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Deconstructing Today’s Ongoing Revolution In Finance

March 19, 2007

General reader, today's Outside the Box is one that you are going to want to put your thinking caps on for. My good friend Woody Brock has kindly allowed me to present you with one of the sections from his quarterly comments. In his chapter "Deconstructing Today's Ongoing Revolution in Finance," Woody has written a particularly interesting and somewhat controversial section titled "Why the Economy Needs Vastly More Derivates, Not Less."

An all too common myth is that the total value of derivates is in and of itself dangerous because they are a form of leverage...but that is not the case. Derivatives, per se, are not a form of leverage; rather they afford the opportunity and make it easier and less risky for others to use leverage across many different assets and instruments (i.e. - mortgages, insurance, etc...). It is the leverage which is then the issue, as paradoxically, the decreased risk (hedging) aspects of derivatives allows investors to feel more comfortable with increased leverage, which sends a variety of signals to market participants.

The problem lies not in the instruments but in how the risk is distributed. While many of the larger, institutional players have used the offshoots of derivates to better hedge themselves, much of the smaller investor community has unwisely used the medium in a speculative manner. If a small homeowner is in trouble because of leverage on their mortgage, there just isn't anyone left to bail them out. Just as in the greater fool theory, the party only continues while someone is more foolish and irrational than the last fool.

Again, this is one of the more insightful articles featured in an Outside the Box. I believe it to be very important as its implications tie into what we are now seeing in the subprime mortgage market. May you enjoy Woody's insights and analysis.

John Mauldin, Editor
Outside the Box

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Deconstructing Today's Ongoing Revolution In Finance


- Why the Economy Needs Vastly More Derivatives, Not Less -

In this chapter, we draw upon some of the basic concepts lying at the heart of modern finance so as to clarify what today's revolution in finance is all about, and whether it constitutes a significant net gain for society. Particular emphasis is placed on the nature and role of derivative securities.

Three Questions Addressed

QUESTION 1: By some estimates, over $300 trillion worth of derivative contracts are now outstanding (measured on a "gross," not "net" basis). This exceeds the size of global GDP six times over! How can this explosion in the number and value of contracts have occurred? Should the outstanding value of derivative contracts be as large as it is? Indeed, is there some theoretically optimal level of contracts, and if so, has this been exceeded during the frenzy of the past decade?

Answer:The answer is that the enterprise of creating hedging instruments is still in its infancy, and will indeed continue to grow. The value of outstanding contracts will continue to mushroom. And yes, there is a theoretically optimal value of contracts that ideally "should" exist: Incredibly, it is a number millions of times larger than today's value (see below). Finally, even if there is a freeze-up and/or meltdown in the future, extinguishing millions of contracts in the process, then the volume of contracts would once again soar thereafter. For the forces that have been unleashed are vast and unstoppable, and are dictated by the most elementary of economic concepts, as we shall now see.

Why This Is the Case - An Elementary Proof: To support these assertions, we must draw upon two of the most important results in the modern Economics of Uncertainty, namely the celebrated theorems of Arrow (1953) and Ross (1976) that we review below.[1] We show that, at least in theory, there would be infinite derivative contracts. Thus the number of contracts outstanding today is a fraction of what would ideally exist--regardless of how huge that number seems to most of us. The sketch of a proof that follows is deliberately non-mathematical, and should cause no problem for the reader.

First, Arrow's Theorem of 1953 demonstrates that an efficient allocation of resources and risk requires that a "complete" set of securities exist permitting agents to hedge all risks. Let us explain this remarkable result. A security such as a share of stock represents a promise to pay a given amount for each set of uncertain possible states that may occur in the future. "State" is a very abstract concept, and refers to any exogenous event (e.g., Fed policy next month, earnings of ABC Co. in 2008, rainfall in Kansas in October 2025, etc.) that may occur at any date in the future relevant to the value of the security. Now the collection of all possible uncertain future states is called the "state space" of the economy, and the dimension of this space will be incredibly large.

What Arrow's model required, then, is that a sufficient number of securities exist to make it possible for every investor to hedge uncertainty about any and every possible future state. Moreover, any such security (or portfolio thereof) can be represented as a linear combination of the set of "elementary" Arrow securities. An Arrow security defined for state s is a security that pays 1 unit (e.g., one dollar) if state soccurs, and 0 otherwise. Such a security is assumed to exist for every state. Given the vast dimension of the state space, there will therefore be a vast number of elementary securities.

Writing some 23 years later than Arrow, Stephen Ross confronted the reality that a complete set of securities will never exist--partly because of transactions costs, and partly because of incentive structure issues. Nonetheless, he showed that a few Arrow securities combined with a suitable mix of options suffices to make possible the hedging of all risks, as required for overall economic efficiency. That is, options utilized in the right manner make it possible to "complete" the markets in securities. [2]

This is of course where "derivatives" enter the picture, since options are the most basic kind of derivative security. A derivative security derives its value not from the future exogenous state of the world (like the "primitive" securities in Arrow's model), but rather from the future prices of primitive securities. An option characterized by its strike price is the most elementary type of derivative security.

Now the future price of a (primitive) security can in principle assume an infinite number of values. Thus, the ability to perfectly hedge all risks in Ross's model implies the need for an infinity of hedging securities: For securities now become functions not only of the finite-dimensional state space in Arrow's model, but also of future prices--and indeed all possible sequences of future prices over time since "returns" are usually defined in terms of sequences of payoffs. In principle, therefore, an infinite number of securities of various kinds will be required to make perfect hedging possible.

This being true, the number of securities now in existence is a mere drop in the bucket of what is required for true economic efficiency to be reached. This completes the sketch of our proof, and it leads quite naturally to the second question we address.

QUESTION 2: During the past twenty-five years, an entire industry has grown up around the derivatives markets. This industry involves wholly new products for those who wish to lay off risks, wholly new types of investments for investors who wish to assume or to diversify risks, and wholly new players such as hedge funds, private equity firms, and proprietary traders. More and more of our most talented students are being siphoned off into careers in "finance"--and at an accelerating rate. What is really going on here? Will it continue? Or is this merely another bubble?

Answer: What is going on is a profound transformation that stemmed partly from the advent of Arrow's Economics of Uncertainty in the early 1950s, and partly from technological change. This revolution is impacting everything from people's ability to hedge and/or to speculate, to the meaning of "public" versus "private" ownership of a firm, to a redefinition of a "stock" versus a "bond" (already an archaic distinction), to the creation of wholly new kinds of investment vehicles, etc.

The elementary primitive and derivative securities of Arrow and Ross can be thought of as the Lego blocks from which all financial instruments can be fashioned, in principle. Their impact far transcends the kinds of securities that are now created and traded, and is permitting new solutions to a broad array of financial and economic problems. As one example, our new found ability to securitize and repackage assets and to slice and dice risk has led to a complete reconceptualization and utilization of leverage.

More generally, these developments are enabling a reassembling of the entire economy, a phenomenon in which the rise of private equity firms is playing a salient role. Just consider the fact that nearly $150 billion of equity was "retired" from New York and London stock exchanges during 2006--a year that also witnessed some $500 billion of private equity deals in total. In the limit, will we observe bedrock firms like IBM being "owned" by an ever-fluctuating assemblage of private equity partnerships sequentially reselling their ownership shares of the company to one another, or to other outside groups?

In such a case, who will be the true boss of IBM responsible for strategic planning? What will ownership mean? Will the concept of a "firm" remain relevant? And what of the fate of "pension fund socialism," the important sociological construct that the late Peter Drucker introduced to link capitalism to the interests of the broader public?

Chart 1

In understanding the true origins of this revolution, Figure 1 is instructive. The purely theoretical work of Kenneth Arrow and Steve Ross laid the foundations for what was to come. But abstract theory was not enough. As Professor Arrow told the author many years ago, digital computers did not exist when he wrote his seminal 1953 paper, so that he never imagined that his concepts would become operational. Likewise, when Ross wrote his paper "Options and Market Efficiency" in 1976, options pricing theory was in its infancy. Thus, today's revolution must be understood as the result of pure theory and the advent of computers and the development of securities pricing models and the education of a suitable number of "quants" to man the assembly line. With these tools now in hand, there will be no way of going back to the simplicities of earlier days. The genie has been let out of the bottle!

QUESTION 3: Warren Buffet has expressed the view that derivatives are "financial weapons of mass destruction." Yet former Fed Chairman Alan Greenspan has praised their role in the economy. What is the truth in this debate about derivatives? And more generally, does today's revolution in finance constitute a net gain for society?

Answer:The proliferation of derivatives and ever more creative financial market instruments is clearly a plus in that it permits increasingly better ways in which to slice, dice, and manage risks of all kinds. To call this a "plus" is not merely an opinion; it is, rather, a theorem of the deepest possible nature. For the most fundamental point made in Arrow's 1953 paper--and it is one of the great insights in the history of economics--is that the ultimate role of securities markets is to permit an optimal reallocation of risk throughout society.

Even more fundamentally, without a complete set of hedging markets in which all agents can hedge all risks, the Invisible Hand of the market will fail to achieve an efficient allocation of all resources--commodities, services, and risk. This is Arrow's main theorem. In brief, if you believe in capitalism, in markets, and in the Invisible Hand, then you had better sing the praises of today's revolution in finance. For it has brought us closer than ever before to the idealized economy of the text book.

In this spirit, Fed Chairman Greenspan was probably correct in his 2004 Kansas City Fed speech in Jackson Hole, Wyoming. He observed that our enhanced ability to slice and dice risk was arguably the principal reason why not a single financial institution went under during the meltdown of 2001.

The Negatives: As is so often the case in economics, the financial market revolution under way is a compromise between the idealized world of economic theory on the one hand, and reality on the other. More specifically, several of the conditions required for efficiency in Arrow's sense simply do not hold true in the real world. Today's revolution is merely depositing us at a financial half-way house that is beset by problems caused by the failure of the real world to match the preconditions of textbook theory. The best way to understand this is to identify which requirements of the textbook do not hold true, and how this in turn creates new problems meriting legitimate concern.

  • The World of Theory: Recall that the economy must possess a complete set of hedging markets. Moreover, in later and more refined versions of Arrow's original model, all agents are assumed to possess "Rational Expectations." That is, everyone correctly knows all risks at all times, and--given the assumed completeness of the hedging markets--has appropriately hedged all risks. [This assumption in turn requires that the environment is "stationary." For if it were not, then it would be impossible for all agents to learn the true conditional probabilities of all future events--and this is exactly what it means to assume that "everyone correctly knows all future risks."] When these stringent conditions are met, then we do indeed enter that idealized world in which all risks are correctly assessed, no one makes mistakes and goes bankrupt, leverage poses no problems at all, and system meltdowns cannot occur. This, of course, is the idealized world of perfectly efficient markets, formalized by such scholars as Robert Lucas in Chicago in the 1970s.
  • The World of Reality: In reality, we live in a messy world in which securities markets are woefully incomplete--and always will be no matter how many more hedging instruments are developed. [This is a theorem.] And we live in a non-stationary environment marked by ongoing structural changes. In such environments, agents cannot know the true probability of all future events, and thus are regularly wrong. By virtue of both being wrong and being incompletely hedged, they can and do go bankrupt. As a result, systems meltdowns can and do occur. Worse, leverage can amplify such meltdowns.

The prospect of a meltdown is spookier today than it used to be. This is because of the fact that counter-party risks are no longer concentrated in large investment banks that can be readily identified and bailed out by the monetary authority during a crisis. Rather, they are diffused through myriad lesser counterparties whose identities and financial health are unknown to the authorities. Moreover, whereas large and visible players have balance sheet liquidity requirements imposed upon them, these lesser counterparties often do not. Thus we run the very real possibility of a cascade of debt defaults by households.

A mathematical description of all these problems that arise in a non-stationary world with incomplete securities markets has been set forth within the new theory of "Rational Beliefs" developed at Stanford University during the past decade, a theory that has been discussed at length in these pages, and that the author has helped to develop and apply in a real world context. In the language of this new theory, all these problems that arise in the real world if not in classical textbooks are captured by the crucially important new concept of "endogenous risk."

The Leverage Issue: As regards this last point about leverage, critics of today's status quo write as if the proliferation of derivatives itself implies greater leverage. This is not the case. It is true, however, that the use of derivatives has made it both more possible and more profitable to utilize leverage than ever before. Moreover, the use of derivatives can help disguise the extent of leverage should traders wish to mask over problems in their books. Thus, critics have a point when they claim that today's proliferation of derivatives could in principle help precipitate a meltdown. But it is often overlooked how leverage has helped to contribute to famous meltdowns throughout history in which derivative securities played no role at all.

All in all, there is at present no known way in which to net out the social cost of these negatives from the gains made possible by the proliferation of new instruments for managing risk. It would seem, however, that there is a huge net gain. Our own concerns center on the failure of government policy to curb excessive leverage, which we discussed in much greater length in our May 2006 essay entitled, "Derivatives Market Meltdown to Come?"


- For the Interested Reader -

Since World War II, three great revolutions have taken place that have profoundly changed our lives: the computer revolution, the financial market revolution, and the molecular biological revolution. Interestingly, all three are based upon one and the same mathematical structure known as finite-state combinatorial analysis. In the first case, the "digital logic" that made possible high-speed numerical computation is based upon 0-1 binary arithmetic. In this formalism, all numbers utilized in computations can be represented by combinations of 0's and 1's. Additionally, these two numbers correspond at a physical level to the "on" or "off" settings of a vast array of electronic switches directing the flow of electricity. The digital computer was thus born out of digital logic.

Second, the developments in modern finance that have made it possible to revolutionize the concept of "financial securities" were based upon a comparably remarkable insight. Virtually any kind of security or hedging instrument can be represented as a linear combination of elementary "Arrow securities," the building blocks of modern finance. An Arrow security is a binary concept, just as 0 - 1 (or base-two) arithmetic is. Specifically, let S denote the set of all uncertain future "states of the world" that will determine the future value of all securities. Then a given Arrow security is defined as a contract that pays exactly 1 unit (e.g., one dollar) if state-of-the-world S occurs in the future, and 0 units otherwise. Ideally, there will be one such security for every possible uncertain future state-of-the-world. And any security can be expressed as a portfolio of these elementary securities.

Third, the molecular biological revolution rests upon a base-four as opposed to a binary base-two set of building blocks. These are the four chemical letters A, G, T, and C out of which the genetic code is constructed: Adenine, Guanine, Thymine, and Cytosine. In the late 1990s, the human genome was finally decoded. That is, after years of sorting and sifting, the right sequence of these four chemical letters (out of trillions of possible sequences) was discovered.

Note that in all three revolutions cited, what is involved is a sorting, mixing, and matching of a finite but huge number of combinations of the building blocks at hand--a mathematical "Lego-land," in effect. Within this province, there is nothing that is continuous, smooth, or differentiable as in the functions of physics. Hence no fundamental role can be played by that branch of mathematics that gave us modern physics during the past three centuries, namely the differential calculus. Instead, the digital computer must be utilized to perform the trillions of combinatorial sorting operations required.


1 See Arrow, Kenneth J., "The Role of Securities in the Optimal Allocation of Risk-Bearing." Econometrie, 1953; translated and reprinted in 1964, Review of Economic Studies, Vol. 31, p.91-96; and Ross, Stephen A., "Options and Efficiency." The Quarterly Journal of Economics, Vol. 90., No. 1 (Feb. 1976): pp. 75-89.

2 Of particular interest, Ross showed that the options required can be constructed from a class of "simple options" whose role in his theory parallels the role of elementary 0-1 Arrow securities in Arrow's theory.


You can learn more about Woody and his brilliant research by going to www.SEDinc.com.

Your worrying about the derivative effects of the subprime mortgage world analyst,

John Mauldin

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