# 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, EditorOutside the Box*

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## Deconstructing Today's Ongoing Revolution In Finance

**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 **s**occurs, 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 thetrueboss 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?

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?"

**TODAY'S FINANCIAL REVOLUTION IN PROPER HISTORICAL PERSPECTIVE**

**- 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.

**Footnotes:**

^{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.

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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