The actuarial valuation worksheet also includes valuation parameters as well as the Bernoulli moment vectors.  All of this leads to a brand new look at scientific management for the treasurer.

Conclusion.  Peter Bernstein once said that risk is no longer bad news—rather it is a harbinger of opportunity to be harnessed for our benefit.  This essay describes the process of putting into play an executive risk management, decisionmaking and forecasting system.  Sir James Jeans once said that God is a mathematician.  The notion of God as a mathematician is in fact consistent with the idea that there is only on God.