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Article Excerpt
Introduction
It has been well said that Paul A. Samuelson is the last great general economist--never again will any one person make such foundational contributions to so many distinct areas of economics. His profound theoretical contributions over nearly seven decades of published research have been ecumenical and his ramified influence on the whole of economics has led economists in just about every branch of economics to claim him as one of their own. I am delighted to take part in this celebration of his Ninetieth Birthday.
This Volume provides a special opportunity to honor this universal man of economics as he enters his 10th decade. On such Festschrift occasions, the common practice is to write a substantive piece building upon the honoree's work. However, here I try my hand at a different format: synthesizing Samuelson's work in financial economics itself. As everyone knows, Paul Samuelson is his own best synthesizer and critic, and so the format as executed will only be at best second-best. (1) Synthesis, we know, involves abstraction from the complex original. With Samuelson, we must be severely selective since even with confinement to a single branch of economics, the wide-ranging scope and unflagging volume of his researches allows only a few elements of the work to be examined. Within that brute reality, I limit my discussion to just three of his chief contributions to the field of financial economics: 1) The Efficient Market Hypothesis; 2) Warrant and option pricing; and 3) Investing for the long run.
Happily, I had the great good fortune to explore this same synthesizing theme in print nearly a quarter century ago [Merton, 1983], covering early major contributions of Samuelson a number of which are not discussed here, such as expected utility theory (from reconciling its axioms with non-stochastic theories of choice to its reconciliation with the ubiquitous and practical mean-variance criterion of choice), the foundations of diversification and optimal portfolio selection when facing fat-tailed, infinite-variance return distributions. (2) As we shall see, however, it is remarkable how much of Samuelson's early research remains in the mainstream of current financial economic thought decades later, having gained even greater significance to the field with the passage of time. (3) Samuelson's discoveries in finance theory, as in economic theory generally, constitute the manifest core of his multiform writings. His accomplishments in both the problem-finding and problem-solving domains of theory are legend. Another, latent but no less deep, theme of Samuelson's writings is trying to divert us away from the paths of error, whether in finance research, private-sector finance practice or public finance policy.
Samuelson's attacks on error are not limited to engagements in the economics arena. He has upon occasion used the life works of other economists to discredit the widely held myth in the history of science that scientific productivity declines after a certain chronological age. The strongest debunking of this ill-founded belief would, of course, have been the self-exemplifying one. While my brief search of the literature produced neither an exact cutoff age where productivity is purported to decline nor whether this decline is to be measured by the flow of research output per unit time or by its rate of change, the data provided by Paul Samuelson's lifetime pattern of contributions are robust in rejecting this proposed result on all counts. Representing twenty-seven years of scientific writing from 1937 to the middle of 1964, the first two volumes of his Collected Scientific Papers contain 129 articles and 1772 pages. These were followed by the publication in 1972 of the 897-page third volume, which registers the succeeding seven years' product of seventy-eight articles published when he was between the ages of 49 and 56. A mere five years later, at the age of 61, Samuelson had published another eighty-six papers, which fill the 944 pages of the fourth volume. A decade later the fifth volume appeared with 108 articles and 1064 pages. Simple extrapolation (along with a glance at his list of publications since 1986) assures us that the sixth and even a seventh volume cannot be far away.
Nearly a quarter century ago, I presented Paul with a list of his then thirty articles in financial economics and asked him to select his favorite ones, leaving the criteria for choice purposely vague. By the not-so-tacit demanding criterion that was evidently applied, he was drastically selective, choosing only six. I list these below. Four of the six articles appear in journals not on the beaten path of most economists, but happily they are reproduced in Samuelson's collected scientific papers.
Paul Samuelson's 1982 Selection of his favorite financial economics papers
1. "Probability, Utility, and the Independence Axiom," Econometrica 20, no. 4, October 1952, pp. 670-678; [1952b, I, Chap. 14].
2. "General Proof that Diversification Pays," Journal of Financial and Quantitative Analysis 2, no. l, March 1967, pp. 1-13; [1967a, III, Chap. 201].
3. "The Fundamental Approximation Theorem of Portfolio Analysis in Terms of Means, Variances, and Higher Moments," Review of Economic Studies 37, no. 4, October 1970, pp. 537-542; [1970a, III, Chap. 203].
4. "Stochastic Speculative Price," Proceedings of the National Academy of Sciences, U.S.A. 68, no. 2, February 1971, pp. 335-337; [1971a, III, Chap. 206].
5. "Proof that Properly Anticipated Prices Fluctuate Randomly," Industrial Management Review 6, no. 2, Spring 1965, pp. 41-49; [1965a, III, Chap. 198].
6. "Rational Theory of Warrant Pricing," Industrial Management Review 6, no. 2, Spring 1965, p. 13-39; [1965b, III, Chap. 199].
Perhaps a bit selfishly, we in financial economics are especially thankful that Paul paid no heed to the myth of debilitating age in science. Five of the six articles he selected in 1982 as his most important papers in our branch of economics and all but six of his more than three-score contributions to our field to date were published after he had reached the age of 50.
Along with his foundational research and important directives on avoiding the paths of error, there are the characteristic Samuelsonian observations in the history of economic science. Samuelson's writings on Smith, Ricardo, Marx and his many essays on the evolution of more contemporary economic thought provide much grist for the mill of the historian of science. But, to focus exclusively on those explicit undertakings in the history of economic science is to miss much. Part of an unmistakable stamp of a Paul Samuelson article is the interjections of anecdotes and stories around and between his substantive derivations, which serve to entertain and enlighten the reader on the developmental chain of thought underlying that substantive analysis.
One happy example in financial economics is Samuelson's brief description in the "Mathematics of Speculative Price" [1972a, IV, Chap. 240, p. 428] of the rediscovery of Bachelier's pioneering work on the pricing of options. In the text, he wrote:
In 1900 a French mathematician, Louis Bachelier, wrote a Sorbonne thesis on the Theory of Speculation. This was largely lost in the literature, even though Bachelier does receive occasional citation in standard works on probability. Twenty years ago a circular letter by L. J. Savage (now, sadly, lost to us), asking whether economists had any knowledge or interest in a 1914 popular exposition by Bachelier, led to his being rediscovered. Since the 1900 work deserves an honored place in the physics of Brownian motion as well as in the pioneering of stochastic processes, let me say a few words about the Bachelier Theory.
The footnote elaborates
Since illustrious French geometers almost never die, it is possible that Bachelier still survives in Paris supplementing his professional retirement pension by judicious arbitrage in puts and calls. But my widespread lecturing on him over the last 20 years has not elicited any information on the subject. How much Pioncare, to whom he dedicates the thesis, contributed to it, I have no knowledge. Finally, as Bachelier's cited life works suggest, he seems to have had something of a one-track mind. But what a track! The rather supercilious references to him, as an unrigorous pioneer in stochastic processes and stimulator of work in that area by more rigorous mathematicians such as Kolmogorov, hardly does Bachelier justice. His methods can hold their own in rigor with the best scientific work of his time, and his fertility was outstanding. Einstein is properly revered for his basic, and independent, discovery of the theory of Brownian motion 5 years after Bachelier. But years ago when I compared the two texts, I formed the judgment (which I have not checked back on) that Bachelier's methods dominated Einstein's in every element of the vector. Thus, the Einstein-Fokker-Planck Fourier equation for diffusion of probabilities is already in Bachelier, along with subtle uses of the now-standard method of reflected images.
In addition to providing the facts on how Bachelier's seminal work found its way into the mainstream of financial economics after more than a half century of obscurity, Samuelson's compact description provides a prime example of multiple and independent discoveries across the fields of physics, mathematics, and economics. (4) On the issue of allocating the credit due innovative scholars, he also provides an evaluation of the timing and relative quality of the independent discoveries. His mention of Poincare provides a hint that there may be still more to the complete story. Furthermore, note his signature use of a chain of eponyms, the "Einstein-Fokker-Planck Fourier equation ...", to compactly remind us of the sequence of scientists to whom we owe credit. And, of course, what economist wouldn't relish this revelation of the great debt owed to this early financial economist by the mathematical physicists and probabilists to be added to the well-known debt owed to Malthus by the Darwinian biologists?
Although most would agree that finance, micro investment theory and much of the economics of uncertainty are within the sphere of modern financial economics, the boundaries of this sphere, like those of other specialties, are both permeable and flexible. It is enough to say here that the core of the subject is the study of the individual behavior of households in the intertemporal allocation of their resources in an environment of uncertainty and of the role of economic organizations in facilitating these allocations. It is the complexity of the interaction of time and uncertainty that provides intrinsic excitement to study of the subject, and, indeed, the mathematics of financial economics contains some of the most interesting applications of probability and optimization theory. Yet, for all its seemingly obtrusive mathematical complexity, the research has had a direct and significant influence on practice. The impact of efficient market theory, portfolio selection, risk analysis, and option pricing theory on asset management and capital budgeting procedures is evident from even a casual comparison of current practices with, for example, those of the early 1960s when Paul Samuelson was just publishing his early foundational papers in finance.
New financial product and market designs, improved computer and telecommunications technology and advances in the science of finance during the past four decades have led to dramatic and rapid changes in the structure of global financial markets and institutions. The scientific breakthroughs in financial economics in this period both shaped and were shaped by the extraordinary flow of financial innovation, which coincided with those changes. The cumulative impact has significantly affected all of us--as users, producers, or overseers of the financial system.
The extraordinary growth in size and scope of financial markets and financial institutions including the creation of the enormous national mortgage market in the United States were significantly influenced by the models developed in financial economic research. The effects of that research have also been observed in legal proceedings such as appraisal cases, rate of return hearings for regulated industries, and revisions of the "prudent person" laws governing behavior for fiduciaries. Evidence that this influence on practice will continue can be found in the curricula of the best-known schools of management where the fundamental financial research papers (often with their mathematics included) are routinely assigned to MBA students. Although not unique, this conjoining of intrinsic intellectual interest with extrinsic application is a prevailing theme of research in financial economics. Samuelson, once again, did much to establish this theme as a commonplace and to exemplify it in his substantive writings.
It was not always thus. Fifty years ago, before the birth of the economics of uncertainty and before the rediscovery of Bachelier, finance was essentially a collection of anecdotes, rules of thumb, and manipulations of accounting data with an almost exclusive focus on corporate financial management. The most sophisticated technique was discounted value and the central intellectual controversy centered on whether to use present value or internal rate of return to rank corporate investment projects. The subsequent evolution from this conceptual potpourri to a rigorous economic theory subjected to systematic empirical examination was the work of many and, of course, the many included Paul Samuelson.
After this brief overview of Samuelson's multifaceted influence on the ethos of financial economic research, I turn now to that promised discussion of three of his chief contributions to the field.
II. The Efficient Market Hypothesis
A question repeatedly arises in both financial economic theory and practice: When are the market prices of securities traded in capital markets equal to the best estimate of their values? I need hardly point out that if value is defined as "that price at which one can either buy or sell in the market," then the answer is trivially "always" But, of course, the question is rarely, if ever, asked in this tautological sense, although the distinction between value and price is often subtle. Moreover, as the following examples suggest, the answer to this question has important implications for a wide range of financial economic behavior.
In the fundamentalist approach of Graham and Dodd to security analysis, the distinction between value and price is made in terms of the (somewhat vague) notion of intrinsic value. Indeed, the belief that the market price of a security need not always equal its intrinsic value is essential to this approach because it is disparities such as these that provide meaningful content to the classic prescription for successful portfolio management: buy low (when intrinsic value is larger than market price) and sell high (when intrinsic value is smaller than market price).
In appraisal law, the question is phrased in terms of how much weight to give to market price in relation to other non-market measures of value in arriving at a fair value assessment to compensate those whose property has been involuntarily expropriated. In corporation finance, the answer to that question determines the extent to which corporate managers should rely upon capital market prices as the correct signals for the firm's production and financing decisions.
Characteristically, Samuelson's version provides both a clear distinction between value and price and a focus on the broadest and most important issue raised by this question: When are prices in a decentralized capital market system the best estimate of the corresponding shadow values of an idealized central planner who efficiently allocates society's resources? Thus, in "Mathematics of Speculative Price" [1972a, IV, Chap. 240, p. 425], he wrote:
A question, for theoretical and...
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