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Über dieses Buch

Read examines probability, risk, and uncertainty through the contributions of John von Neumann, Leonard Jimmie Savage, Kenneth Arrow and Harry Markowitz. These Portfolio Theorists provided us with a dramatic leap forward in our understanding of and insights into financial rewards under risk and uncertainty.

Inhaltsverzeichnis

Frontmatter

Introduction

1. Introduction

Abstract
This book is the second in a series of discussions about the great minds in the history and theory of finance. The series addresses the contributions of brilliant individuals to our understanding of financial decisions and markets.
Colin Read

A Roadmap to Resolve the Big Question

2. A Roadmap to Resolve the Big Question

Abstract
In 1738, Daniel Bernoulli of the renowned Bernoulli mathematics family posed what we now call the St Petersburg Paradox. In its simplest form, it asked if one would be willing to bet one ducat for the opportunity to flip a coin and possibly win two ducats. If such a toss is actuarially fair, why are few willing to bet 1,000 ducats for a 50/50 chance to win 2,000 ducats or a million to win two million?
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John von Neumann

Frontmatter

3. The Early Years of John von Neumann and Oskar Morgenstern

Abstract
There was a time when scholars were generalists. The great philosophers of ancient Greece were lawyers, theologians, playwrights, political scientists, and naturalists. For instance, Archimedes (287–212 BC) was a mathematician and engineer, physicist, astronomer, and statesman. In the early Renaissance, Leonardo da Vinci (1452–1519) made significant contributions in art, architecture, music, technology, mathematics, anatomy, geology, botany, physics, and invention. Isaac Newton (1643–1727) was a physicist, astronomer, mathematician, theologian, and philosopher, while Galileo Galilei (1564–1642) was a technologist, physicist, mathematician, philosopher, and astronomer. As late as the nineteenth century, the mathematician and statistician Carl Friedrich Gauss (1777–1855) was also an astronomer, physicist and geophysicist, theologian, and expert at optics.
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4. The Times and the Beginning of an Era

Abstract
Oskar Morgenstern and John von Neumann lived at a time when the nascent prevailing formalism in the study of finance had only recently provided an understanding of the meaning of simple financial returns. Once the financial literature appreciated how returns affected individual decision-making, researchers sought to incorporate risk and uncertainty into their models. Inevitably, this would require significant new work in the understanding of uncertainty and probability, and significantly new complexity in financial models.
Colin Read

5. The Theory of von Neumann and Morgenstern

Abstract
Before the Great Depression, the simple financial theories of the 1920s had not been put to task. There was little need for nuanced model sophistication to include uncertainty in the ever-rising financial markets of the Roaring Twenties. By the end of the decade, the markets began to falter. Soon, the economy was plagued with waves of uncertainty that would soon poison financial markets worldwide. The imposition of financial risk on humanity has remained a central topic in finance ever since. There became a pressing need to incorporate uncertainty into our understanding of financial markets.
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6. Applications and Elaborations of the von Neumann-Morgenstern Model

Abstract
The concepts developed in the Theory of Games and Economic Behavior have spawned an incredible literature on strategic behavior in mathematics, economics, finance, political science, sociology, psychology, and many other fields. However, game theory itself has yielded few tools that are of immediate utility in the field of finance. This is because the implications of game theory are primarily descriptive rather than prescriptive.
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7. The Later Life and Legacy of von Neumann and Morgenstern

Abstract
There have been few great minds that have spawned so many contributions from others as has John von Neumann. Nor has there likely been a great mind that has imparted so many contributions to so many different scientific fields. Countless scholars have received Nobel Prizes in Physics and Chemistry as a consequence of his pioneering work in a variety of mathematical areas. The Swedish Academy even awarded a Crafoord Prize in Biology to a game theoretic mathematician, John Maynard Smith.
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Leonard Jimmie Savage

Frontmatter

8. The Early Years

Abstract
In the period from the late nineteenth century to the first part of the twentieth century, the classical economic model took center stage, just as the classical model had dominated physics until Albert Einstein shattered its foundations. Calculus was the primary tool for the deterministic models of physics and economics in those days. However, it depends on well-understood and deterministic relationships using the building blocks of functions that have been used for centuries.
Colin Read

9. Friedman and Savage’s Times

Abstract
The St Petersburg Paradox demonstrated the fundamental incongruency between the measurement of probability and risk, and our human response to it. Bernoulli pointed out that humans would not pay an arbitrarily large amount for an infinite return with a probability of less than one. In his hints at how to resolve the Paradox, he noted that it is our subjective human regard for probability that is more relevant than the sterile, rational, mathematic measurement of objective probability.
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10. The Theory of Friedman and Savage

Abstract
The collaboration between Milton Friedman and Leonard Jimmie Savage was serendipitous. These two great minds began discussions as part of the Second World War research effort while both were researchers at the Columbia University-associated Division for War Research. By that time, Friedman was already a towering figure in the Statistical Research Group at Columbia.
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11. Applications of the Concept of Subjective Probabilities

Abstract
It is likely that Leonard Jimmie Savage began to ponder the interdependency of probability and behavior during the year he worked as the statistical analysis assistant to John von Neumann. Both were pure mathematicians who had informed their research based on their extent of human understanding from the emerging economics literature. When their collaboration ended in 1942, each went in slightly different directions. Von Neumann developed a collaboration with Oskar Morgenstern, while Savage did likewise with Milton Friedman. These new partners bent their once convergent research paths in subtly different directions and finance theory is richer for it.
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12. Life and Legacy

Abstract
Before Bruno de Finetti’s preversions, it was not possible to price risk, and before Leonard Jimmie Savage’s 1954 publication of The Foundations of Statistics, no researcher had been able to do the same with uncertainty. The special case of de Finetti and the more general case of Savage revised how risk and uncertainty affect human decision-making and revolutionized the field of finance.
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Kenneth J. Arrow

Frontmatter

13. The Early Years

Abstract
There is a significant debate over whether genius is innate or nurtured. While it is impossible to determine how our genetic stock might influence the paths we take, we often see genius emerge in consistent ways at young ages. Each of the great minds covered in this series demonstrated flashes, streaks, or consistent and precocious brilliance in their youth. Kenneth J. Arrow, a groundbreaker in finance and almost every other area of the decision sciences, is no exception.
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14. The Times

Abstract
Like John von Neumann and Leonard Jimmie Savage, Kenneth Arrow was an early pioneer in the sort of sophisticated mathematical methods called topology and set theory that now reside in the mathematical toolbox of modern finance theorists.
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15. Arrow’s Great Idea

Abstract
Often, brilliant inspirations come quite by chance. Kenneth Arrow’s contribution came through serendipity. His concern that he could not forge a postgraduate career in economics induced him to consider a career in statistics or insurance. As he studied, he found work in these two areas and, through his work and study, gained a valuable perspective that would influence his life’s work and contribution in finance.
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16. Applications of the Contingent Claims Model

Abstract
Arrow prices are a natural and an ingenious extension of the Arrow-Debreu general equilibrium model. The differentiation of commodities by the present and by states of nature in the future created an equivalency between the conventional certainty model to one of production and consumption with uncertainty. Arrow’s extension to futures markets and financial securities also extended the two fundamental theorems of welfare economics to finance: The first, that every competitive equilibrium is a Pareto optimum, and the second, that any Pareto optimal allocation can be supported by a competitive equilibrium, given some redistribution of income, were the impetus for generations of study in finance that continues to this day.
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17. Life, Legacy, and the Nobel Prize

Abstract
In one fell swoop, Kenneth Arrow helped answer a number of unresolved or only partially resolved questions. In parallel with the work of Gerard Debreu, he provided the first truly general competitive equilibrium existence proof. He also incorporated an extension of the von Neumann-Morgenstern expected utility hypothesis into a model that has since become the standard of analysis in finance. Finally, he provided the first formal model of futures markets and he explicitly described the ways in which uncertainty and information relate in general equilibrium.
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Harry Markowitz

Frontmatter

18. The Early Years

Abstract
When Harold Maxwell Markowitz was a child, he showed all the signs of normality, at least in comparison with the cohort of intellectually precocious great minds in finance. He was born on August 24, 1927, in Chicago, the only child of Morris and Mildred Markowitz. He shared a quality with the majority of other great minds covered in the series so far in that he was born to parents who arrived from or were themselves children of parents from Central or Eastern Europe.
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19. The Times and a New Paradigm in Personal Finance

Abstract
By the late 1940s, when Harry Markowitz took the advice of his supervisor and began to explore securities pricing, the pioneering and related work by John Burr Williams was already a decade old. The stock market was yet to return to its lofty 1929 values, as the economy was buffeted first by the Great Depression, then the Second World War, and the recession that followed as economies tried to regroup after the war. The Great Depression had left a legacy of suspicion about institutions and financial markets, despite John Burr Williams’ best efforts to forge renewed interest in personal finance based on the rationality model and a scientific approach to securities pricing.
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20. The Theory of an Efficient Portfolio

Abstract
Some argue that the finance world can be broken down into two parts, BM and PM (before and post Markowitz). In 1952, Harry Markowitz, a 24-year-old graduate student at the University of Chicago, published a short article titled “Portfolio Selection” in the seventh volume of the Journal of Finance that revolutionized personal finance and portfolio theory.168
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21. Applications of Portfolio Theory

Abstract
The genius of the Markowitz model of portfolio selection is that even a small investor can create a portfolio that is efficient in the sense that it minimizes variability for any degree of desired returns. Markowitz’s approach required that the investor has access to the risk-free asset with return Rf and a portfolio of assets that could place the investor on the Markowitz bullet and the capital allocation line.
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22. Life, Legacy, and the Nobel Prize

Abstract
Harry Markowitz’s career path proved unconventional, even for great minds in finance and for Nobel Prize winners. His Nobel Prize-winning work shared commonality with Kenneth Arrow and the brilliant game theorist John Nash in that it was completed before he finished his PhD. To his credit, he almost always maintained at least one foot in the world of financial practice. Following his stay at the RAND Corporation, he worked for many years on software development, first with Consolidated Analysis Centers from 1963 to 1968, then with the Arbitrage Management Company from 1969 to 1972, and finally with the T.J. Watson Research Center of IBM (International Business Machines) from 1974 to 1983.
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What We Have Learned

Frontmatter

23. Combined Contributions in Portfolio Theory

Abstract
Finance theory had been slow to develop until a dramatic explosion in results occurred over just a handful of years. Before 1937, there had been a gradual evolution in our understanding of the significance of the interest rate. Irving Fisher had given finance theory the tools to understand why people save. John Burr Williams had created the present value approach to the pricing of securities based on their expected future profits. Meanwhile, John Maynard Keynes, the financier turned macroeconomist, demonstrated to the literature that our financial portfolio contains not one generic asset, but rather many assets, with the share we keep in each is dependent on such things as income, interest rates, and overall market perceptions. Finally, in the late 1940s and early 1950s, we began to gain a better understanding of how our savings decisions evolved over our life cycle through the works of Franco Modigliani, Richard Brumberg, and Milton Friedman.
Colin Read

24. Conclusions

Abstract
This book is the second in a series of discussions about the great minds in the history and theory of finance. While the series addresses the variety of contributions of significant individuals to our understanding of financial decisions and markets, the first book in the series, The Life Cyclists, began by establishing a framework upon which all subsequent discussions rest. It described how individuals make decisions over time and why these decisions change as we age and our circumstances change.
Colin Read

Backmatter

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